[ { "text": "[MUSIC PLAYING]", "start": 0.499, "duration": 3.704 }, { "text": "SPEAKER 1: All right.", "start": 15.844, "duration": 0.956 }, { "text": "So this is CS50.", "start": 16.8, "duration": 1.8 }, { "text": "And this is the start of week 3.", "start": 18.6, "duration": 1.81 }, { "text": "And you'll recall that last time,\nwe introduced a number of new ideas", "start": 20.41, "duration": 3.23 }, { "text": "that we'll now start taking for granted\nas being already under our belt.", "start": 23.64, "duration": 3.48 }, { "text": "In particular, we looked last\ntime at debugging more generally.", "start": 27.12, "duration": 3.47 }, { "text": "And recall that debugging is the\nprocess of removing bugs from your code,", "start": 30.59, "duration": 3.11 }, { "text": "removing mistakes from your code.", "start": 33.7, "duration": 1.69 }, { "text": "And we proposed these\nthree CS50-specific tools.", "start": 35.39, "duration": 3.34 }, { "text": "In particular, help50, which\nis a command line tool.", "start": 38.73, "duration": 2.589 }, { "text": "Something that you can\nrun at your keyboard", "start": 41.319, "duration": 1.791 }, { "text": "and actually run it\nbefore your own command.", "start": 43.11, "duration": 2.22 }, { "text": "So that if you don't\nunderstand some error", "start": 45.33, "duration": 1.75 }, { "text": "message from a program you're\ncompiling or a command you're running,", "start": 47.08, "duration": 2.833 }, { "text": "you can actually see some\nhelpful output from CS50 staff.", "start": 49.913, "duration": 3.297 }, { "text": "eprintf, which, by contrast, is\nsomething you can put into your code,", "start": 53.21, "duration": 4.36 }, { "text": "like printf, and print\na message to yourself.", "start": 57.57, "duration": 2.23 }, { "text": "And nicely enough, it's going to\nactually include the line number", "start": 59.8, "duration": 2.758 }, { "text": "and the file name from which it came.", "start": 62.558, "duration": 1.541 }, { "text": "So you can identify where\nsome output is coming.", "start": 64.099, "duration": 2.171 }, { "text": "And then lastly, debug 50 which is the\nmost sophisticated of these programs.", "start": 66.27, "duration": 3.75 }, { "text": "And debug 50 when you run\nit at the command line,", "start": 70.02, "duration": 2.7 }, { "text": "followed by the name of your\nprogram in the usual way,", "start": 72.72, "duration": 2.417 }, { "text": "it's actually going to open\nup what's called a debugger.", "start": 75.137, "duration": 2.333 }, { "text": "A graphical user interface\nthat CS50 staff put together", "start": 77.47, "duration": 3.517 }, { "text": "that will actually let you\nstep through your code,", "start": 80.987, "duration": 2.083 }, { "text": "see variables, and generally\nunderstand it better.", "start": 83.07, "duration": 3.52 }, { "text": "So we also looked at this\nin the context of Ovaltine", "start": 86.59, "duration": 2.91 }, { "text": "in particular, and Little Ralphy.", "start": 89.5, "duration": 1.39 }, { "text": "And we looked at cryptography,\nthe art of concealing information.", "start": 90.89, "duration": 4.28 }, { "text": "And indeed, among the\nchallenges in CS50,", "start": 95.17, "duration": 2.31 }, { "text": "ultimately if you choose\nto accept them, are", "start": 97.48, "duration": 2.08 }, { "text": "things like implementing\nCaesar cipher and Vigenere", "start": 99.56, "duration": 2.88 }, { "text": "cipher, cracking passwords.", "start": 102.44, "duration": 2.04 }, { "text": "So indeed, those problems lie ahead\nand draw inspiration from this domain.", "start": 104.48, "duration": 4.1 }, { "text": "And then, we focused more\ntechnically on what a string is.", "start": 108.58, "duration": 3.31 }, { "text": "So Zamyla, a name we keep taking for\ngranted, that a computer can express.", "start": 111.89, "duration": 3.58 }, { "text": "Z-A-M-Y-L-A, as a string\nor a phrase in a program.", "start": 115.47, "duration": 5.16 }, { "text": "But it turns out that\nunderneath the hood,", "start": 120.63, "duration": 2.83 }, { "text": "strings are a little more mundane.", "start": 123.46, "duration": 2.0 }, { "text": "They really are just\nthis grid of information.", "start": 125.46, "duration": 2.82 }, { "text": "And we might draw Zamyla's\ncharacters boxed in like this.", "start": 128.28, "duration": 2.534 }, { "text": "But if you think of what's\ninside of your computer itself,", "start": 130.814, "duration": 2.416 }, { "text": "you have a whole bunch\nof memory, or RAM.", "start": 133.23, "duration": 2.24 }, { "text": "And inside of that RAM,\nyou have Z-A-M-Y-L-A,", "start": 135.47, "duration": 3.95 }, { "text": "but then this special character.", "start": 139.42, "duration": 1.57 }, { "text": "What is this /0 used for.", "start": 140.99, "duration": 2.97 }, { "text": "Why is there this seemingly strange\ncharacter at the end of Zamyla's name?", "start": 143.96, "duration": 5.1 }, { "text": "Anyone?", "start": 149.06, "duration": 1.1 }, { "text": "Yeah.", "start": 150.16, "duration": 0.944 }, { "text": "AUDIENCE: [INAUDIBLE].", "start": 151.104, "duration": 0.916 }, { "text": "SPEAKER 1: Yeah, to denote\nthe end of the string.", "start": 152.02, "duration": 1.75 }, { "text": "Because after all, if we were to\nhave someone else's name here,", "start": 153.77, "duration": 2.624 }, { "text": "if the next string I got\nis Maria, for instance.", "start": 156.394, "duration": 2.846 }, { "text": "M-A-R-I-A, we need to be able\nto know where Zamyla's name ends", "start": 159.24, "duration": 5.1 }, { "text": "and Maria's name starts in memory.", "start": 164.34, "duration": 1.59 }, { "text": "Because at the end of the day,\nC, and programming in particular,", "start": 165.93, "duration": 3.42 }, { "text": "isn't really all that sophisticated.", "start": 169.35, "duration": 1.5 }, { "text": "At the end of the day, the only\nplace you have to store things", "start": 170.85, "duration": 2.583 }, { "text": "is your computer's memory or RAM.", "start": 173.433, "duration": 1.537 }, { "text": "And each of these boxes represents a\nbyte of memory inside of your computer.", "start": 174.97, "duration": 4.27 }, { "text": "And so if all this is-- so\nfar as the computer cares--", "start": 179.24, "duration": 2.96 }, { "text": "is a sequence of six\nalphabetical letters,", "start": 182.2, "duration": 2.44 }, { "text": "the computer needs to be told\nor given a hint as with this /0,", "start": 184.64, "duration": 4.46 }, { "text": "which just represents 8 zero bits, as to\nwhere Zamyla's name ends and something", "start": 189.1, "duration": 4.22 }, { "text": "else begins.", "start": 193.32, "duration": 1.64 }, { "text": "And we use this as an opportunity\nto introduce ultimately", "start": 194.96, "duration": 2.6 }, { "text": "command line arguments.", "start": 197.56, "duration": 1.22 }, { "text": "So in particular, we've been\nwriting programs thus far", "start": 198.78, "duration": 2.25 }, { "text": "with just int main void.", "start": 201.03, "duration": 1.12 }, { "text": "And void, we realized, signifies that\na program takes no command line inputs.", "start": 202.15, "duration": 5.21 }, { "text": "It can still call functions, like get\nstring and get int and get [? flow. ?]", "start": 207.36, "duration": 3.74 }, { "text": "But when you run the program, you can't\nput any additional words at the prompt", "start": 211.1, "duration": 3.57 }, { "text": "after it if you've declared\nmain as taking void as input.", "start": 214.67, "duration": 3.64 }, { "text": "Nothing as input.", "start": 218.31, "duration": 1.34 }, { "text": "But we introduced instead\nthis, int main int arg", "start": 219.65, "duration": 3.01 }, { "text": "c string arg v open bracket\nclose bracket, which", "start": 222.66, "duration": 3.0 }, { "text": "means main can alternatively take two\ninputs from the so-called command line", "start": 225.66, "duration": 4.294 }, { "text": "when you run it.", "start": 229.954, "duration": 0.666 }, { "text": "It can take arg c and arg\nv. And what was arg c?", "start": 230.62, "duration": 4.91 }, { "text": "What was arg c?", "start": 235.53, "duration": 2.86 }, { "text": "Arg c.", "start": 238.39, "duration": 1.57 }, { "text": "Yeah, argument.", "start": 239.96, "duration": 1.0 }, { "text": "Yeah.", "start": 240.96, "duration": 0.94 }, { "text": "AUDIENCE: [INAUDIBLE].", "start": 241.9, "duration": 0.94 }, { "text": "SPEAKER 1: Yeah, the number\nof command line arguments.", "start": 242.84, "duration": 2.25 }, { "text": "Arg c for argument count.", "start": 245.09, "duration": 1.55 }, { "text": "So how many words did\nyou type at the prompt?", "start": 246.64, "duration": 2.19 }, { "text": "And arg v means argument\nvector, which is", "start": 248.83, "duration": 2.69 }, { "text": "another way of saying it's an\narray, a contiguous block of memory", "start": 251.52, "duration": 5.58 }, { "text": "inside of which are all\nof the words themselves", "start": 257.1, "duration": 2.32 }, { "text": "that you might have typed at the prompt.", "start": 259.42, "duration": 1.8 }, { "text": "So this time, we're\ngoing to build on that.", "start": 261.22, "duration": 1.88 }, { "text": "We're going to focus\ntoday mostly on ideas.", "start": 263.1, "duration": 3.1 }, { "text": "Mostly on algorithms.", "start": 266.2, "duration": 1.08 }, { "text": "Mostly on problem-solving and less\non the lower-level implementation", "start": 267.28, "duration": 2.86 }, { "text": "details of code.", "start": 270.14, "duration": 0.85 }, { "text": "Though, we'll look at\na couple of examples.", "start": 270.99, "duration": 1.81 }, { "text": "So this more generally is\nwhat's called an array.", "start": 272.8, "duration": 2.64 }, { "text": "If you think of your computer's\nmemory as just a block of memory,", "start": 275.44, "duration": 3.43 }, { "text": "block of bytes.", "start": 278.87, "duration": 1.17 }, { "text": "And maybe it's byte 0, then byte 1.", "start": 280.04, "duration": 1.98 }, { "text": "Then, byte 2, just because you\ncan number them, certainly.", "start": 282.02, "duration": 2.64 }, { "text": "If you think of them that way, this\nis kind of an arbitrary generic data", "start": 284.66, "duration": 5.63 }, { "text": "structure, if you will.", "start": 290.29, "duration": 1.24 }, { "text": "A generic way of just storing\nthings underneath the hood.", "start": 291.53, "duration": 2.93 }, { "text": "Now, what do I mean by that?", "start": 294.46, "duration": 1.42 }, { "text": "And why is this useful?", "start": 295.88, "duration": 1.51 }, { "text": "Well, consider something like this.", "start": 297.39, "duration": 2.92 }, { "text": "Consider having 8 doors,\nbehind which are some numbers.", "start": 300.31, "duration": 3.56 }, { "text": "And the goal at hand\nis to solve a problem.", "start": 303.87, "duration": 2.07 }, { "text": "Find a number behind these doors.", "start": 305.94, "duration": 2.3 }, { "text": "Now, unfortunately, you\ndon't know in advance", "start": 308.24, "duration": 2.76 }, { "text": "what numbers are behind those\ndoors and where they are.", "start": 311.0, "duration": 2.9 }, { "text": "Indeed, that's why the doors are closed.", "start": 313.9, "duration": 1.74 }, { "text": "But you know that, say, the number\n50 is somewhere behind those doors.", "start": 315.64, "duration": 4.39 }, { "text": "So what do we do to actually find this?", "start": 320.03, "duration": 2.43 }, { "text": "Well, let's go ahead and do this.", "start": 322.46, "duration": 1.41 }, { "text": "Let me go ahead and summon up\na brave volunteer if you would.", "start": 323.87, "duration": 5.482 }, { "text": "There's a CS50 stress\nball in it for you.", "start": 329.352, "duration": 1.708 }, { "text": "OK, come on up.", "start": 331.06, "duration": 1.26 }, { "text": "You want to come up on up over here?", "start": 332.32, "duration": 2.77 }, { "text": "So we have not 8, but\nrather 7 doors here.", "start": 335.09, "duration": 4.1 }, { "text": "Even easier.", "start": 339.19, "duration": 1.56 }, { "text": "So 7/8 the size.", "start": 340.75, "duration": 0.751 }, { "text": "And what's your name?", "start": 341.501, "duration": 0.874 }, { "text": "AUDIENCE: Derek [INAUDIBLE].", "start": 342.375, "duration": 0.905 }, { "text": "SPEAKER 1: Derek?", "start": 343.28, "duration": 0.45 }, { "text": "OK.", "start": 343.73, "duration": 0.61 }, { "text": "David, come on up.", "start": 344.34, "duration": 2.04 }, { "text": "Nice to meet you.", "start": 346.38, "duration": 0.89 }, { "text": "All right.", "start": 347.27, "duration": 0.82 }, { "text": "So here we have 7 doors.", "start": 348.09, "duration": 1.55 }, { "text": "And the goal at hand for you is\nto simply find the number 50.", "start": 349.64, "duration": 5.07 }, { "text": "How do we find it?", "start": 354.71, "duration": 0.83 }, { "text": "What are you going to do?", "start": 355.54, "duration": 1.715 }, { "text": "AUDIENCE: [INAUDIBLE].", "start": 357.255, "duration": 2.325 }, { "text": "SPEAKER 1: It's behind one\nof these doors, I think.", "start": 359.58, "duration": 2.735 }, { "text": "AUDIENCE: All right.", "start": 362.315, "duration": 1.94 }, { "text": "I'll just try a door?", "start": 364.255, "duration": 1.295 }, { "text": "SPEAKER 1: Try a door.", "start": 365.55, "duration": 1.73 }, { "text": "Not the door.", "start": 367.28, "duration": 0.7 }, { "text": "So 16 turns up.", "start": 367.98, "duration": 1.27 }, { "text": "OK.", "start": 369.25, "duration": 1.19 }, { "text": "Stress ball gets one step away.", "start": 370.44, "duration": 3.4 }, { "text": "Try another.", "start": 373.84, "duration": 1.27 }, { "text": "42.", "start": 375.11, "duration": 1.52 }, { "text": "Answer to life, the universe, and\neverything, but not this question.", "start": 376.63, "duration": 5.2 }, { "text": "50.", "start": 381.83, "duration": 0.65 }, { "text": "OK, very well done.", "start": 382.48, "duration": 1.33 }, { "text": "So a round of applause if\nwe could for Derek here.", "start": 383.81, "duration": 2.6 }, { "text": "Very nicely done.", "start": 386.41, "duration": 1.3 }, { "text": "OK.", "start": 387.71, "duration": 0.5 }, { "text": "And let's pause for just a moment.", "start": 388.21, "duration": 1.25 }, { "text": "What was the algorithm?", "start": 389.46, "duration": 0.958 }, { "text": "What was the set of instructions\nthat you used to find the number 50?", "start": 390.418, "duration": 3.102 }, { "text": "AUDIENCE: Just try and see if I\ncould find any sort of arrangement.", "start": 393.52, "duration": 5.57 }, { "text": "But otherwise, try random doors.", "start": 399.09, "duration": 1.787 }, { "text": "SPEAKER 1: OK.", "start": 400.877, "duration": 0.583 }, { "text": "So try random doors.", "start": 401.46, "duration": 0.97 }, { "text": "And indeed, given no\nadditional information from me,", "start": 402.43, "duration": 2.675 }, { "text": "that's the best you can do.", "start": 405.105, "duration": 1.125 }, { "text": "Just try random doors.", "start": 406.23, "duration": 1.13 }, { "text": "Or, if it's a little easier, just\ngo left to right or right to left.", "start": 407.36, "duration": 3.05 }, { "text": "But random is perfectly equivalent\nto all of those algorithms", "start": 410.41, "duration": 2.75 }, { "text": "because you don't know\nanything necessarily a priori.", "start": 413.16, "duration": 3.16 }, { "text": "So how about for two stress balls?", "start": 416.32, "duration": 4.63 }, { "text": "Find the number 50 this time,\nbut the additional ingredient", "start": 420.95, "duration": 2.702 }, { "text": "is that we have taken\nthe time in advance", "start": 423.652, "duration": 1.708 }, { "text": "to sort the numbers behind these doors.", "start": 425.36, "duration": 2.04 }, { "text": "Does that change your\nthinking in any way?", "start": 427.4, "duration": 1.841 }, { "text": "AUDIENCE: Well, I don't\nknow whether you're", "start": 429.241, "duration": 1.791 }, { "text": "sorting increasing left or right.", "start": 431.032, "duration": 1.688 }, { "text": "SPEAKER 1: Good.", "start": 432.72, "duration": 0.32 }, { "text": "So good challenge.", "start": 433.04, "duration": 0.75 }, { "text": "He doesn't know if we've sorted\nfrom left to right or right to left.", "start": 433.79, "duration": 3.25 }, { "text": "Left to right.", "start": 437.04, "duration": 0.59 }, { "text": "So generally, a computer scientist\nwhen he or she says \"sorted\"", "start": 437.63, "duration": 2.625 }, { "text": "would say left to right.", "start": 440.255, "duration": 1.015 }, { "text": "But reasonable question.", "start": 441.27, "duration": 1.38 }, { "text": "AUDIENCE: Left to right\nincreasing or decreasing?", "start": 442.65, "duration": 1.2 }, { "text": "SPEAKER 1: Left to right increasing.", "start": 443.85, "duration": 1.499 }, { "text": "Yes.", "start": 445.349, "duration": 0.581 }, { "text": "It would be left to right in any way.", "start": 445.93, "duration": 2.48 }, { "text": "16.", "start": 448.41, "duration": 0.86 }, { "text": "Not 50.", "start": 449.27, "duration": 0.5 }, { "text": "So what are you going to do?", "start": 449.77, "duration": 1.166 }, { "text": "AUDIENCE: Well, let's see.", "start": 450.936, "duration": 1.217 }, { "text": "I know these have to be\nless, so I can remove them.", "start": 452.153, "duration": 2.357 }, { "text": "SPEAKER 1: Good.", "start": 454.51, "duration": 0.666 }, { "text": "AUDIENCE: [INAUDIBLE].", "start": 455.176, "duration": 2.284 }, { "text": "SPEAKER 1: 42 is still not 50.", "start": 457.46, "duration": 2.43 }, { "text": "And to the right.", "start": 459.89, "duration": 0.82 }, { "text": "Very well done for Derek.", "start": 460.71, "duration": 1.9 }, { "text": "OK, come on.", "start": 462.61, "duration": 1.11 }, { "text": "OK.", "start": 463.72, "duration": 0.575 }, { "text": "They're less impressed that time.", "start": 464.295, "duration": 1.375 }, { "text": "So what did you do, though, that second\ntime that was actually more effective?", "start": 465.67, "duration": 4.76 }, { "text": "I mean, frankly, at first glance it\nlooks like this approach was just as", "start": 470.43, "duration": 3.279 }, { "text": "fast or just as slow\nas your first approach", "start": 473.709, "duration": 1.791 }, { "text": "because it still took you through steps.", "start": 475.5, "duration": 1.666 }, { "text": "AUDIENCE: So what I did was since\nyou told me that it was sorted left", "start": 477.166, "duration": 2.914 }, { "text": "to right increasing, I decided to\nlook at the middle number first", "start": 480.08, "duration": 3.42 }, { "text": "and see whether it was\ngreater than or less than--", "start": 483.5, "duration": 2.475 }, { "text": "SPEAKER 1: Good", "start": 485.975, "duration": 0.625 }, { "text": "AUDIENCE: --the target number.", "start": 486.6, "duration": 1.8 }, { "text": "SPEAKER 1: Good.", "start": 488.4, "duration": 0.7 }, { "text": "AUDIENCE: And since it was less than,\nI knew that all of these three values--", "start": 489.1, "duration": 2.88 }, { "text": "SPEAKER 1: Wonderful.", "start": 491.98, "duration": 0.874 }, { "text": "And indeed, are smaller by design.", "start": 492.854, "duration": 1.775 }, { "text": "And so you can throw half of that\nproblem away, much like in week 0", "start": 494.629, "duration": 2.791 }, { "text": "when we tore the phone book in half.", "start": 497.42, "duration": 1.5 }, { "text": "You can throw half of that\nphone book away as well.", "start": 498.92, "duration": 2.72 }, { "text": "So thank you very much for\nfinding us the number 50.", "start": 501.64, "duration": 2.25 }, { "text": "So this is something that we\ndid see, indeed, in week 0.", "start": 503.89, "duration": 2.91 }, { "text": "And it's what we would\ngenerally call binary search.", "start": 506.8, "duration": 2.52 }, { "text": "Or more generally, just a\ndivide and conquer algorithm.", "start": 509.32, "duration": 3.2 }, { "text": "But today, what we\nstart to do is to assess", "start": 512.52, "duration": 2.289 }, { "text": "just how much better this actually is.", "start": 514.809, "duration": 2.291 }, { "text": "And how we can go about finding\nthings more programmatically.", "start": 517.1, "duration": 3.85 }, { "text": "So what Derek could have tried\nis what someone would generally", "start": 520.95, "duration": 4.45 }, { "text": "call linear search.", "start": 525.4, "duration": 1.65 }, { "text": "And as the name suggests,\nlinear, meaning line,", "start": 527.05, "duration": 2.07 }, { "text": "you can just kind of solve a\nproblem from left to right.", "start": 529.12, "duration": 2.42 }, { "text": "And indeed, while Derek\ndid take a random approach,", "start": 531.54, "duration": 2.58 }, { "text": "it would have been\nfunctionally equivalent", "start": 534.12, "duration": 1.87 }, { "text": "for him simply to go left to right or\nright to left and find the number 50.", "start": 535.99, "duration": 4.53 }, { "text": "It's indeed there.", "start": 540.52, "duration": 0.947 }, { "text": "So let's introduce some\npseudocode for this.", "start": 541.467, "duration": 1.833 }, { "text": "And there is no one right\nway to implement pseudocode.", "start": 543.3, "duration": 3.29 }, { "text": "Here is one of the most\nsuccinct ways I could come up", "start": 546.59, "duration": 2.35 }, { "text": "with for expressing this kind\nof left to right approach.", "start": 548.94, "duration": 2.333 }, { "text": "Or equivalently, right to left.", "start": 551.273, "duration": 1.507 }, { "text": "For each element in the array, if\nelement you're looking for return true.", "start": 552.78, "duration": 5.41 }, { "text": "And so this is a very common\nparadigm in programming.", "start": 558.19, "duration": 2.61 }, { "text": "Just say something generally,\nlike for each element in an array.", "start": 560.8, "duration": 2.667 }, { "text": "And the implication is that you\nwould generally go left to right,", "start": 563.467, "duration": 2.708 }, { "text": "but it's equivalent to go right to left.", "start": 566.175, "duration": 1.675 }, { "text": "And if we indeed see at\nsome location in that array", "start": 567.85, "duration": 4.01 }, { "text": "that array of boxes, the element we're\nlooking for, we can just return true.", "start": 571.86, "duration": 4.27 }, { "text": "And yet, here I have return false.", "start": 576.13, "duration": 2.77 }, { "text": "But the indentation, so to\nspeak, is very different.", "start": 578.9, "duration": 2.92 }, { "text": "Why have I aligned return\nfalse with the for loop", "start": 581.82, "duration": 3.34 }, { "text": "here all the way on the left as opposed\nto it being aligned in the middle", "start": 585.16, "duration": 3.88 }, { "text": "or one line deeper?", "start": 589.04, "duration": 3.73 }, { "text": "Yeah.", "start": 592.77, "duration": 0.785 }, { "text": "AUDIENCE: [INAUDIBLE].", "start": 593.555, "duration": 0.916 }, { "text": "SPEAKER 1: Yeah.", "start": 597.314, "duration": 0.666 }, { "text": "In order to denote that all\nof the indented elements", "start": 597.98, "duration": 1.96 }, { "text": "are within the for loop.", "start": 599.94, "duration": 1.0 }, { "text": "So it doesn't strictly\nmatter how much you indent.", "start": 600.94, "duration": 2.647 }, { "text": "And indeed, in some\nlanguages, C among them,", "start": 603.587, "duration": 1.833 }, { "text": "it doesn't matter that\nyou indent at all.", "start": 605.42, "duration": 2.48 }, { "text": "But for the sake of good\nstyle and readability,", "start": 607.9, "duration": 2.84 }, { "text": "we've indented this\nto convey to the human", "start": 610.74, "duration": 2.1 }, { "text": "especially that this \"if\" is only\napplicable when you're inside", "start": 612.84, "duration": 4.27 }, { "text": "of the for loop.", "start": 617.11, "duration": 0.69 }, { "text": "This return is only applicable when\nyou're inside of this \"if\" condition.", "start": 617.8, "duration": 3.27 }, { "text": "And this return false\nreally only happens", "start": 621.07, "duration": 3.1 }, { "text": "as the very last step in this program if\nnothing else actually returns a value.", "start": 624.17, "duration": 4.95 }, { "text": "So only if return true\nhappens does this program say,", "start": 629.12, "duration": 4.18 }, { "text": "yes, I found the element\nyou're looking for.", "start": 633.3, "duration": 2.2 }, { "text": "And you can think of this, therefore,\nas the sort of default case.", "start": 635.5, "duration": 2.81 }, { "text": "Now, just to toss it out\nthere, why would this be wrong?", "start": 638.31, "duration": 5.17 }, { "text": "Let me go ahead and\ntemporarily change this program", "start": 643.48, "duration": 4.74 }, { "text": "to be a more familiar if/else block.", "start": 648.22, "duration": 2.87 }, { "text": "So why is this seemingly logically fine?", "start": 651.09, "duration": 3.93 }, { "text": "It's a valid puzzle piece\nif you will, a la scratch.", "start": 655.02, "duration": 3.23 }, { "text": "But this program is now incorrect.", "start": 658.25, "duration": 1.525 }, { "text": "Why?", "start": 659.775, "duration": 2.185 }, { "text": "Yeah.", "start": 661.96, "duration": 0.762 }, { "text": "AUDIENCE: [INAUDIBLE].", "start": 662.722, "duration": 0.916 }, { "text": "SPEAKER 1: Once you hit\nit, it's automatically", "start": 669.004, "duration": 1.916 }, { "text": "going to come out of the for loop when?", "start": 670.92, "duration": 1.2 }, { "text": "Exactly.", "start": 672.12, "duration": 0.499 }, { "text": "When will this come out of the for loop?", "start": 672.619, "duration": 2.113 }, { "text": "AUDIENCE: [INAUDIBLE].", "start": 674.732, "duration": 1.942 }, { "text": "SPEAKER 1: Good.", "start": 676.674, "duration": 0.666 }, { "text": "So it's going to return false\nif the first element isn't", "start": 677.34, "duration": 3.09 }, { "text": "what you're looking for.", "start": 680.43, "duration": 1.0 }, { "text": "In so far as for each\nelement in an array", "start": 681.43, "duration": 1.939 }, { "text": "kind of implies that you should\nbe looking from left to right", "start": 683.369, "duration": 2.541 }, { "text": "or right to left, the\nfirst question you're", "start": 685.91, "duration": 2.02 }, { "text": "asking yourself when looking\nin that first element", "start": 687.93, "duration": 2.1 }, { "text": "is, is this the element\nyou're looking for?", "start": 690.03, "duration": 2.25 }, { "text": "If it is, great.", "start": 692.28, "duration": 0.667 }, { "text": "You're going to return true.", "start": 692.947, "duration": 1.166 }, { "text": "And your answer is correct.", "start": 694.113, "duration": 1.217 }, { "text": "But if it's not the\nelement you're looking", "start": 695.33, "duration": 1.8 }, { "text": "for, you're executing else return false\nimmediately saying no, the element", "start": 697.13, "duration": 4.19 }, { "text": "I'm looking for is not here.", "start": 701.32, "duration": 1.67 }, { "text": "But when really the only question\nyou've asked is, is the element", "start": 702.99, "duration": 3.08 }, { "text": "I'm looking for the\nvery first in the array?", "start": 706.07, "duration": 2.74 }, { "text": "And so, indeed, this would\njust be logically incorrect", "start": 708.81, "duration": 2.25 }, { "text": "because you might as well\nnot look at any of the array", "start": 711.06, "duration": 2.25 }, { "text": "if you're only looking at\nthat very first element.", "start": 713.31, "duration": 2.88 }, { "text": "So not what we intended.", "start": 716.19, "duration": 1.29 }, { "text": "So indeed, that original\npseudocode is just fine.", "start": 717.48, "duration": 3.22 }, { "text": "So alternatively, there's something\ncalled binary search, which", "start": 720.7, "duration": 3.03 }, { "text": "Derek actually used intuitively\nfor his second approach,", "start": 723.73, "duration": 3.73 }, { "text": "where he was told in advance that the\narray is sorted numerically from left", "start": 727.46, "duration": 4.24 }, { "text": "to right.", "start": 731.7, "duration": 0.5 }, { "text": "This gives him more information,\nmuch like I had in week 0", "start": 732.2, "duration": 2.416 }, { "text": "when I searched a phone book\nthat I knew was alphabetical.", "start": 734.616, "duration": 3.134 }, { "text": "And you can write this algorithm\nin any number of ways, too.", "start": 737.75, "duration": 2.54 }, { "text": "I kind of borrowed the spirit of\nour Mike Smith algorithm from week 0", "start": 740.29, "duration": 3.947 }, { "text": "and I proposed this.", "start": 744.237, "duration": 0.833 }, { "text": "Look at the middle of the array.", "start": 745.07, "duration": 1.87 }, { "text": "If element you're\nlooking for return true.", "start": 746.94, "duration": 2.09 }, { "text": "We just get lucky if it's smack\ndab in the middle of the array.", "start": 749.03, "duration": 2.68 }, { "text": "Else if the element is to\nthe left, because the element", "start": 751.71, "duration": 3.99 }, { "text": "you're seeing in the middle is too big,\nthen search the left half of the array.", "start": 755.7, "duration": 4.69 }, { "text": "Else if the element is to the\nright, as it was in Derek's case,", "start": 760.39, "duration": 3.3 }, { "text": "search the right half of the\narray, else return false.", "start": 763.69, "duration": 4.16 }, { "text": "But there is no go-to instruction here.", "start": 767.85, "duration": 2.27 }, { "text": "And there's no line numbers.", "start": 770.12, "duration": 1.206 }, { "text": "Recall from week 0 when we\nsearched for Mike Smith,", "start": 771.326, "duration": 2.124 }, { "text": "I deliberately numbered\nall of the lines.", "start": 773.45, "duration": 1.93 }, { "text": "And then I said, go back to\nstep 2 or 3 I think it was.", "start": 775.38, "duration": 4.08 }, { "text": "Here, I seem to be cutting a corner.", "start": 779.46, "duration": 2.13 }, { "text": "I'm just kind of waving\nmy hand and saying,", "start": 781.59, "duration": 2.106 }, { "text": "search the left half of the list.", "start": 783.696, "duration": 1.374 }, { "text": "Or, search the right half of the list.", "start": 785.07, "duration": 2.0 }, { "text": "But what algorithm should we\nuse in either of these cases?", "start": 787.07, "duration": 3.66 }, { "text": "How do you search the\nleft half of a list?", "start": 793.62, "duration": 2.03 }, { "text": "How do you search the\nright half of a list?", "start": 795.65, "duration": 1.855 }, { "text": "How do I do this?", "start": 801.13, "duration": 1.72 }, { "text": "Well, where do I have an\nalgorithm for searching?", "start": 802.85, "duration": 2.49 }, { "text": "Well, we saw one a moment ago.", "start": 805.34, "duration": 1.47 }, { "text": "I've already got in my toolkit,\nso to speak, linear search.", "start": 806.81, "duration": 2.9 }, { "text": "So I could certainly use that.", "start": 809.71, "duration": 1.31 }, { "text": "But sort of cyclically,\nor sort of confusingly,", "start": 811.02, "duration": 3.15 }, { "text": "I also have this other seemingly\nfancier, faster algorithm", "start": 814.17, "duration": 3.09 }, { "text": "called binary search.", "start": 817.26, "duration": 1.2 }, { "text": "And yet, I'm in the middle of defining\nbinary search with my pseudocode.", "start": 818.46, "duration": 4.46 }, { "text": "And yet, here I am sort of trying\nto define myself with myself.", "start": 822.92, "duration": 3.234 }, { "text": "You can't get away with this in English.", "start": 826.154, "duration": 1.666 }, { "text": "If you're asked to\ndefine an English word", "start": 827.82, "duration": 1.74 }, { "text": "and you use the word in the definition,\nusually a teacher or someone", "start": 829.56, "duration": 2.96 }, { "text": "in a conversation will sort of\nverbally slap you on the wrist", "start": 832.52, "duration": 2.35 }, { "text": "because you're not\nanswering the question.", "start": 834.87, "duration": 1.75 }, { "text": "And yet somehow in programming,\nyou can get away with this.", "start": 836.62, "duration": 3.61 }, { "text": "Somehow, you can get away with defining\na problem with a solution like this,", "start": 840.23, "duration": 5.62 }, { "text": "and then using that same\nsolution inside of your solution", "start": 845.85, "duration": 2.95 }, { "text": "because something is changing.", "start": 848.8, "duration": 2.66 }, { "text": "This line here, search the\nleft half of the array,", "start": 851.46, "duration": 2.54 }, { "text": "and this line here, search\nright half of the array,", "start": 854.0, "duration": 2.4 }, { "text": "is not equivalent to asking\nthe same question again.", "start": 856.4, "duration": 4.24 }, { "text": "Is this element in the array?", "start": 860.64, "duration": 1.65 }, { "text": "What changes when I either search\nthe left half or the right half that", "start": 862.29, "duration": 4.38 }, { "text": "makes this acceptable?", "start": 866.67, "duration": 2.26 }, { "text": "AUDIENCE: [INAUDIBLE].", "start": 868.93, "duration": 1.427 }, { "text": "SPEAKER 1: What's that?", "start": 870.357, "duration": 0.958 }, { "text": "AUDIENCE: [INAUDIBLE].", "start": 871.315, "duration": 2.475 }, { "text": "SPEAKER 1: Yes.", "start": 873.79, "duration": 0.93 }, { "text": "That's the key ingredient.", "start": 874.72, "duration": 1.18 }, { "text": "In so far as search left half\nand search right half imply", "start": 875.9, "duration": 3.8 }, { "text": "search in the same way, but\nsearch a smaller problem,", "start": 879.7, "duration": 3.77 }, { "text": "this problem will eventually stop.", "start": 883.47, "duration": 1.82 }, { "text": "You're not going to get stuck\nin an infinite loop so to speak.", "start": 885.29, "duration": 2.583 }, { "text": "Because eventually-- you\ncan't half something forever.", "start": 887.873, "duration": 2.467 }, { "text": "You're eventually going to end\nup with one or zero elements.", "start": 890.34, "duration": 2.17 }, { "text": "At which point, the\nanswer's going to be no.", "start": 892.51, "duration": 1.833 }, { "text": "Return false, it's not here\nper the else condition.", "start": 894.343, "duration": 2.657 }, { "text": "But these sort of reflexive\ncalls or inductive,", "start": 897.0, "duration": 4.78 }, { "text": "or more properly here, recursive\ncalls-- the new buzzword", "start": 901.78, "duration": 3.48 }, { "text": "for today-- means for a function, or in\nthis case pseudocode, to call itself.", "start": 905.26, "duration": 5.4 }, { "text": "To use its own definition\nagain and again", "start": 910.66, "duration": 2.45 }, { "text": "and again, which is bad instinctively,\nunless you keep doing it", "start": 913.11, "duration": 3.53 }, { "text": "on smaller and smaller problems.", "start": 916.64, "duration": 2.3 }, { "text": "And so this is a general\nprinciple, actually,", "start": 918.94, "duration": 2.31 }, { "text": "that we're going to be able to leverage\nultimately, not only for searching but", "start": 921.25, "duration": 3.41 }, { "text": "also, as we shall see, for sorting.", "start": 924.66, "duration": 3.49 }, { "text": "So let's go ahead and\nlet me share actually", "start": 928.15, "duration": 2.48 }, { "text": "how this example went last year.", "start": 930.63, "duration": 1.48 }, { "text": "We're fortunate to capture\nsort of memories on film.", "start": 932.11, "duration": 2.52 }, { "text": "And I thought it would\nbe fun to share this,", "start": 934.63, "duration": 1.985 }, { "text": "when one of your predecessors\nin the class came up,", "start": 936.615, "duration": 2.525 }, { "text": "was asked the exact same\nquestion, find us the number 50.", "start": 939.14, "duration": 2.92 }, { "text": "But it didn't quite go\nas well as we hoped.", "start": 942.06, "duration": 2.61 }, { "text": "Let's take a look at 2014.", "start": 944.67, "duration": 1.934 }, { "text": "[AUDIO PLAYBACK]", "start": 946.604, "duration": 0.666 }, { "text": "-All I want you to do now is\nto find for me and for us,", "start": 947.27, "duration": 3.65 }, { "text": "really, the number 50\none step at a time.", "start": 950.92, "duration": 5.935 }, { "text": "-Number 50?", "start": 956.855, "duration": 1.155 }, { "text": "-The number 50.", "start": 958.01, "duration": 0.74 }, { "text": "And you can reveal what's\nbehind each of these doors", "start": 958.75, "duration": 2.166 }, { "text": "simply by touching it with a finger.", "start": 960.916, "duration": 3.184 }, { "text": "Damn it.", "start": 964.1, "duration": 2.34 }, { "text": "[APPLAUSE]", "start": 966.44, "duration": 2.151 }, { "text": "[END PLAYBACK]", "start": 968.591, "duration": 0.656 }, { "text": "SPEAKER 1: OK.", "start": 969.247, "duration": 0.583 }, { "text": "So that didn't really\ndemonstrate anything that year.", "start": 969.83, "duration": 2.208 }, { "text": "So we tried again, this time saying, all\nright, this time the array is sorted.", "start": 972.038, "duration": 4.202 }, { "text": "What are you going to do this time if\nyou want to find the same number 50,", "start": 976.24, "duration": 3.24 }, { "text": "but the array is now sorted?", "start": 979.48, "duration": 1.76 }, { "text": "I thought I'd share this.", "start": 981.24, "duration": 1.463 }, { "text": "[AUDIO PLAYBACK]", "start": 982.703, "duration": 0.887 }, { "text": "-The goal now is to also find us the\nnumber 50, but do it algorithmically.", "start": 983.59, "duration": 4.31 }, { "text": "And tell us how you're going about it.", "start": 987.9, "duration": 2.55 }, { "text": "And if you find it, you keep the movie.", "start": 990.45, "duration": 2.17 }, { "text": "If you don't find it, you give it back.", "start": 992.62, "duration": 1.924 }, { "text": "-Man. [INAUDIBLE].", "start": 994.544, "duration": 1.828 }, { "text": "OK.", "start": 996.372, "duration": 0.918 }, { "text": "So I'm going to check the ends\nfirst to determine if there's-- oh.", "start": 997.29, "duration": 5.23 }, { "text": "[APPLAUSE]", "start": 1002.52, "duration": 2.742 }, { "text": "[END PLAYBACK]", "start": 1005.761, "duration": 0.929 }, { "text": "SPEAKER 1: OK, now I feel a\nlittle bad because clearly we", "start": 1006.69, "duration": 1.38 }, { "text": "used to give away movies and\nnow we give away stress balls.", "start": 1008.07, "duration": 2.64 }, { "text": "But no one really has DVD players\nanymore, so it's OK probably.", "start": 1010.71, "duration": 3.12 }, { "text": "And then, let me share one other\nclip back from our SD days.", "start": 1013.83, "duration": 3.32 }, { "text": "Many years ago when Shawn, who\nhas since graduated, came up.", "start": 1017.15, "duration": 3.84 }, { "text": "Was asked the same question.", "start": 1020.99, "duration": 1.2 }, { "text": "So Derek, you are in this\nwonderful history of students", "start": 1022.19, "duration": 2.614 }, { "text": "who have tried this demonstration.", "start": 1024.804, "duration": 1.416 }, { "text": "This was, as you can, see before\nwe had touchscreen technology.", "start": 1026.22, "duration": 2.49 }, { "text": "So we had sheets of\npaper up on the screen.", "start": 1028.71, "duration": 1.791 }, { "text": "But the idea was the same.", "start": 1030.501, "duration": 1.389 }, { "text": "And Shawn is perhaps one of\nour favorite memories in so far", "start": 1031.89, "duration": 3.24 }, { "text": "as he, too, was asked to solve\nthe same problem in his way.", "start": 1035.13, "duration": 3.014 }, { "text": "[AUDIO PLAYBACK]", "start": 1038.144, "duration": 0.666 }, { "text": "-OK, so your task here,\nShawn, is the following.", "start": 1038.81, "duration": 3.33 }, { "text": "I have hidden behind\nthese doors the number 7.", "start": 1042.14, "duration": 4.199 }, { "text": "But tucked away in some of these doors\nas well are other non-negative numbers.", "start": 1046.339, "duration": 4.221 }, { "text": "And your goal is to think\nof this top row of numbers", "start": 1050.56, "duration": 2.45 }, { "text": "as just an array, or just a\nsequence of pieces of paper", "start": 1053.01, "duration": 2.87 }, { "text": "with numbers behind them.", "start": 1055.88, "duration": 1.14 }, { "text": "And your goal is only using the top\narray here, find me the number 7.", "start": 1057.02, "duration": 4.09 }, { "text": "And we are then going to critique\nhow you go about doing it.", "start": 1061.11, "duration": 3.43 }, { "text": "Find us the number 7, please.", "start": 1064.54, "duration": 1.671 }, { "text": "No.", "start": 1075.975, "duration": 0.5 }, { "text": "5, 19, 13.", "start": 1080.04, "duration": 4.043 }, { "text": "It's not a trick question.", "start": 1090.24, "duration": 1.105 }, { "text": "1.", "start": 1094.775, "duration": 0.5 }, { "text": "At this point, your score is not very\ngood, so you might as well keep going.", "start": 1100.168, "duration": 3.166 }, { "text": "3.", "start": 1106.17, "duration": 0.5 }, { "text": "Go on.", "start": 1111.84, "duration": 0.69 }, { "text": "-[INAUDIBLE].", "start": 1112.53, "duration": 0.677 }, { "text": "-Frankly, I can't help but wonder\nwhat you're even thinking about.", "start": 1113.207, "duration": 2.75 }, { "text": "Only the top row.", "start": 1118.7, "duration": 0.85 }, { "text": "So you got 3 left.", "start": 1119.55, "duration": 0.95 }, { "text": "So find me 7.", "start": 1120.5, "duration": 2.475 }, { "text": "-[INAUDIBLE].", "start": 1122.975, "duration": 0.541 }, { "text": "-17.", "start": 1140.33, "duration": 2.049 }, { "text": "-[INAUDIBLE].", "start": 1142.379, "duration": 0.541 }, { "text": "-7.", "start": 1150.711, "duration": 0.499 }, { "text": "[END PLAYBACK]", "start": 1151.21, "duration": 1.695 }, { "text": "SPEAKER 1: All right.", "start": 1152.905, "duration": 0.875 }, { "text": "So we don't ask people\nto search for 7 anymore.", "start": 1153.78, "duration": 2.65 }, { "text": "But this invites the\nquestion, how are we", "start": 1156.43, "duration": 2.74 }, { "text": "allowed to have that assumption, right?", "start": 1159.17, "duration": 2.12 }, { "text": "I've been assuming in week 0 that\nthe phone book was alphabetized.", "start": 1161.29, "duration": 3.35 }, { "text": "And therefore, I can find Mike Smith\nreally fast in logarithmic time.", "start": 1164.64, "duration": 3.37 }, { "text": "And we were just assuming\na moment ago that we", "start": 1168.01, "duration": 2.12 }, { "text": "could find the number 50 super-fast\nbecause of divide and conquer.", "start": 1170.13, "duration": 3.62 }, { "text": "Again, but only if\nthat array were sorted.", "start": 1173.75, "duration": 2.71 }, { "text": "Indeed, Derek technically\njust got lucky in so far", "start": 1176.46, "duration": 2.22 }, { "text": "as he found 50 the\nfirst time in 3 steps.", "start": 1178.68, "duration": 3.012 }, { "text": "But it could have been as many as\n7 steps because it was, indeed,", "start": 1181.692, "duration": 2.708 }, { "text": "a random algorithm.", "start": 1184.4, "duration": 0.96 }, { "text": "Or even if he had used linear search.", "start": 1185.36, "duration": 2.0 }, { "text": "So suppose we want to\nactually sort something.", "start": 1187.36, "duration": 3.34 }, { "text": "So these are still used\non campus sometimes.", "start": 1190.7, "duration": 2.27 }, { "text": "So these are blue books for exam period.", "start": 1192.97, "duration": 2.112 }, { "text": "And suppose that we're at the end of\na semester and a bunch of students", "start": 1195.082, "duration": 2.958 }, { "text": "have written their\nnames on these things.", "start": 1198.04, "duration": 1.708 }, { "text": "And so A's and B's and C's and D's.", "start": 1199.748, "duration": 2.202 }, { "text": "And suppose that they're handed\nin at somewhat random times.", "start": 1201.95, "duration": 2.64 }, { "text": "There's always that kid who hands\nin his or her exam at an hour", "start": 1204.59, "duration": 2.43 }, { "text": "into the 3-hour exam,\nand then most of them", "start": 1207.02, "duration": 1.57 }, { "text": "come in around like 2 hours 45 minutes.", "start": 1208.59, "duration": 1.84 }, { "text": "And so therefore, they're all\nin this pretty random arbitrary", "start": 1210.43, "duration": 4.04 }, { "text": "order like this.", "start": 1214.47, "duration": 1.307 }, { "text": "Actually, if I just them down like\nthat, they're not really random at all.", "start": 1215.777, "duration": 3.083 }, { "text": "And so they're just\nin some random order.", "start": 1218.86, "duration": 2.04 }, { "text": "And the goal at hand, ultimately,\nis for the head TF, for instance,", "start": 1220.9, "duration": 2.81 }, { "text": "or the professor to actually\nsort all of these blue books", "start": 1223.71, "duration": 2.719 }, { "text": "and come up with an alphabetical order\nso you can make sure that everyone", "start": 1226.429, "duration": 3.041 }, { "text": "has actually submitted on time.", "start": 1229.47, "duration": 2.06 }, { "text": "So how do we do this?", "start": 1231.53, "duration": 1.54 }, { "text": "What is the algorithm\nwith which to do this?", "start": 1233.07, "duration": 2.84 }, { "text": "Because indeed, if he\nor she, the professor,", "start": 1235.91, "duration": 2.17 }, { "text": "later wants to find a certain\nname of the alphabet, like Smith,", "start": 1238.08, "duration": 4.15 }, { "text": "it'd be nice if they don't have to sift\nthrough all 26, or all 100, or all 500", "start": 1242.23, "duration": 4.03 }, { "text": "blue books.", "start": 1246.26, "duration": 0.5 }, { "text": "They can just jump\nroughly to the middle,", "start": 1246.76, "duration": 1.71 }, { "text": "and then divide and conquer\nand find Smith there after.", "start": 1248.47, "duration": 2.41 }, { "text": "Can we get one volunteer to\ncome up and propose how to sort?", "start": 1250.88, "duration": 3.46 }, { "text": "You want come on up?", "start": 1254.34, "duration": 0.97 }, { "text": "Come on up.", "start": 1255.31, "duration": 0.64 }, { "text": "What's your name?", "start": 1255.95, "duration": 0.43 }, { "text": "AUDIENCE: Allison.", "start": 1256.38, "duration": 0.8 }, { "text": "SPEAKER 1: Allison.", "start": 1257.18, "duration": 1.08 }, { "text": "All right, come on up.", "start": 1258.26, "duration": 2.15 }, { "text": "So if you've ever\nsorted something before,", "start": 1260.41, "duration": 1.75 }, { "text": "now's your chance to\nshow that off, Allison.", "start": 1262.16, "duration": 1.941 }, { "text": "All right.", "start": 1264.101, "duration": 0.499 }, { "text": "So here are a whole bunch of blue books.", "start": 1264.6, "duration": 1.66 }, { "text": "And I've just arbitrarily written\nnot names, but first letters", "start": 1266.26, "duration": 2.14 }, { "text": "of the alphabet on them.", "start": 1268.4, "duration": 0.999 }, { "text": "So go ahead and sort them.", "start": 1269.399, "duration": 1.381 }, { "text": "AUDIENCE: So I start with a letter.", "start": 1270.78, "duration": 2.415 }, { "text": "And if this is before\nthat, I just put it on top.", "start": 1273.195, "duration": 2.502 }, { "text": "SPEAKER 1: OK.", "start": 1275.697, "duration": 0.583 }, { "text": "So that's X and L. Gotcha.", "start": 1276.28, "duration": 1.614 }, { "text": "AUDIENCE: And because Z is after that--", "start": 1277.894, "duration": 0.828 }, { "text": "SPEAKER 1: There's Z.", "start": 1278.722, "duration": 0.828 }, { "text": "AUDIENCE: --I put it below.", "start": 1279.55, "duration": 1.124 }, { "text": "And D is here.", "start": 1280.674, "duration": 1.181 }, { "text": "SPEAKER 1: OK.", "start": 1281.855, "duration": 0.584 }, { "text": "So you seem to be taking them one at a\ntime and just dealing with the problem", "start": 1282.439, "duration": 3.207 }, { "text": "then and now?", "start": 1285.646, "duration": 0.589 }, { "text": "AUDIENCE: Yes.", "start": 1286.235, "duration": 0.365 }, { "text": "SPEAKER 1: OK.", "start": 1286.6, "duration": 0.583 }, { "text": "So that's J. What happens next?", "start": 1287.183, "duration": 1.567 }, { "text": "AUDIENCE: [INAUDIBLE].", "start": 1292.7, "duration": 1.677 }, { "text": "SPEAKER 1: OK.", "start": 1294.377, "duration": 0.583 }, { "text": "That's K. K, L, good.", "start": 1294.96, "duration": 3.77 }, { "text": "B, that's easy.", "start": 1298.73, "duration": 0.91 }, { "text": "On top.", "start": 1299.64, "duration": 0.55 }, { "text": "A, even easier.", "start": 1300.19, "duration": 1.02 }, { "text": "On top.", "start": 1301.21, "duration": 1.036 }, { "text": "AUDIENCE: Am I going to\nfinish this entire thing?", "start": 1302.246, "duration": 1.314 }, { "text": "SPEAKER 1: Yes.", "start": 1303.56, "duration": 0.74 }, { "text": "We need 13 more, give or take.", "start": 1304.3, "duration": 2.498 }, { "text": "M and--", "start": 1306.798, "duration": 0.952 }, { "text": "AUDIENCE: N.", "start": 1307.75, "duration": 0.5 }, { "text": "SPEAKER 1: N, O. I didn't\ndo a very good job there.", "start": 1308.25, "duration": 3.51 }, { "text": "U, V. OK, definitely not good.", "start": 1311.76, "duration": 2.97 }, { "text": "Y. That's good.", "start": 1314.73, "duration": 1.06 }, { "text": "It goes toward the end.", "start": 1315.79, "duration": 1.01 }, { "text": "R, a little harder.", "start": 1316.8, "duration": 2.77 }, { "text": "But this is actually a\ngood situation for us", "start": 1319.57, "duration": 1.92 }, { "text": "to be in because-- you keep\ngoing, I'll keep talking.", "start": 1321.49, "duration": 2.208 }, { "text": "So even as Allison is\nsorting this, she's", "start": 1323.698, "duration": 2.682 }, { "text": "dealing with each of these\nblue books one at a time.", "start": 1326.38, "duration": 2.25 }, { "text": "But notice what's happening\nto her right hand.", "start": 1328.63, "duration": 2.14 }, { "text": "There literally is more and more work,\nit seems, happening in her right hand", "start": 1330.77, "duration": 3.77 }, { "text": "because as she encounters R or now W,\nnot only does she need more thought,", "start": 1334.54, "duration": 3.58 }, { "text": "she also needs to do more\nflipping to actually find", "start": 1338.12, "duration": 2.41 }, { "text": "the right spot for W. This is H.\nShe's doing the same thing again.", "start": 1340.53, "duration": 2.98 }, { "text": "So it feels like the algorithm\nhas started to slow down.", "start": 1343.51, "duration": 3.3 }, { "text": "At first, it was pretty easy\nto just make a short list.", "start": 1346.81, "duration": 2.61 }, { "text": "But now that the list\nis getting longer, it", "start": 1349.42, "duration": 2.01 }, { "text": "feels like she's fixing a lot of\nwork, or finding a location is", "start": 1351.43, "duration": 3.91 }, { "text": "getting harder and harder.", "start": 1355.34, "duration": 2.49 }, { "text": "Or at least taking longer and longer.", "start": 1357.83, "duration": 1.83 }, { "text": "Maybe the alphabet itself is\nnot that much more difficult.", "start": 1359.66, "duration": 2.51 }, { "text": "Now, we have I. I can\nonly stall so much longer.", "start": 1362.17, "duration": 3.01 }, { "text": "G.", "start": 1365.18, "duration": 0.5 }, { "text": "AUDIENCE: Sorry.", "start": 1365.68, "duration": 0.29 }, { "text": "SPEAKER 1: No, that's fine.", "start": 1365.97, "duration": 1.125 }, { "text": "E, good.", "start": 1367.095, "duration": 0.505 }, { "text": "OK.", "start": 1367.6, "duration": 0.5 }, { "text": "So it's getting a little easier\nbecause we're at the beginning.", "start": 1368.1, "duration": 3.28 }, { "text": "Sorted.", "start": 1371.38, "duration": 0.77 }, { "text": "So what were you thinking?", "start": 1372.15, "duration": 1.39 }, { "text": "What was that algorithm?", "start": 1373.54, "duration": 1.255 }, { "text": "AUDIENCE: It was just take a\nletter, take another letter,", "start": 1374.795, "duration": 2.375 }, { "text": "and then test to see if the\nletter is before or after.", "start": 1377.17, "duration": 3.294 }, { "text": "SPEAKER 1: OK, good.", "start": 1380.464, "duration": 0.833 }, { "text": "AUDIENCE: And then put it in the\ncorrect place on either side.", "start": 1381.297, "duration": 2.103 }, { "text": "SPEAKER 1: Perfect.", "start": 1383.4, "duration": 0.43 }, { "text": "So a perfect way of\nthinking about this as well.", "start": 1383.83, "duration": 1.82 }, { "text": "So thank you so much.", "start": 1385.65, "duration": 0.945 }, { "text": "AUDIENCE: Thank you.", "start": 1386.595, "duration": 0.405 }, { "text": "SPEAKER 1: Very nicely done.", "start": 1387.0, "duration": 1.166 }, { "text": "And suppose the problem's\na little harder.", "start": 1388.166, "duration": 2.144 }, { "text": "I'll do this one myself here.", "start": 1390.31, "duration": 2.21 }, { "text": "But suppose we have some playing cards.", "start": 1392.52, "duration": 2.22 }, { "text": "And these are the type that\nprobably everyone here can see.", "start": 1394.74, "duration": 3.42 }, { "text": "So here is a standard\ndeck of cards, including", "start": 1398.16, "duration": 4.09 }, { "text": "the jokers, which we won't need.", "start": 1402.25, "duration": 1.636 }, { "text": "How do you go about\nsorting things like this?", "start": 1403.886, "duration": 1.874 }, { "text": "I don't know if-- actually,\nI didn't think in advance.", "start": 1405.76, "duration": 4.88 }, { "text": "I should have shuffled these.", "start": 1410.64, "duration": 1.88 }, { "text": "So if you want to shuffle these cards.", "start": 1412.52, "duration": 2.35 }, { "text": "This is not going to end well.", "start": 1414.87, "duration": 2.11 }, { "text": "OK.", "start": 1416.98, "duration": 0.73 }, { "text": "So suppose we have all of these\ncards nicely shuffled here.", "start": 1417.71, "duration": 3.45 }, { "text": "And I have before me a big\nproblem, a big pile of cards.", "start": 1421.16, "duration": 3.215 }, { "text": "And the goal, for whatever reason,\nyou wanted to start the game", "start": 1424.375, "duration": 2.625 }, { "text": "or you like to be orderly,\nis to sort the cards.", "start": 1427.0, "duration": 2.1 }, { "text": "What's your algorithm going\nto be for sorting these cards?", "start": 1429.1, "duration": 4.081 }, { "text": "What might you do?", "start": 1433.181, "duration": 0.749 }, { "text": "Yeah.", "start": 1437.56, "duration": 0.702 }, { "text": "AUDIENCE: [INAUDIBLE].", "start": 1438.262, "duration": 0.916 }, { "text": "SPEAKER 1: Do them in\npiles based on the number.", "start": 1441.651, "duration": 1.999 }, { "text": "OK, so here's the number 2.", "start": 1443.65, "duration": 1.51 }, { "text": "So you want to make a\npile for all the 2's?", "start": 1445.16, "duration": 2.02 }, { "text": "OK, so we can do that.", "start": 1447.18, "duration": 1.19 }, { "text": "So here's a pile for all the 4's.", "start": 1448.37, "duration": 1.467 }, { "text": "And let me make myself some more room.", "start": 1449.837, "duration": 1.583 }, { "text": "So we can put 2's here.", "start": 1451.42, "duration": 1.2 }, { "text": "4's here.", "start": 1452.62, "duration": 0.77 }, { "text": "Here's a 3.", "start": 1453.39, "duration": 0.584 }, { "text": "So I'm going to put this\nin between the 2 and the 4.", "start": 1453.974, "duration": 2.166 }, { "text": "Here's a 5.", "start": 1456.14, "duration": 0.96 }, { "text": "I'm going to put that over here.", "start": 1457.1, "duration": 1.43 }, { "text": "And if I jump around, here's a Jack.", "start": 1458.53, "duration": 1.52 }, { "text": "So this is going to go way over there.", "start": 1460.05, "duration": 2.09 }, { "text": "7, 8.", "start": 1462.14, "duration": 1.0 }, { "text": "6 can go over here.", "start": 1463.14, "duration": 1.59 }, { "text": "Here's another 4, so I can put it here.", "start": 1464.73, "duration": 2.83 }, { "text": "And I can bucketize all of the cards.", "start": 1467.56, "duration": 2.47 }, { "text": "So this is good intuition because it\nmakes a pretty big problem, 52 cards,", "start": 1470.03, "duration": 4.11 }, { "text": "a little more tenable.", "start": 1474.14, "duration": 1.149 }, { "text": "You can just now flip through\nall of the cards one at a time,", "start": 1475.289, "duration": 2.541 }, { "text": "or whatever you encounter first.", "start": 1477.83, "duration": 1.53 }, { "text": "And just drop it in the correct bucket.", "start": 1479.36, "duration": 2.01 }, { "text": "But that's, of course, not\ngoing to get you to the end.", "start": 1481.37, "duration": 2.291 }, { "text": "Let's assume we fast\nforward to the ending.", "start": 1483.661, "duration": 1.869 }, { "text": "And now I have these 13 piles\nfrom Ace all the way up to King.", "start": 1485.53, "duration": 4.64 }, { "text": "What do I then do?", "start": 1490.17, "duration": 0.75 }, { "text": "What's step 2?", "start": 1490.92, "duration": 2.24 }, { "text": "AUDIENCE: Stack them.", "start": 1493.16, "duration": 0.98 }, { "text": "SPEAKER 1: So I want to stack them.", "start": 1494.14, "duration": 1.03 }, { "text": "So I can take all the 2's,\nall the 3's, all the 4's.", "start": 1495.17, "duration": 2.167 }, { "text": "And I didn't specify\nearlier, one of the things", "start": 1497.337, "duration": 1.958 }, { "text": "that complicates this problem with\ncards is that you have different suits.", "start": 1499.295, "duration": 3.115 }, { "text": "And so if you really\nwant to be nit-picky,", "start": 1502.41, "duration": 1.75 }, { "text": "maybe you want to keep\nall the suits the same,", "start": 1504.16, "duration": 1.916 }, { "text": "which is like a nested\nsorting problem of some sort.", "start": 1506.076, "duration": 3.114 }, { "text": "But this general idea of bucketizing\nin this way is good intuition,", "start": 1509.19, "duration": 3.57 }, { "text": "but it clearly takes some time.", "start": 1512.76, "duration": 1.915 }, { "text": "I mean, enough time that I'm not\ngoing to sort of drag this out", "start": 1514.675, "duration": 2.625 }, { "text": "by sorting all of those cards myself.", "start": 1517.3, "duration": 1.88 }, { "text": "And therein lies the point, though.", "start": 1519.18, "duration": 1.81 }, { "text": "Even though in week 0 with Mike\nSmith, we had that sorted phone book.", "start": 1520.99, "duration": 2.95 }, { "text": "And even though a moment ago,\nDerek, albeit with a few numbers,", "start": 1523.94, "duration": 2.94 }, { "text": "had them already presorted,\nsorting takes time.", "start": 1526.88, "duration": 3.64 }, { "text": "And even when we were just sorting\nthe blue books alphabetically,", "start": 1530.52, "duration": 3.42 }, { "text": "even though it felt pretty fast, pretty\nobvious, it starts to drag eventually.", "start": 1533.94, "duration": 3.74 }, { "text": "And god forbid there\nwere more than 26 books.", "start": 1537.68, "duration": 1.92 }, { "text": "Maybe there were 260 books, or\n2,600 books, or 2 million books.", "start": 1539.6, "duration": 5.32 }, { "text": "Or web pages.", "start": 1544.92, "duration": 1.19 }, { "text": "Or database records.", "start": 1546.11, "duration": 1.63 }, { "text": "Any number of problems in this\nworld now require sorting sometimes.", "start": 1547.74, "duration": 3.674 }, { "text": "Whether it's on Google, or\nFacebook, or your own computer.", "start": 1551.414, "duration": 2.416 }, { "text": "It feels like we need a good algorithm\nfor actually doing that sorting.", "start": 1553.83, "duration": 3.36 }, { "text": "So how can we go about doing that,\nnot just with blue books, not", "start": 1557.19, "duration": 3.05 }, { "text": "just with cards, but more generally?", "start": 1560.24, "duration": 2.3 }, { "text": "Well, let's try to frame the\nproblem first with a simpler world.", "start": 1562.54, "duration": 3.78 }, { "text": "In fact, we can generalize\nblue books and playing cards", "start": 1566.32, "duration": 3.92 }, { "text": "as really just numbers.", "start": 1570.24, "duration": 1.06 }, { "text": "Or some piece of data that there is\na defined order or sequence to them.", "start": 1571.3, "duration": 4.55 }, { "text": "And suppose I have these numbers here.", "start": 1575.85, "duration": 1.78 }, { "text": "How do I actually go about\nsorting this many numbers?", "start": 1577.63, "duration": 3.469 }, { "text": "Well, for this-- and this\nwill be our last chance", "start": 1581.099, "duration": 2.041 }, { "text": "for audience participation here.", "start": 1583.14, "duration": 1.62 }, { "text": "I need eight brave volunteers\nto actually come on up.", "start": 1584.76, "duration": 3.13 }, { "text": "All right, so 1, 2.", "start": 1587.89, "duration": 0.863 }, { "text": "This is what everyone's\nbeen waiting for.", "start": 1588.753, "duration": 1.708 }, { "text": "1, 2, 3, 4, 5, 6, 7, and 8.", "start": 1590.461, "duration": 6.719 }, { "text": "Thank you.", "start": 1597.18, "duration": 0.5 }, { "text": "Come on up.", "start": 1597.68, "duration": 1.52 }, { "text": "And I will meet you over here.", "start": 1599.2, "duration": 1.58 }, { "text": "All right.", "start": 1607.46, "duration": 0.73 }, { "text": "Come on over here.", "start": 1608.19, "duration": 0.75 }, { "text": "If you want to grab two music stands.", "start": 1608.94, "duration": 1.541 }, { "text": "OK.", "start": 1613.4, "duration": 0.5 }, { "text": "So let's go ahead and turn these\naround like this if you could,", "start": 1613.9, "duration": 2.19 }, { "text": "as though the music's\ngoing to face the audience.", "start": 1616.09, "duration": 2.041 }, { "text": "OK.", "start": 1621.94, "duration": 2.77 }, { "text": "All right.", "start": 1624.71, "duration": 0.5 }, { "text": "And let me go ahead and give you sheets\nof paper, and then we'll resume here.", "start": 1625.21, "duration": 4.01 }, { "text": "All right.", "start": 1629.22, "duration": 0.5 }, { "text": "So here is our eighth music stand.", "start": 1629.72, "duration": 2.05 }, { "text": "And what we have here\nis 8 pieces of paper.", "start": 1631.77, "duration": 2.427 }, { "text": "And each of you guys is going to take on\nthe role of a certain number right now.", "start": 1634.197, "duration": 3.333 }, { "text": "So I'm going to go ahead and give\neach of you a number in sorted order", "start": 1637.53, "duration": 5.17 }, { "text": "initially, but that would be too easy.", "start": 1642.7, "duration": 2.59 }, { "text": "So if you don't mind, let's go ahead and\narrange yourselves behind these music", "start": 1645.29, "duration": 5.444 }, { "text": "stands in the same order\nthat you see on the screen.", "start": 1650.734, "duration": 2.166 }, { "text": "So on the left end here near\nme should be the number 4.", "start": 1652.9, "duration": 3.02 }, { "text": "Then, 2.", "start": 1655.92, "duration": 1.76 }, { "text": "Then, 6.", "start": 1657.68, "duration": 1.7 }, { "text": "Then, 8.", "start": 1659.38, "duration": 0.51 }, { "text": "Good job.", "start": 1659.89, "duration": 0.84 }, { "text": "Then, 1.", "start": 1660.73, "duration": 0.85 }, { "text": "Then, 3.", "start": 1661.58, "duration": 1.03 }, { "text": "Then, 7.", "start": 1662.61, "duration": 0.92 }, { "text": "Then, 5.", "start": 1663.53, "duration": 0.57 }, { "text": "All right.", "start": 1664.1, "duration": 0.5 }, { "text": "And you can put the\nnumbers on the music stand", "start": 1664.6, "duration": 1.76 }, { "text": "there, but just move\nthem with you as you go.", "start": 1666.36, "duration": 1.875 }, { "text": "So now the question is, here\nis a seemingly random list", "start": 1668.235, "duration": 3.435 }, { "text": "in just some order I came up\nwith somewhat arbitrarily.", "start": 1671.67, "duration": 2.3 }, { "text": "And I want now to sort my list.", "start": 1673.97, "duration": 3.2 }, { "text": "How do I go about doing it?", "start": 1677.17, "duration": 1.3 }, { "text": "What would you propose?", "start": 1678.47, "duration": 1.77 }, { "text": "The goal is to get from 1 to 8.", "start": 1680.24, "duration": 2.95 }, { "text": "What are our possible approaches here?", "start": 1683.19, "duration": 4.74 }, { "text": "Oh, you want-- sure, OK.", "start": 1687.93, "duration": 1.28 }, { "text": "We'll just do it over here.", "start": 1689.21, "duration": 1.124 }, { "text": "AUDIENCE: Take out the smallest number.", "start": 1690.334, "duration": 1.856 }, { "text": "SPEAKER 1: OK.", "start": 1692.19, "duration": 0.583 }, { "text": "AUDIENCE: Take it, shift\neveryone else down.", "start": 1692.773, "duration": 1.858 }, { "text": "Have the smallest number\nin the first place.", "start": 1694.631, "duration": 1.519 }, { "text": "SPEAKER 1: OK, good.", "start": 1696.15, "duration": 0.686 }, { "text": "AUDIENCE: [INAUDIBLE].", "start": 1696.836, "duration": 0.916 }, { "text": "SPEAKER 1: So let's\ngo ahead and do that.", "start": 1697.752, "duration": 1.962 }, { "text": "For those tuning in at home,\nwhat's your name again?", "start": 1699.714, "duration": 2.166 }, { "text": "AUDIENCE: Allison.", "start": 1701.88, "duration": 0.61 }, { "text": "SPEAKER 1: Allison.", "start": 1702.49, "duration": 0.46 }, { "text": "And?", "start": 1702.95, "duration": 0.54 }, { "text": "AUDIENCE: Alex.", "start": 1703.49, "duration": 0.37 }, { "text": "SPEAKER 1: Alex.", "start": 1703.86, "duration": 0.412 }, { "text": "AUDIENCE: Adam.", "start": 1704.272, "duration": 0.625 }, { "text": "SPEAKER 1: Adam.", "start": 1704.897, "duration": 0.673 }, { "text": "AUDIENCE: Brandon.", "start": 1705.57, "duration": 0.75 }, { "text": "SPEAKER 1: Brandon.", "start": 1706.32, "duration": 0.365 }, { "text": "AUDIENCE: Joseph.", "start": 1706.685, "duration": 0.365 }, { "text": "SPEAKER 1: Joseph.", "start": 1707.05, "duration": 0.4 }, { "text": "AUDIENCE: Vicky.", "start": 1707.45, "duration": 0.305 }, { "text": "SPEAKER 1: Vicky.", "start": 1707.755, "duration": 0.765 }, { "text": "AUDIENCE: [? Arpin. ?]", "start": 1708.52, "duration": 0.27 }, { "text": "SPEAKER 1: [? Arpin. ?]", "start": 1708.79, "duration": 0.27 }, { "text": "AUDIENCE: Derek.", "start": 1709.06, "duration": 0.666 }, { "text": "SPEAKER 1: Derek.", "start": 1709.726, "duration": 0.784 }, { "text": "OK.", "start": 1710.51, "duration": 0.66 }, { "text": "So now, because that all\njust was too much to absorb.", "start": 1711.17, "duration": 3.13 }, { "text": "Number 1 is now the\nfirst smallest element", "start": 1714.3, "duration": 4.15 }, { "text": "according to the proposed algorithm.", "start": 1718.45, "duration": 1.5 }, { "text": "So what are we going to\ndo exactly with number 1?", "start": 1719.95, "duration": 2.22 }, { "text": "AUDIENCE: He's going to [INAUDIBLE].", "start": 1722.17, "duration": 1.499 }, { "text": "We're [INAUDIBLE].", "start": 1723.669, "duration": 1.218 }, { "text": "SPEAKER 1: OK, good.", "start": 1724.887, "duration": 0.833 }, { "text": "So pop back if you would.", "start": 1725.72, "duration": 1.39 }, { "text": "You guys are going to shift\nthree places this way.", "start": 1727.11, "duration": 2.104 }, { "text": "And we're going to insert number\n1 at the beginning of the list.", "start": 1729.214, "duration": 2.666 }, { "text": "All right, so what's the\nnext step just to be clear?", "start": 1731.88, "duration": 1.5 }, { "text": "AUDIENCE: Number 2 is going to pop up.", "start": 1733.38, "duration": 2.03 }, { "text": "SPEAKER 1: Good.", "start": 1735.41, "duration": 0.666 }, { "text": "AUDIENCE: I'm going to shift down.", "start": 1736.076, "duration": 0.912 }, { "text": "Number 1 is going to stay in place.", "start": 1736.988, "duration": 0.456 }, { "text": "SPEAKER 1: Good.", "start": 1737.444, "duration": 0.456 }, { "text": "So we find the next smallest\nelement, which happens to be 2.", "start": 1737.9, "duration": 2.37 }, { "text": "We insert him at the\nbeginning of the list here.", "start": 1740.27, "duration": 2.07 }, { "text": "And now, we move on to the\nnumber 3 problem Excellent.", "start": 1742.34, "duration": 2.47 }, { "text": "So pop back.", "start": 1744.81, "duration": 1.56 }, { "text": "Shift.", "start": 1746.37, "duration": 1.39 }, { "text": "And insert.", "start": 1747.76, "duration": 0.55 }, { "text": "Good.", "start": 1748.31, "duration": 0.5 }, { "text": "4, we got lucky.", "start": 1748.81, "duration": 0.809 }, { "text": "So we don't have to do\nany extra work here.", "start": 1749.619, "duration": 1.791 }, { "text": "So that's a freebie.", "start": 1751.41, "duration": 0.833 }, { "text": "Now we look for 5.", "start": 1752.243, "duration": 0.837 }, { "text": "Oh, there's 5 at the end.", "start": 1753.08, "duration": 3.34 }, { "text": "Good.", "start": 1756.42, "duration": 1.14 }, { "text": "And now 6.", "start": 1757.56, "duration": 0.99 }, { "text": "We got lucky.", "start": 1758.55, "duration": 0.77 }, { "text": "7 and 8, we need to fix that.", "start": 1759.32, "duration": 2.01 }, { "text": "OK, good.", "start": 1761.33, "duration": 0.83 }, { "text": "So I like this.", "start": 1762.16, "duration": 0.89 }, { "text": "It felt pretty fast.", "start": 1763.05, "duration": 1.02 }, { "text": "Though, to be fair, the\nlist is pretty short.", "start": 1764.07, "duration": 2.1 }, { "text": "But we were doing kind of a lot of work.", "start": 1766.17, "duration": 2.167 }, { "text": "In fact, that was perfect the fact\nthat number 1 was all the way over here", "start": 1768.337, "duration": 3.083 }, { "text": "because we shifted 3 humans.", "start": 1771.42, "duration": 1.762 }, { "text": "And can you guys reset\nfor just a moment?", "start": 1773.182, "duration": 1.708 }, { "text": "Let me propose an alternative approach.", "start": 1774.89, "duration": 1.89 }, { "text": "So if number 1 is in the middle here\nand really belongs all the way there", "start": 1776.78, "duration": 4.15 }, { "text": "on the left, we went\nto great lengths, it", "start": 1780.93, "duration": 2.8 }, { "text": "seems, to shift all of these volunteers\nto the left, which is a lot of steps.", "start": 1783.73, "duration": 3.292 }, { "text": "Because at the end of the day,\nlet's assume for today's purposes,", "start": 1787.022, "duration": 2.708 }, { "text": "that a computer can only\ndo one thing at once.", "start": 1789.73, "duration": 2.061 }, { "text": "So even though all of you\nhumans moved pretty quickly,", "start": 1791.791, "duration": 2.249 }, { "text": "that was really like one of you moved.", "start": 1794.04, "duration": 1.88 }, { "text": "Then, the next of you moved.", "start": 1795.92, "duration": 1.2 }, { "text": "Then, the next of you moved.", "start": 1797.12, "duration": 1.07 }, { "text": "Then, the next.", "start": 1798.19, "duration": 0.63 }, { "text": "So that was like 4 total steps just\nto put number 1 on the end there.", "start": 1798.82, "duration": 4.057 }, { "text": "Let me propose this.", "start": 1802.877, "duration": 0.833 }, { "text": "1, can you pop out again?", "start": 1803.71, "duration": 1.65 }, { "text": "Now, this list, so far as I'm\nconcerned as the computer,", "start": 1805.36, "duration": 2.9 }, { "text": "is perfectly random from the get-go.", "start": 1808.26, "duration": 2.26 }, { "text": "So why do I even care\nthat you guys move?", "start": 1810.52, "duration": 2.96 }, { "text": "I haven't even looked at\nthe rest of these elements", "start": 1813.48, "duration": 2.869 }, { "text": "yet or done anything with them.", "start": 1816.349, "duration": 1.291 }, { "text": "Why don't I just evict number\n4 where number 1 belongs?", "start": 1817.64, "duration": 2.684 }, { "text": "If you want to go over here.", "start": 1820.324, "duration": 1.166 }, { "text": "And if the list is already\nrandomly sorted in the beginning,", "start": 1821.49, "duration": 2.499 }, { "text": "well, then fine.", "start": 1823.989, "duration": 0.761 }, { "text": "4, you're going to go over here.", "start": 1824.75, "duration": 1.333 }, { "text": "So I've made the problem no worse,\nbut I have made it slightly better", "start": 1826.083, "duration": 3.027 }, { "text": "by putting 1 on the end.", "start": 1829.11, "duration": 1.385 }, { "text": "Now I'm going to go ahead and select\nthe next smallest element again.", "start": 1830.495, "duration": 2.875 }, { "text": "2, I got lucky.", "start": 1833.37, "duration": 1.34 }, { "text": "Now, I'm going to look for\nthe next smallest element.", "start": 1834.71, "duration": 2.58 }, { "text": "3 indeed is the smallest.", "start": 1837.29, "duration": 1.524 }, { "text": "So let me do the same thing.", "start": 1838.814, "duration": 1.166 }, { "text": "3, if you could pop back.", "start": 1839.98, "duration": 1.3 }, { "text": "6, you're out of there.", "start": 1841.28, "duration": 2.11 }, { "text": "And notice that we're doing less work.", "start": 1843.39, "duration": 1.69 }, { "text": "Now, the humans are moving a little\nfarther physically, but that's fine.", "start": 1845.08, "duration": 3.0 }, { "text": "The computer can just move values\naround in memory pretty fast.", "start": 1848.08, "duration": 3.51 }, { "text": "But I've moved fewer of you.", "start": 1851.59, "duration": 1.63 }, { "text": "So this is a slight optimization.", "start": 1853.22, "duration": 1.55 }, { "text": "It turns out this isn't\nfundamentally better as we'll see.", "start": 1854.77, "duration": 2.75 }, { "text": "But it's this instinct\nthat you should appreciate", "start": 1857.52, "duration": 2.16 }, { "text": "of trying to do the least\namount of work possible.", "start": 1859.68, "duration": 2.083 }, { "text": "Because otherwise, it's going to add up.", "start": 1861.763, "duration": 2.507 }, { "text": "Let's try another one.", "start": 1864.27, "duration": 2.02 }, { "text": "Well, let me clarify one thing then.", "start": 1866.29, "duration": 1.66 }, { "text": "So what am I doing on each\niteration of this algorithm?", "start": 1867.95, "duration": 3.1 }, { "text": "As you suggested, I'm\nselecting the smallest element.", "start": 1871.05, "duration": 3.21 }, { "text": "But the only catch is, if I'm\nnow looking for the next smallest", "start": 1874.26, "duration": 3.01 }, { "text": "element, that's going to be 4.", "start": 1877.27, "duration": 1.7 }, { "text": "But I'm only sure that it's\n4 once I get to the end", "start": 1878.97, "duration": 2.42 }, { "text": "and realize, yep, that was the\nsmallest element and then I act.", "start": 1881.39, "duration": 3.0 }, { "text": "So once we fix that problem--\nif you guys want to switch--", "start": 1884.39, "duration": 3.11 }, { "text": "I start again over here.", "start": 1887.5, "duration": 1.485 }, { "text": "And I have to find the\nnext smallest element.", "start": 1888.985, "duration": 1.875 }, { "text": "And let's see, 8 is pretty big.", "start": 1890.86, "duration": 1.82 }, { "text": "6 is smaller.", "start": 1892.68, "duration": 0.69 }, { "text": "Good.", "start": 1893.37, "duration": 0.5 }, { "text": "7, not smaller.", "start": 1893.87, "duration": 1.95 }, { "text": "But only once I get to the end do I\nrealize, oh, here is the smallest.", "start": 1895.82, "duration": 3.07 }, { "text": "So in short, to find\nthe smallest element", "start": 1898.89, "duration": 2.56 }, { "text": "as you proposed again and again, I have\nto keep going through the whole list", "start": 1901.45, "duration": 4.349 }, { "text": "because it might be\nall the way at the end.", "start": 1905.799, "duration": 1.791 }, { "text": "We, humans, have the\nadvantage of just kind", "start": 1907.59, "duration": 1.49 }, { "text": "of looking, sort of taking\na step back and saying,", "start": 1909.08, "duration": 2.19 }, { "text": "OK, this is obviously unsorted.", "start": 1911.27, "duration": 1.44 }, { "text": "I know where everything is.", "start": 1912.71, "duration": 1.17 }, { "text": "A computer can only look\nat one number at a time,", "start": 1913.88, "duration": 3.05 }, { "text": "one element of an array at a time.", "start": 1916.93, "duration": 1.99 }, { "text": "So let's try a fundamentally\ndifferent approach.", "start": 1918.92, "duration": 2.0 }, { "text": "If you guys could reset to\nyour original 8 locations.", "start": 1920.92, "duration": 2.53 }, { "text": "Let me propose that we\njust looked at an algorithm", "start": 1923.45, "duration": 4.27 }, { "text": "that we'll call selection sort.", "start": 1927.72, "duration": 1.54 }, { "text": "Selection sort in so far as you\niteratively again and again select", "start": 1929.26, "duration": 4.24 }, { "text": "the next smallest element.", "start": 1933.5, "duration": 1.63 }, { "text": "Let's now do an approach that\nwe'll call bubble sort, which", "start": 1935.13, "duration": 4.46 }, { "text": "has sort of the visual effect of numbers\nbubbling up over time as follows.", "start": 1939.59, "duration": 4.277 }, { "text": "You know what?", "start": 1943.867, "duration": 0.583 }, { "text": "I'm just going to look,\nnot at the whole list", "start": 1944.45, "duration": 1.76 }, { "text": "because it felt like that was\ncreating a lot of work for me.", "start": 1946.21, "duration": 2.51 }, { "text": "I'm going to look at 2\nnumbers at a time, 4 and 2.", "start": 1948.72, "duration": 2.54 }, { "text": "Are these in order or out of order?", "start": 1951.26, "duration": 1.63 }, { "text": "Obviously.", "start": 1952.89, "duration": 1.44 }, { "text": "So they're out of order.", "start": 1954.33, "duration": 1.0 }, { "text": "So you know what?", "start": 1955.33, "duration": 0.48 }, { "text": "I don't care about the\nrest of the problem.", "start": 1955.81, "duration": 1.791 }, { "text": "Let me just swap you two.", "start": 1957.601, "duration": 1.619 }, { "text": "All right.", "start": 1959.22, "duration": 0.5 }, { "text": "Now, let me take one step.", "start": 1959.72, "duration": 1.51 }, { "text": "Look at 4 and 6.", "start": 1961.23, "duration": 0.94 }, { "text": "In order or out of order?", "start": 1962.17, "duration": 1.32 }, { "text": "In order.", "start": 1963.49, "duration": 0.53 }, { "text": "So I'm going to leave it be.", "start": 1964.02, "duration": 1.24 }, { "text": "6 and 8?", "start": 1965.26, "duration": 0.86 }, { "text": "In order.", "start": 1966.12, "duration": 0.81 }, { "text": "8 and 1?", "start": 1966.93, "duration": 0.55 }, { "text": "Not in order.", "start": 1967.48, "duration": 0.76 }, { "text": "So let me swap that again.", "start": 1968.24, "duration": 1.555 }, { "text": "8 and 3?", "start": 1969.795, "duration": 1.005 }, { "text": "Out of order.", "start": 1970.8, "duration": 0.57 }, { "text": "Let me swap that again.", "start": 1971.37, "duration": 1.52 }, { "text": "8 and 7?", "start": 1972.89, "duration": 1.219 }, { "text": "Out of order.", "start": 1974.109, "duration": 0.541 }, { "text": "Let me swap that again.", "start": 1974.65, "duration": 1.78 }, { "text": "8 and 5?", "start": 1976.43, "duration": 0.969 }, { "text": "Out of order.", "start": 1977.399, "duration": 0.541 }, { "text": "Let me swap that again.", "start": 1977.94, "duration": 1.69 }, { "text": "And now, what has happened?", "start": 1979.63, "duration": 1.16 }, { "text": "Is the list sorted because I\nfixed all the pairwise mistakes?", "start": 1980.79, "duration": 5.51 }, { "text": "So obviously not.", "start": 1986.3, "duration": 1.01 }, { "text": "But is it better, the list?", "start": 1987.31, "duration": 1.412 }, { "text": "Why is it better?", "start": 1988.722, "duration": 0.708 }, { "text": "Derek.", "start": 1989.43, "duration": 0.66 }, { "text": "AUDIENCE: Because now you have\none less element to worry about.", "start": 1990.09, "duration": 2.02 }, { "text": "SPEAKER 1: Yeah, exactly.", "start": 1992.11, "duration": 1.041 }, { "text": "8 bubbled all the way up\nto the top, if you will.", "start": 1993.151, "duration": 2.879 }, { "text": "So now he is effectively done.", "start": 1996.03, "duration": 1.83 }, { "text": "And frankly, every other\nnumber that's smaller", "start": 1997.86, "duration": 1.98 }, { "text": "bubbled one step closer to its position.", "start": 1999.84, "duration": 2.899 }, { "text": "So we've taken one big pass through this\nto solve at least one of the problems.", "start": 2002.739, "duration": 3.291 }, { "text": "And now maximally, 7 problems remain.", "start": 2006.03, "duration": 2.58 }, { "text": "So let me go back to the end here.", "start": 2008.61, "duration": 1.86 }, { "text": "And let me look at pairwise.", "start": 2010.47, "duration": 1.31 }, { "text": "2 and 4?", "start": 2011.78, "duration": 0.55 }, { "text": "You're good.", "start": 2012.33, "duration": 0.55 }, { "text": "4 and 6?", "start": 2012.88, "duration": 0.55 }, { "text": "You're good.", "start": 2013.43, "duration": 0.5 }, { "text": "6 and 1?", "start": 2013.93, "duration": 0.9 }, { "text": "Let's fix that.", "start": 2014.83, "duration": 1.47 }, { "text": "6 and 3?", "start": 2016.3, "duration": 0.82 }, { "text": "Let's fix that.", "start": 2017.12, "duration": 1.59 }, { "text": "6 and 7?", "start": 2018.71, "duration": 0.58 }, { "text": "We're good.", "start": 2019.29, "duration": 0.5 }, { "text": "7 and 5?", "start": 2019.79, "duration": 0.73 }, { "text": "Let's fix that.", "start": 2020.52, "duration": 1.35 }, { "text": "And now I can ignore number 8 because\nI know the end of my list is sorted.", "start": 2021.87, "duration": 3.65 }, { "text": "So now, I've improved it slightly.", "start": 2025.52, "duration": 1.8 }, { "text": "7 has bubbled up to\nwhere he needs to be.", "start": 2027.32, "duration": 2.06 }, { "text": "I just have 6 problems\nleft to solve at most.", "start": 2029.38, "duration": 2.22 }, { "text": "So now I look again.", "start": 2031.6, "duration": 0.88 }, { "text": "2 and 4?", "start": 2032.48, "duration": 0.53 }, { "text": "You're good.", "start": 2033.01, "duration": 0.77 }, { "text": "1 and 4?", "start": 2033.78, "duration": 0.78 }, { "text": "Let's swap that.", "start": 2034.56, "duration": 1.01 }, { "text": "And notice, 1 is moving closer\nto the left of the list.", "start": 2035.57, "duration": 2.93 }, { "text": "4 and 3?", "start": 2038.5, "duration": 0.51 }, { "text": "Let's swap.", "start": 2039.01, "duration": 1.3 }, { "text": "4 and 6?", "start": 2040.31, "duration": 0.6 }, { "text": "You're good.", "start": 2040.91, "duration": 0.5 }, { "text": "6 and 5?", "start": 2041.41, "duration": 0.61 }, { "text": "You're not.", "start": 2042.02, "duration": 1.01 }, { "text": "But now I fixed 6.", "start": 2043.03, "duration": 1.35 }, { "text": "And I can stop here, leaving me\nwith just five potential problems.", "start": 2044.38, "duration": 3.042 }, { "text": "And then you can see\nwhere this is going.", "start": 2047.422, "duration": 1.708 }, { "text": "2 and 1?", "start": 2049.13, "duration": 0.5 }, { "text": "Let's swap.", "start": 2049.63, "duration": 0.97 }, { "text": "2 and 3?", "start": 2050.6, "duration": 0.5 }, { "text": "You're good.", "start": 2051.1, "duration": 0.43 }, { "text": "3 and 4?", "start": 2051.53, "duration": 0.55 }, { "text": "You're good.", "start": 2052.08, "duration": 0.67 }, { "text": "We already solved these problems.", "start": 2052.75, "duration": 1.42 }, { "text": "So let me go back.", "start": 2054.17, "duration": 1.61 }, { "text": "And now, 1 and 2?", "start": 2055.78, "duration": 1.22 }, { "text": "You're good.", "start": 2057.0, "duration": 0.84 }, { "text": "2 and 3?", "start": 2057.84, "duration": 0.54 }, { "text": "You're good.", "start": 2058.38, "duration": 0.56 }, { "text": "3 and 4, 4 and 5, 5 and\n6, 6 and 7, 7 and 8.", "start": 2058.94, "duration": 3.14 }, { "text": "What do I know now as the computer?", "start": 2062.08, "duration": 3.61 }, { "text": "What's that?", "start": 2065.69, "duration": 0.56 }, { "text": "AUDIENCE: It's sorted.", "start": 2066.25, "duration": 0.31 }, { "text": "SPEAKER 1: It's sorted.", "start": 2066.56, "duration": 0.958 }, { "text": "Why?", "start": 2067.518, "duration": 0.911 }, { "text": "AUDIENCE: Because everything's in order", "start": 2068.429, "duration": 1.901 }, { "text": "SPEAKER 1: Everything is in order.", "start": 2070.33, "duration": 0.889 }, { "text": "But what does that mean?", "start": 2071.219, "duration": 1.0 }, { "text": "We humans can see that, but the computer\ncan only look at individual values", "start": 2072.219, "duration": 3.171 }, { "text": "at a time.", "start": 2075.39, "duration": 0.499 }, { "text": "It can't take a step back\nand say, yep, sorted.", "start": 2075.889, "duration": 2.966 }, { "text": "AUDIENCE: [INAUDIBLE].", "start": 2078.855, "duration": 2.229 }, { "text": "SPEAKER 1: Good.", "start": 2081.084, "duration": 0.666 }, { "text": "At a lower level implementation\ndetail, I did no swaps.", "start": 2081.75, "duration": 3.46 }, { "text": "There were no two numbers\nthat were out of order.", "start": 2085.21, "duration": 2.08 }, { "text": "So it would just be\nfoolish of me and wasteful", "start": 2087.29, "duration": 3.31 }, { "text": "for me to bother doing another pass.", "start": 2090.6, "duration": 1.78 }, { "text": "Because assuming the numbers\nare not changing on their own,", "start": 2092.38, "duration": 2.67 }, { "text": "I'm just going to do the same\nthing again and again otherwise.", "start": 2095.05, "duration": 2.583 }, { "text": "So I can just stop.", "start": 2097.633, "duration": 1.227 }, { "text": "And indeed, the bubble sort\nallows us to stop like this.", "start": 2098.86, "duration": 2.53 }, { "text": "Let's do one last approach.", "start": 2101.39, "duration": 1.29 }, { "text": "If you could, let me toss the\nstarting points on the board again.", "start": 2102.68, "duration": 4.04 }, { "text": "Let's reset one last time to this.", "start": 2106.72, "duration": 3.589 }, { "text": "And let me propose-- let me\ndraw inspiration, actually,", "start": 2110.309, "duration": 2.291 }, { "text": "from the approach you took\nwith the blue books, which was", "start": 2112.6, "duration": 2.374 }, { "text": "a little different from how we began.", "start": 2114.974, "duration": 1.706 }, { "text": "Which was recall that you took\nthe problem on your left hand", "start": 2116.68, "duration": 3.572 }, { "text": "and you just dealt\nwith it one at a time.", "start": 2120.252, "duration": 1.708 }, { "text": "You didn't go sifting\nthrough looking for A.", "start": 2121.96, "duration": 1.83 }, { "text": "You didn't go sifting\nthrough looking for B.", "start": 2123.79, "duration": 1.7 }, { "text": "You didn't go sifting through\nlooking for C, which would really", "start": 2125.49, "duration": 2.11 }, { "text": "be the analog of what you\nproposed a moment ago.", "start": 2127.6, "duration": 2.12 }, { "text": "Instead, you just dealt with\neach problem as it came.", "start": 2129.72, "duration": 2.23 }, { "text": "And this is our third\nand final algorithm", "start": 2131.95, "duration": 1.94 }, { "text": "for sorting called insertion sort.", "start": 2133.89, "duration": 2.53 }, { "text": "Take each problem one at a time and\njust deal with it then and there.", "start": 2136.42, "duration": 3.85 }, { "text": "Don't postpone.", "start": 2140.27, "duration": 1.1 }, { "text": "So here's 4.", "start": 2141.37, "duration": 0.923 }, { "text": "You know what?", "start": 2142.293, "duration": 1.167 }, { "text": "Done.", "start": 2143.46, "duration": 0.58 }, { "text": "I now claim that this list, which\nwe'll visually make a little separate,", "start": 2144.04, "duration": 3.7 }, { "text": "is sorted.", "start": 2147.74, "duration": 0.85 }, { "text": "So I'm going to mentally divide my\nlist into a left half and a right half.", "start": 2148.59, "duration": 3.14 }, { "text": "And now I just claim trivially-- I\nmean, almost silly-- this is sorted.", "start": 2151.73, "duration": 4.31 }, { "text": "Because it is.", "start": 2156.04, "duration": 0.83 }, { "text": "But now the right half\nof my list remains.", "start": 2156.87, "duration": 1.88 }, { "text": "So let's go ahead and do this.", "start": 2158.75, "duration": 1.249 }, { "text": "So number 2.", "start": 2159.999, "duration": 0.931 }, { "text": "OK, where does this belong?", "start": 2160.93, "duration": 1.17 }, { "text": "So if you want to go ahead\nand pick up the number.", "start": 2162.1, "duration": 2.083 }, { "text": "The stand can stay.", "start": 2164.183, "duration": 1.297 }, { "text": "Number 2 goes where?", "start": 2165.48, "duration": 1.79 }, { "text": "Here's my left list.", "start": 2167.27, "duration": 1.045 }, { "text": "And we'll make a little more\nspace here just to be clear.", "start": 2168.315, "duration": 2.375 }, { "text": "It goes over to this side.", "start": 2170.69, "duration": 1.6 }, { "text": "So what has to happen?", "start": 2172.29, "duration": 2.74 }, { "text": "So this time, we do\nneed to shift you over.", "start": 2175.03, "duration": 2.84 }, { "text": "So let's take 2 out.", "start": 2177.87, "duration": 1.37 }, { "text": "Let's shift 4 over.", "start": 2179.24, "duration": 2.017 }, { "text": "And now we won't move the stand.", "start": 2181.257, "duration": 1.333 }, { "text": "We'll just assume now that\nmy left half is of size 2", "start": 2182.59, "duration": 3.25 }, { "text": "and the right half is of size 6.", "start": 2185.84, "duration": 1.445 }, { "text": "But now, the left half of\nthe list is still sorted,", "start": 2187.285, "duration": 2.125 }, { "text": "but it costs me a little bit of work.", "start": 2189.41, "duration": 1.541 }, { "text": "I had to move 4 over.", "start": 2190.951, "duration": 1.32 }, { "text": "All right, let me deal with 6.", "start": 2192.271, "duration": 1.249 }, { "text": "Where does 6 go?", "start": 2193.52, "duration": 1.684 }, { "text": "It's already in order.", "start": 2195.204, "duration": 0.916 }, { "text": "I don't need to shift anyone.", "start": 2196.12, "duration": 1.208 }, { "text": "Where does 8 go?", "start": 2197.328, "duration": 0.792 }, { "text": "Phew, it doesn't need to go anywhere.", "start": 2198.12, "duration": 1.541 }, { "text": "It's already in order.", "start": 2199.661, "duration": 0.935 }, { "text": "Uh-oh, 1.", "start": 2200.596, "duration": 0.774 }, { "text": "Where does it go?", "start": 2201.37, "duration": 0.94 }, { "text": "Now we incur a good amount of cost.", "start": 2202.31, "duration": 2.052 }, { "text": "So let's do this.", "start": 2204.362, "duration": 0.708 }, { "text": "Where do you go?", "start": 2205.07, "duration": 1.19 }, { "text": "One shift, two shift,\nthree shifts, four shifts.", "start": 2206.26, "duration": 3.8 }, { "text": "Feels-- yep-- as bad as\nour original approach.", "start": 2210.06, "duration": 3.49 }, { "text": "But notice I only have\n4 more problems left.", "start": 2213.55, "duration": 1.979 }, { "text": "I don't have to keep going\nback through the list.", "start": 2215.529, "duration": 2.041 }, { "text": "So where does 3 go?", "start": 2217.57, "duration": 0.75 }, { "text": "All right, let's pop you out.", "start": 2218.32, "duration": 1.208 }, { "text": "Shift you in there.", "start": 2219.528, "duration": 1.862 }, { "text": "7.", "start": 2221.39, "duration": 0.5 }, { "text": "We got a little lucky.", "start": 2221.89, "duration": 0.916 }, { "text": "Let's pop you out and insert\nyou right where you belong.", "start": 2222.806, "duration": 2.724 }, { "text": "And then 5, you belong\na few shifts over.", "start": 2225.53, "duration": 2.8 }, { "text": "So let's shift three of you.", "start": 2228.33, "duration": 2.4 }, { "text": "And then, done.", "start": 2230.73, "duration": 1.6 }, { "text": "All right.", "start": 2232.33, "duration": 0.5 }, { "text": "So let's give all of you a stress ball.", "start": 2232.83, "duration": 1.72 }, { "text": "And maybe a round of applause.", "start": 2234.55, "duration": 1.249 }, { "text": "And let's see if we can't tease\napart what just happened here.", "start": 2235.799, "duration": 3.261 }, { "text": "All right.", "start": 2239.06, "duration": 1.59 }, { "text": "And then you can exit stage\nleft-- right if you'd like.", "start": 2240.65, "duration": 3.255 }, { "text": "All right, thank you.", "start": 2243.905, "duration": 0.875 }, { "text": "Derek, you're really\nracking them up here.", "start": 2244.78, "duration": 1.435 }, { "text": "All right.", "start": 2246.215, "duration": 0.275 }, { "text": "AUDIENCE: I'll [INAUDIBLE].", "start": 2246.49, "duration": 0.96 }, { "text": "SPEAKER 1: All right.", "start": 2247.45, "duration": 0.875 }, { "text": "Thank you.", "start": 2248.325, "duration": 0.745 }, { "text": "All right.", "start": 2249.07, "duration": 0.771 }, { "text": "Sure.", "start": 2249.841, "duration": 0.499 }, { "text": "So what was the point of this exercise?", "start": 2250.34, "duration": 1.624 }, { "text": "And how do we actually now get to\na decision point where one of these", "start": 2251.964, "duration": 3.806 }, { "text": "is the way to go?", "start": 2255.77, "duration": 1.89 }, { "text": "So in bubble sort, recall that\nthe key was to do something", "start": 2257.66, "duration": 2.59 }, { "text": "again and again until we did no swaps.", "start": 2260.25, "duration": 2.494 }, { "text": "At which point we could conclude\nthat the list was sorted.", "start": 2262.744, "duration": 2.416 }, { "text": "So let's do exactly that,\nrepeat until no swaps.", "start": 2265.16, "duration": 2.692 }, { "text": "And then, let's give\nourselves a counter,", "start": 2267.852, "duration": 1.708 }, { "text": "just to make things a\nlittle more methodical,", "start": 2269.56, "duration": 1.874 }, { "text": "and say for i from 0 to n\nminus 1-- rather n minus 2.", "start": 2271.434, "duration": 4.946 }, { "text": "Why?", "start": 2276.38, "duration": 0.68 }, { "text": "Well, the end of the list\nrecall is it n minus 1.", "start": 2277.06, "duration": 3.11 }, { "text": "Because if you have a list of\nsize n, the beginning is at 0.", "start": 2280.17, "duration": 3.12 }, { "text": "The end is at n minus 1.", "start": 2283.29, "duration": 1.95 }, { "text": "And so one shy of the end\nis going to be n minus 2.", "start": 2285.24, "duration": 3.25 }, { "text": "So we want to do this up through\nthe second to last element.", "start": 2288.49, "duration": 3.42 }, { "text": "If the i-th and the i-th plus\n1 elements are out of order.", "start": 2291.91, "duration": 4.87 }, { "text": "So if left hand and right hand\nare out of order, swap them.", "start": 2296.78, "duration": 3.62 }, { "text": "And repeat this again\nand again and again.", "start": 2300.4, "duration": 1.8 }, { "text": "And thanks to that\nouter loop, we're going", "start": 2302.2, "duration": 1.75 }, { "text": "to do it again and again and\nagain until we have no such swaps.", "start": 2303.95, "duration": 4.04 }, { "text": "And now to be clear, why this n minus 2?", "start": 2307.99, "duration": 2.31 }, { "text": "We want to make sure as we're sort\nof walking down our row of volunteers", "start": 2310.3, "duration": 3.21 }, { "text": "that my left hand does not actually\npoint at the last human on stage", "start": 2313.51, "duration": 4.1 }, { "text": "because then, where would\nmy right hand point?", "start": 2317.61, "duration": 2.04 }, { "text": "There's no person to beyond that point.", "start": 2319.65, "duration": 3.264 }, { "text": "So this then is bubble sort.", "start": 2322.914, "duration": 1.166 }, { "text": "Now, let's propose pseudocode for\nour other algorithm, selection sort,", "start": 2324.08, "duration": 4.23 }, { "text": "wherein we walked through\nthe list iteratively", "start": 2328.31, "duration": 2.44 }, { "text": "trying to select on each\npass the smallest element", "start": 2330.75, "duration": 3.28 }, { "text": "and putting it into its place.", "start": 2334.03, "duration": 1.51 }, { "text": "So for i from 0 to n\nminus 1, we're going", "start": 2335.54, "duration": 2.77 }, { "text": "to do this from beginning\nthrough the end,", "start": 2338.31, "duration": 2.13 }, { "text": "find the smallest element between\ni-th and n-th minus 1 element.", "start": 2340.44, "duration": 4.69 }, { "text": "Swap the smallest with\nthat i-th element.", "start": 2345.13, "duration": 3.68 }, { "text": "In other words, walk through the list.", "start": 2348.81, "duration": 1.78 }, { "text": "Find the smallest, put it on the end.", "start": 2350.59, "duration": 1.62 }, { "text": "Walk through the list, swap\nit with the second to the end.", "start": 2352.21, "duration": 3.58 }, { "text": "Walk through the list, do the\nsame, do the same, do the same,", "start": 2355.79, "duration": 2.74 }, { "text": "each time grabbing the\nthen smallest element.", "start": 2358.53, "duration": 2.87 }, { "text": "And then lastly, we had insertion sort,\nwhereby we iterated through the list,", "start": 2361.4, "duration": 5.0 }, { "text": "but we pretty much dealt with\nevery element as we encountered it.", "start": 2366.4, "duration": 3.057 }, { "text": "So let me propose this\npseudocode code here.", "start": 2369.457, "duration": 1.833 }, { "text": "For i from 1 to n minus 1.", "start": 2371.29, "duration": 3.087 }, { "text": "So let's just assume that the\nvery beginning of the list", "start": 2374.377, "duration": 2.333 }, { "text": "is sort of trivially sorted, no\nmatter what number he or she is.", "start": 2376.71, "duration": 3.35 }, { "text": "Because if that left side of the list\nis of size 1, it is, indeed, sorted.", "start": 2380.06, "duration": 4.09 }, { "text": "And indeed, let's call the 0-th element\nthrough the i minus [? 1-th ?] element,", "start": 2384.15, "duration": 4.57 }, { "text": "wherever we are, the sorted side.", "start": 2388.72, "duration": 2.26 }, { "text": "So essentially, call the\nleft the sorted side.", "start": 2390.98, "duration": 1.93 }, { "text": "And you can think of the right-hand\nside as the unsorted side.", "start": 2392.91, "duration": 2.75 }, { "text": "Remove the i-th element, whatever\nelement you're dealing with,", "start": 2395.66, "duration": 3.53 }, { "text": "and insert it into the\nsorted side in order.", "start": 2399.19, "duration": 3.56 }, { "text": "In other words, just walk\nthrough the list, one at a time,", "start": 2402.75, "duration": 2.79 }, { "text": "plucking out elements, and\nthen forcibly insert them", "start": 2405.54, "duration": 2.78 }, { "text": "into the sorted side of\nthe list, making room,", "start": 2408.32, "duration": 2.65 }, { "text": "as our humans did, for that\nlist by shuffling everyone over.", "start": 2410.97, "duration": 4.21 }, { "text": "This then was bubble sort,\nselection sort, and insertion sort.", "start": 2415.18, "duration": 5.12 }, { "text": "But which to choose?", "start": 2420.3, "duration": 1.86 }, { "text": "So let's introduce now an answer to why.", "start": 2422.16, "duration": 2.929 }, { "text": "Not just what these things are, but\nwhy you might use one over the other.", "start": 2425.089, "duration": 3.041 }, { "text": "So the running time\nof an algorithm might", "start": 2428.13, "duration": 2.22 }, { "text": "be the number of seconds\nan algorithm takes to run,", "start": 2430.35, "duration": 2.26 }, { "text": "or the number of minutes, or the number\nof steps, or the number of comparisons.", "start": 2432.61, "duration": 3.06 }, { "text": "It doesn't really matter\nwhat your unit of measure", "start": 2435.67, "duration": 1.78 }, { "text": "is, so long as you're consistent,\nwhatever feels the most", "start": 2437.45, "duration": 2.374 }, { "text": "expensive or useful to express.", "start": 2439.824, "duration": 2.346 }, { "text": "So let's consider an\nexample, like bubble sort.", "start": 2442.17, "duration": 2.62 }, { "text": "If we want to consider the\nefficiency of bubble sort", "start": 2444.79, "duration": 3.432 }, { "text": "and make a claim as to\nwhether we should or shouldn't", "start": 2448.222, "duration": 2.208 }, { "text": "use it because it's good or bad, let's\nconsider it a little formulaically.", "start": 2450.43, "duration": 3.56 }, { "text": "So a little mathy, but\npretty generically.", "start": 2453.99, "duration": 2.37 }, { "text": "So if there are n elements to\nstore, and a computer scientist,", "start": 2456.36, "duration": 3.72 }, { "text": "recall from week 0, will generally just\ncall n the size of his or her problem.", "start": 2460.08, "duration": 3.78 }, { "text": "n is the number of numbers\nto sort, or humans to sort.", "start": 2463.86, "duration": 3.52 }, { "text": "How many steps is it going to\ntake to sort that many people?", "start": 2467.38, "duration": 4.81 }, { "text": "Well, when I had 8 music stands\nand 8 people here before,", "start": 2472.19, "duration": 3.63 }, { "text": "I considered a pair, a pair,\na pair, a pair, a pair.", "start": 2475.82, "duration": 4.737 }, { "text": "And so if there were n humans up here.", "start": 2480.557, "duration": 1.583 }, { "text": "Or let's speak concretely,\n8 people initially.", "start": 2482.14, "duration": 2.53 }, { "text": "How many pairs of people did\nI consider in my first pass?", "start": 2484.67, "duration": 4.321 }, { "text": "Say again.", "start": 2488.991, "duration": 0.499 }, { "text": "AUDIENCE: 7.", "start": 2489.49, "duration": 0.499 }, { "text": "SPEAKER 1: 7.", "start": 2489.989, "duration": 0.921 }, { "text": "Because if you pair the\nfirst and the second,", "start": 2490.91, "duration": 2.019 }, { "text": "then the second and the third,\nthen the third and the fourth,", "start": 2492.929, "duration": 2.541 }, { "text": "that gives you n minus\n1 generally speaking.", "start": 2495.47, "duration": 2.13 }, { "text": "You can't make 8 pairs out of 8 people.", "start": 2497.6, "duration": 1.65 }, { "text": "You can make 7 pairs if you\nkeep walking through the list.", "start": 2499.25, "duration": 2.542 }, { "text": "We're not doing permutations.", "start": 2501.792, "duration": 1.208 }, { "text": "We're just doing adjacent neighbors.", "start": 2503.0, "duration": 2.25 }, { "text": "OK.", "start": 2505.25, "duration": 0.5 }, { "text": "So that might generically\nbe n minus 1 total steps", "start": 2505.75, "duration": 3.3 }, { "text": "for the first pass of my algorithm.", "start": 2509.05, "duration": 1.72 }, { "text": "But the upside of that was that\nour eighth volunteer, number 8,", "start": 2510.77, "duration": 3.39 }, { "text": "bubbled his way all\nthe way up to the end.", "start": 2514.16, "duration": 2.95 }, { "text": "And so with bubble sort, I didn't\nneed to consider him again.", "start": 2517.11, "duration": 3.01 }, { "text": "The biggest number\nbubbled all the way up.", "start": 2520.12, "duration": 2.3 }, { "text": "And so that was done.", "start": 2522.42, "duration": 1.14 }, { "text": "So how many pairs did I need to consider\nthe second time through bubble sort?", "start": 2523.56, "duration": 6.03 }, { "text": "6.", "start": 2529.59, "duration": 0.5 }, { "text": "Or more generically, n minus 2.", "start": 2530.09, "duration": 3.68 }, { "text": "And then dot, dot, dot, until there\nwas just one pair of two people left.", "start": 2533.77, "duration": 4.41 }, { "text": "So I'll just do plus\ndot, dot, dot plus 1.", "start": 2538.18, "duration": 2.727 }, { "text": "Now, you might recall from\nhigh school especially,", "start": 2540.907, "duration": 2.083 }, { "text": "at least my math or\nphysics textbooks always", "start": 2542.99, "duration": 1.833 }, { "text": "had a little cheat sheet for like what\nthese kinds of recurrences or formulas", "start": 2544.823, "duration": 3.277 }, { "text": "add up to.", "start": 2548.1, "duration": 0.5 }, { "text": "Does anyone recall what this\none adds up to in a math book?", "start": 2548.6, "duration": 3.96 }, { "text": "Or just mathematically?", "start": 2552.56, "duration": 3.27 }, { "text": "So if we actually do this out,\nit's the same thing, beautifully,", "start": 2555.83, "duration": 3.57 }, { "text": "as n times n minus 1 over 2.", "start": 2559.4, "duration": 3.25 }, { "text": "And that, of course if\nyou multiply things out,", "start": 2562.65, "duration": 3.63 }, { "text": "is just the same thing as\nn squared minus n over 2.", "start": 2566.28, "duration": 3.26 }, { "text": "And that, of course, feels like it\nwould just multiply out to this.", "start": 2569.54, "duration": 6.35 }, { "text": "So in other words, if asked, what\nis the efficiency of bubble sort,", "start": 2575.89, "duration": 2.97 }, { "text": "or what is the running time of\nbubble sort to soar n elements,", "start": 2578.86, "duration": 3.47 }, { "text": "you might sort of\nimpressively say, well, it's", "start": 2582.33, "duration": 1.94 }, { "text": "n squared divided by 2 minus n over 2.", "start": 2584.27, "duration": 2.37 }, { "text": "But what does that actually mean?", "start": 2586.64, "duration": 1.51 }, { "text": "Well, it turns out that when talking\nabout the efficiency of algorithms,", "start": 2588.15, "duration": 3.42 }, { "text": "you should really generally\ncare about the component that", "start": 2591.57, "duration": 3.4 }, { "text": "has the biggest order of magnitude.", "start": 2594.97, "duration": 2.07 }, { "text": "The number that contributes\nthe most to the total cost.", "start": 2597.04, "duration": 2.94 }, { "text": "And by that I mean this, which is\nobviously bigger, n squared or n?", "start": 2599.98, "duration": 4.04 }, { "text": "Assuming positive values of n.", "start": 2604.02, "duration": 1.68 }, { "text": "So n squared, right?", "start": 2605.7, "duration": 1.13 }, { "text": "Especially as n gets bigger, n squared\nis going to get even bigger than n.", "start": 2606.83, "duration": 3.692 }, { "text": "So you know what?", "start": 2610.522, "duration": 0.708 }, { "text": "I'm just going to kind of propose,\nlet's just ignore the n minus 2", "start": 2611.23, "duration": 3.77 }, { "text": "because as n gets really big,\nthe dominating factor really", "start": 2615.0, "duration": 2.69 }, { "text": "is going to be n square.", "start": 2617.69, "duration": 1.24 }, { "text": "And for that matter, the n over 2,\nlike who cares about the over 2?", "start": 2618.93, "duration": 2.82 }, { "text": "n squared is kind of the essence\nof this formula right now.", "start": 2621.75, "duration": 3.672 }, { "text": "So what does that mean?", "start": 2625.422, "duration": 0.958 }, { "text": "Well, let's just do a concrete\nexample to convince you of the fact", "start": 2626.38, "duration": 2.749 }, { "text": "that we can cut a little bit\nof mathematical corner here", "start": 2629.129, "duration": 2.911 }, { "text": "and only care about the big\nnumber for the following example.", "start": 2632.04, "duration": 2.792 }, { "text": "This is proof by example, which\nis not a proof of anything.", "start": 2634.832, "duration": 2.458 }, { "text": "It's just really to paint a picture\nof why we do this intuitively.", "start": 2637.29, "duration": 4.03 }, { "text": "So suppose that there are a million\nvolunteers on stage or a million", "start": 2641.32, "duration": 2.892 }, { "text": "numbers that we want to sort.", "start": 2644.212, "duration": 1.208 }, { "text": "Much bigger than 8.", "start": 2645.42, "duration": 1.55 }, { "text": "Let's plug this in.", "start": 2646.97, "duration": 1.15 }, { "text": "So if the total cost of bubble sort\nis n squared over 2 minus n over 2,", "start": 2648.12, "duration": 3.83 }, { "text": "let's plug that in.", "start": 2651.95, "duration": 0.85 }, { "text": "So that's a million squared divided\nby 2 minus a million divided by 2.", "start": 2652.8, "duration": 4.75 }, { "text": "So if we multiply that out, that\nis 500 billion minus 500,000.", "start": 2657.55, "duration": 5.39 }, { "text": "Big numbers.", "start": 2662.94, "duration": 0.86 }, { "text": "But when you multiply that out,\nI mean-- my god, 499,999,500,000.", "start": 2663.8, "duration": 5.25 }, { "text": "I mean, to my own eyes, that's\npretty darn close to 500 billion", "start": 2669.05, "duration": 5.24 }, { "text": "in the first place.", "start": 2674.29, "duration": 0.797 }, { "text": "Why don't we just call it 500 billion?", "start": 2675.087, "duration": 1.583 }, { "text": "So n squared, in other words.", "start": 2676.67, "duration": 1.489 }, { "text": "So again, this is not a\nformal proof of anything.", "start": 2678.159, "duration": 2.041 }, { "text": "But this is why, especially\nas n gets bigger,", "start": 2680.2, "duration": 2.25 }, { "text": "that lower-ordered term,\nthe minus n over 2,", "start": 2682.45, "duration": 2.53 }, { "text": "just matters less and less\nand less in absolute form.", "start": 2684.98, "duration": 3.37 }, { "text": "And so we'll generally say that\nsomething like bubble sort,", "start": 2688.35, "duration": 2.98 }, { "text": "its running time is on\nthe order of n squared.", "start": 2691.33, "duration": 3.6 }, { "text": "Big O is actually formal computer\nscience notation for on the order of.", "start": 2694.93, "duration": 4.097 }, { "text": "And it has a formal\nmathematical definition.", "start": 2699.027, "duration": 1.833 }, { "text": "But for us, we'll consider it really\nto be an upper bound on the running", "start": 2700.86, "duration": 5.57 }, { "text": "time of this algorithm.", "start": 2706.43, "duration": 1.38 }, { "text": "So an upper bound on how long this\nalgorithm might take given n steps.", "start": 2707.81, "duration": 4.29 }, { "text": "So big O itself is a formal notation.", "start": 2712.1, "duration": 2.14 }, { "text": "We'll see it in a number\nof different contexts.", "start": 2714.24, "duration": 2.04 }, { "text": "Depending on the algorithms\nwe talk about in class,", "start": 2716.28, "duration": 2.31 }, { "text": "we might say that the\nrunning time of an algorithm", "start": 2718.59, "duration": 2.083 }, { "text": "is on the order of n\nsquared, which is pretty bad.", "start": 2720.673, "duration": 2.687 }, { "text": "Pretty slow. $500 billion\nsounds like a lot.", "start": 2723.36, "duration": 2.21 }, { "text": "Well, maybe it's a little better\non the order of n times log n.", "start": 2725.57, "duration": 2.625 }, { "text": "And more on that some\nother time-- later.", "start": 2728.195, "duration": 2.955 }, { "text": "But on the order of\nn, it was pretty good.", "start": 2731.15, "duration": 2.5 }, { "text": "If there's n elements, it only\ntakes you roughly n steps.", "start": 2733.65, "duration": 2.54 }, { "text": "Maybe it's even better big O of log n.", "start": 2736.19, "duration": 2.88 }, { "text": "Or really best would be big O of 1.", "start": 2739.07, "duration": 2.565 }, { "text": "It just takes 1 step, or\n10 steps, or 100 steps,", "start": 2741.635, "duration": 2.595 }, { "text": "but a constant number of steps\nis what big O of 1 represents.", "start": 2744.23, "duration": 4.05 }, { "text": "And there's any number\nof other formulas we", "start": 2748.28, "duration": 2.2 }, { "text": "could use or equations to express\nthe running time of algorithms.", "start": 2750.48, "duration": 3.89 }, { "text": "But many of the algorithms\nwe'll look at in CS50 certainly", "start": 2754.37, "duration": 2.47 }, { "text": "fall into these categories.", "start": 2756.84, "duration": 1.67 }, { "text": "So let's take an example.", "start": 2758.51, "duration": 2.89 }, { "text": "What algorithm has the running\ntime of big O of n squared?", "start": 2761.4, "duration": 2.73 }, { "text": "Well, bubble sort for one thing.", "start": 2764.13, "duration": 3.02 }, { "text": "And it turns out selection sort.", "start": 2767.15, "duration": 2.12 }, { "text": "And it turns out insertion sort.", "start": 2769.27, "duration": 2.84 }, { "text": "All three of those algorithms\nactually have the same running time,", "start": 2772.11, "duration": 3.81 }, { "text": "even though they're fundamentally\ndifferent in execution.", "start": 2775.92, "duration": 3.44 }, { "text": "But they do share a commonality.", "start": 2779.36, "duration": 2.01 }, { "text": "All of them are comparison-based.", "start": 2781.37, "duration": 2.72 }, { "text": "In each case did we\nactually compare values,", "start": 2784.09, "duration": 2.31 }, { "text": "either adjacent or we would look at a\nnumber there, compare it to a number", "start": 2786.4, "duration": 3.33 }, { "text": "here, and then decide whether\nor not to do a switch.", "start": 2789.73, "duration": 2.234 }, { "text": "So they were all comparison-based.", "start": 2791.964, "duration": 1.416 }, { "text": "And all of them, frankly, involved\nquite a bit of movement or walking,", "start": 2793.38, "duration": 3.24 }, { "text": "either on my part or the\nhumans-- volunteers part.", "start": 2796.62, "duration": 2.48 }, { "text": "For instance, in bubble\nsort's case, I had", "start": 2799.1, "duration": 2.64 }, { "text": "to walk through the whole list,\nsorting elements pairwise like this.", "start": 2801.74, "duration": 3.425 }, { "text": "But that wasn't enough.", "start": 2805.165, "duration": 1.575 }, { "text": "I then had to do it again\nand walk across the stage.", "start": 2806.74, "duration": 4.14 }, { "text": "And then I had to do it again\nand walk across the stage.", "start": 2810.88, "duration": 2.78 }, { "text": "And this is what n squared feels like.", "start": 2813.66, "duration": 1.627 }, { "text": "And even though the problem\nwas getting a little smaller", "start": 2815.287, "duration": 2.333 }, { "text": "as the big elements bubbled up,\nmathematically, even that algorithm,", "start": 2817.62, "duration": 4.32 }, { "text": "it's kind of essentially like doing\nn things, looking at n people,", "start": 2821.94, "duration": 3.76 }, { "text": "n times, iterating n total times, which\nis roughly n times n, or n squared.", "start": 2825.7, "duration": 4.517 }, { "text": "It's just going to add up a lot.", "start": 2830.217, "duration": 1.333 }, { "text": "So what about selection sort?", "start": 2831.55, "duration": 1.61 }, { "text": "What did I do in selection sort's case?", "start": 2833.16, "duration": 1.65 }, { "text": "Here, it's even more obvious, perhaps.", "start": 2834.81, "duration": 1.8 }, { "text": "To find the smallest\nelement in a list, I", "start": 2836.61, "duration": 2.2 }, { "text": "have to look logically at every element\nbefore I can confidently conclude,", "start": 2838.81, "duration": 5.105 }, { "text": "yes, I have found the smallest element.", "start": 2843.915, "duration": 1.625 }, { "text": "Once you find it, you can\nplop it at the beginning.", "start": 2845.54, "duration": 2.125 }, { "text": "And that's easy.", "start": 2847.665, "duration": 0.785 }, { "text": "But then you have to find\nthe second smallest element.", "start": 2848.45, "duration": 1.95 }, { "text": "And even though we humans could\nkind of eyeball things and realize,", "start": 2850.4, "duration": 2.791 }, { "text": "oh, 2 is the next smallest.", "start": 2853.191, "duration": 1.249 }, { "text": "You don't know that as the computer\nunless you look at every element.", "start": 2854.44, "duration": 2.91 }, { "text": "Ah, I found 2.", "start": 2857.35, "duration": 1.49 }, { "text": "And then you could put\n2 where it belongs.", "start": 2858.84, "duration": 1.75 }, { "text": "So again, there's this\nwalking back and forth.", "start": 2860.59, "duration": 2.18 }, { "text": "And if you're going to walk as many as\nn steps and have to do this n times--", "start": 2862.77, "duration": 3.9 }, { "text": "one for every element--\nthat, too, is n times n.", "start": 2866.67, "duration": 2.13 }, { "text": "And insertion sort, same damn\nproblem, even though it's", "start": 2868.8, "duration": 2.9 }, { "text": "sort of logically\ndifferent, the algorithm.", "start": 2871.7, "duration": 1.91 }, { "text": "Insertion sort, beautifully I\nonly move one step at a time", "start": 2873.61, "duration": 4.51 }, { "text": "and I never turn back.", "start": 2878.12, "duration": 1.14 }, { "text": "Because I just deal with, as you did\nfor the blue books, each problem one", "start": 2879.26, "duration": 5.24 }, { "text": "at a time, never again backtracking.", "start": 2884.5, "duration": 2.36 }, { "text": "But where was all the work happening?", "start": 2886.86, "duration": 3.34 }, { "text": "In the shifting of humans.", "start": 2890.2, "duration": 1.44 }, { "text": "Now, technically you guys helped out\nby doing the shifting yourselves.", "start": 2891.64, "duration": 2.92 }, { "text": "But if I'm the computer,\nit actually would", "start": 2894.56, "duration": 1.749 }, { "text": "have been like me tiptoeing back,\nshifting, shifting, shifting,", "start": 2896.309, "duration": 3.391 }, { "text": "inserting, shifting, shifting, shifting.", "start": 2899.7, "duration": 2.18 }, { "text": "So again, in the worst\ncase, I might have", "start": 2901.88, "duration": 1.71 }, { "text": "had to shift everyone all the way\nover to make room for someone.", "start": 2903.59, "duration": 3.94 }, { "text": "Because in the worst case,\nwhat's the worst possible input", "start": 2907.53, "duration": 2.55 }, { "text": "you might get to a sorting algorithm?", "start": 2910.08, "duration": 3.4 }, { "text": "What input would create\nthe most work for you?", "start": 2913.48, "duration": 3.805 }, { "text": "AUDIENCE: Backwards.", "start": 2917.285, "duration": 0.86 }, { "text": "SPEAKER 1: Backwards.", "start": 2918.145, "duration": 0.875 }, { "text": "If the list is perfectly\nbackwards, every darn element", "start": 2919.02, "duration": 2.69 }, { "text": "is out of place, which means you\nhave to traipse back and forth", "start": 2921.71, "duration": 3.14 }, { "text": "and back and forth to insert or to\nselect or to swap all of those elements", "start": 2924.85, "duration": 5.85 }, { "text": "that many times.", "start": 2930.7, "duration": 1.1 }, { "text": "So in all of these cases, they\nare not numerically identical.", "start": 2931.8, "duration": 3.53 }, { "text": "Some of those algorithms might take\nfewer steps than others in totality,", "start": 2935.33, "duration": 3.97 }, { "text": "but they're all on the order\nof n squared for the reason", "start": 2939.3, "duration": 2.86 }, { "text": "that they're all involving comparisons\nas many as n times n times.", "start": 2942.16, "duration": 4.79 }, { "text": "All right.", "start": 2946.95, "duration": 0.68 }, { "text": "What about an algorithm\nthat's big O of n?", "start": 2947.63, "duration": 3.2 }, { "text": "An algorithm that only takes n steps?", "start": 2950.83, "duration": 3.65 }, { "text": "We've seen one.", "start": 2954.48, "duration": 0.878 }, { "text": "Derek showed us one.", "start": 2958.05, "duration": 1.26 }, { "text": "What's an algorithm that takes n steps?", "start": 2962.45, "duration": 1.68 }, { "text": "Derek, hopefully.", "start": 2964.13, "duration": 1.094 }, { "text": "AUDIENCE: [INAUDIBLE].", "start": 2965.224, "duration": 0.916 }, { "text": "SPEAKER 1: A random search?", "start": 2966.14, "duration": 1.49 }, { "text": "Kind of, sort of.", "start": 2967.63, "duration": 1.07 }, { "text": "It's a little harder to\nput a number to because it", "start": 2968.7, "duration": 3.244 }, { "text": "depends what you mean by \"random.\"", "start": 2971.944, "duration": 1.416 }, { "text": "Because if you have random\nwith repetition such", "start": 2973.36, "duration": 2.11 }, { "text": "that you're checking foolishly\nthe same elements again and again,", "start": 2975.47, "duration": 2.877 }, { "text": "it can actually add up\nto more than n steps.", "start": 2978.347, "duration": 1.833 }, { "text": "So not random, but-- yeah.", "start": 2980.18, "duration": 2.805 }, { "text": "AUDIENCE: Binary.", "start": 2982.985, "duration": 0.8 }, { "text": "SPEAKER 1: Binary is even better.", "start": 2983.785, "duration": 1.375 }, { "text": "Hold that answer.", "start": 2985.16, "duration": 0.708 }, { "text": "You're about to be correct.", "start": 2985.868, "duration": 2.012 }, { "text": "Linear search, right?", "start": 2987.88, "duration": 1.0 }, { "text": "If you just blindly\ngo from left to right", "start": 2988.88, "duration": 1.88 }, { "text": "or right to left looking\nfor some element,", "start": 2990.76, "duration": 1.81 }, { "text": "that is on the order of n steps.", "start": 2992.57, "duration": 1.49 }, { "text": "Because you are just doing\nfoolishly unnecessary", "start": 2994.06, "duration": 2.61 }, { "text": "work if you go beyond\nthe end of the list", "start": 2996.67, "duration": 2.2 }, { "text": "or beyond the beginning of the list.", "start": 2998.87, "duration": 1.5 }, { "text": "You only need n steps for linear search.", "start": 3000.37, "duration": 2.07 }, { "text": "But what if you want to instead find\nan algorithm that's logarithmic?", "start": 3002.44, "duration": 4.72 }, { "text": "What algorithm that we used\nmight be logarithmic in nature?", "start": 3007.16, "duration": 5.03 }, { "text": "Binary.", "start": 3012.19, "duration": 0.62 }, { "text": "So binary search, as Derek proposed,\nonce we knew the list was sorted", "start": 3012.81, "duration": 4.54 }, { "text": "was an alternative to that.", "start": 3017.35, "duration": 2.32 }, { "text": "And constant time.", "start": 3019.67, "duration": 0.94 }, { "text": "What about this?", "start": 3020.61, "duration": 2.46 }, { "text": "What's an algorithm, maybe\nindependent of today,", "start": 3023.07, "duration": 2.0 }, { "text": "that allows you constant\ntime, running time?", "start": 3025.07, "duration": 2.63 }, { "text": "It could be anything.", "start": 3034.986, "duration": 0.874 }, { "text": "How about hello world?", "start": 3035.86, "duration": 2.79 }, { "text": "The [? say ?] block,\nor printf like that.", "start": 3038.65, "duration": 1.95 }, { "text": "If you can just say a\nwhole phrase at once.", "start": 3040.6, "duration": 2.15 }, { "text": "Or maybe just adding two numbers\ntogether is like one step.", "start": 3042.75, "duration": 3.57 }, { "text": "No matter how big the numbers\nare, it still just takes one step", "start": 3046.32, "duration": 2.674 }, { "text": "to add them all together.", "start": 3048.994, "duration": 1.041 }, { "text": "It depends on some of the\nlower-level implementation details.", "start": 3050.035, "duration": 2.365 }, { "text": "And even printf or the [? say ?]\nblock has multiple characters.", "start": 3052.4, "duration": 2.56 }, { "text": "So we'll actually come\nback to this in the future", "start": 3054.96, "duration": 2.041 }, { "text": "as to what it really means to be a step.", "start": 3057.001, "duration": 1.819 }, { "text": "But anything that takes a\nconstant number of steps.", "start": 3058.82, "duration": 2.95 }, { "text": "Checking an \"if\" condition,\nreturning a value.", "start": 3061.77, "duration": 2.4 }, { "text": "Statements, generally, might be\nbroadly speaking just constant time,", "start": 3064.17, "duration": 3.24 }, { "text": "but we'll see contradictions\nto that before long.", "start": 3067.41, "duration": 2.82 }, { "text": "So let's take a look\nat two other symbols.", "start": 3070.23, "duration": 2.02 }, { "text": "This one being a capital omega symbol.", "start": 3072.25, "duration": 2.56 }, { "text": "And this omega symbol is the\nopposite, really, of big O. Big O", "start": 3074.81, "duration": 3.64 }, { "text": "is an upper bound on the running time.", "start": 3078.45, "duration": 1.61 }, { "text": "In the worst case, how\nmany steps might it", "start": 3080.06, "duration": 1.75 }, { "text": "take to find an element\nin a list of n elements?", "start": 3081.81, "duration": 2.97 }, { "text": "n steps.", "start": 3084.78, "duration": 1.05 }, { "text": "So big O of n.", "start": 3085.83, "duration": 1.137 }, { "text": "Bubble sort, selection\nsort, insertion sort?", "start": 3086.967, "duration": 1.833 }, { "text": "They're on the order of n squared.", "start": 3088.8, "duration": 1.69 }, { "text": "But what about the lower bound?", "start": 3090.49, "duration": 1.78 }, { "text": "Especially when you get lucky\nin the best case so to speak,", "start": 3092.27, "duration": 2.9 }, { "text": "how few steps might you\nsolve problems with?", "start": 3095.17, "duration": 2.58 }, { "text": "So for instance, if we\nconsider the same formulas,", "start": 3097.75, "duration": 2.78 }, { "text": "but this time with capital\nomega, what's an algorithm", "start": 3100.53, "duration": 3.22 }, { "text": "that no matter what\ntakes n squared steps,", "start": 3103.75, "duration": 3.58 }, { "text": "even if, for instance,\nthe list is sorted?", "start": 3107.33, "duration": 3.88 }, { "text": "So suppose our 8 volunteers here\nwere already 1, 2, 3, 4, 5, 6, 7, 8.", "start": 3111.21, "duration": 4.58 }, { "text": "Which of those algorithms would\nstill have required n squared steps?", "start": 3115.79, "duration": 3.79 }, { "text": "So not linear search or binary\nsearch because those are much lower.", "start": 3125.52, "duration": 3.25 }, { "text": "But insertion, bubble\nsort, selection sort.", "start": 3128.77, "duration": 4.55 }, { "text": "Well, what about selection sort?", "start": 3133.32, "duration": 1.66 }, { "text": "Even if the list is already sorted,\nhow do I find the smallest element?", "start": 3134.98, "duration": 3.71 }, { "text": "I'm lucky and it's right here,\nbut I don't know that yet, right?", "start": 3138.69, "duration": 3.62 }, { "text": "To know that, I have to confidently\nwalk the whole list and realize,", "start": 3142.31, "duration": 3.209 }, { "text": "well, that was a waste of time.", "start": 3145.519, "duration": 1.291 }, { "text": "1 is indeed the smallest element.", "start": 3146.81, "duration": 1.54 }, { "text": "It's sorted.", "start": 3148.35, "duration": 0.93 }, { "text": "How do I find the next smallest element?", "start": 3149.28, "duration": 3.09 }, { "text": "Start at the left.", "start": 3152.37, "duration": 0.844 }, { "text": "But you can ignore number 1.", "start": 3153.214, "duration": 1.166 }, { "text": "So it's a minor savings.", "start": 3154.38, "duration": 1.39 }, { "text": "OK, 2.", "start": 3155.77, "duration": 0.77 }, { "text": "Feel's pretty small, but got to check.", "start": 3156.54, "duration": 3.16 }, { "text": "Dammit, that was the smallest.", "start": 3159.7, "duration": 1.65 }, { "text": "And so selection sort, even in the best\ncase when the list is already sorted,", "start": 3161.35, "duration": 5.72 }, { "text": "is going to take at least\non the order of n squared", "start": 3167.07, "duration": 4.09 }, { "text": "steps because of that naivete of it.", "start": 3171.16, "duration": 2.09 }, { "text": "Because of that underlying\ndesign of just looking", "start": 3173.25, "duration": 2.23 }, { "text": "for the smallest element\nwith no optimizations means", "start": 3175.48, "duration": 2.77 }, { "text": "the algorithm's always going\nto take us that many steps.", "start": 3178.25, "duration": 2.34 }, { "text": "But it doesn't have to be that way.", "start": 3180.59, "duration": 1.458 }, { "text": "What about bubble sort?", "start": 3182.048, "duration": 1.052 }, { "text": "Suppose that all 8 humans are\nsorted, 1 all the way through 8.", "start": 3183.1, "duration": 3.52 }, { "text": "And here I am comparing the first two.", "start": 3186.62, "duration": 1.77 }, { "text": "1 and 2?", "start": 3188.39, "duration": 0.76 }, { "text": "Not out of order.", "start": 3189.15, "duration": 1.13 }, { "text": "2 and 3, 3 and 4, 4 and 5,\n5 and 6, 6 and 7, 7 and 8.", "start": 3190.28, "duration": 5.04 }, { "text": "OK, everything looks good.", "start": 3195.32, "duration": 1.43 }, { "text": "And in particular, what did I not\ndo while walking from left to right?", "start": 3196.75, "duration": 5.714 }, { "text": "I didn't do any swaps.", "start": 3202.464, "duration": 0.916 }, { "text": "So it would be foolish of me\nalgorithmically to do any of that", "start": 3203.38, "duration": 3.03 }, { "text": "again because the answer\nis not going to change.", "start": 3206.41, "duration": 2.27 }, { "text": "And so done.", "start": 3208.68, "duration": 0.63 }, { "text": "It took me n steps to sort\nn elements with bubble sort", "start": 3209.31, "duration": 3.69 }, { "text": "if the list is already sorted.", "start": 3213.0, "duration": 2.08 }, { "text": "So it would be omega of n because in\nthe best case, it takes you n steps.", "start": 3215.08, "duration": 4.33 }, { "text": "Could a sorting algorithm\nbe constant time", "start": 3219.41, "duration": 3.58 }, { "text": "or logarithmic, log n or order of 1?", "start": 3222.99, "duration": 3.74 }, { "text": "Or omega of 1 rather?", "start": 3226.73, "duration": 3.32 }, { "text": "Can you sort n elements in\nlogarithmic time or constant time?", "start": 3230.05, "duration": 5.494 }, { "text": "What's the intuition there?", "start": 3239.26, "duration": 1.36 }, { "text": "These are kind of like now the\nfundamental meaning of computing", "start": 3240.62, "duration": 3.36 }, { "text": "and what you can actually do.", "start": 3243.98, "duration": 1.63 }, { "text": "What does it mean for me to\nask, can you sort n elements", "start": 3245.61, "duration": 3.08 }, { "text": "in log n time or constant time?", "start": 3248.69, "duration": 2.37 }, { "text": "Well, that effectively\nis like saying, can you", "start": 3251.06, "duration": 2.76 }, { "text": "sort n elements without even\nlooking at some of those elements?", "start": 3253.82, "duration": 4.81 }, { "text": "Because both log n and\n1-- or mathematically,", "start": 3258.63, "duration": 3.14 }, { "text": "and if you don't recall, take it on\nfaith today-- less than omega of n", "start": 3261.77, "duration": 4.19 }, { "text": "in general.", "start": 3265.96, "duration": 1.27 }, { "text": "So can you possibly,\nintuitively, in the real world,", "start": 3267.23, "duration": 3.29 }, { "text": "sort n elements in some random\norder in fewer than n steps?", "start": 3270.52, "duration": 6.17 }, { "text": "Yeah.", "start": 3276.69, "duration": 1.098 }, { "text": "AUDIENCE: [INAUDIBLE].", "start": 3277.788, "duration": 0.916 }, { "text": "SPEAKER 1: Good question.", "start": 3283.779, "duration": 1.041 }, { "text": "Could you make the whole\nlist a big integer?", "start": 3284.82, "duration": 1.86 }, { "text": "You could, that and other tricks.", "start": 3286.68, "duration": 1.73 }, { "text": "But to do that, you're going to\nneed to touch or somehow manipulate", "start": 3288.41, "duration": 4.28 }, { "text": "all of those values at least once\nto kind of do that, I would think.", "start": 3292.69, "duration": 3.83 }, { "text": "And so you've already spent n steps.", "start": 3296.52, "duration": 2.824 }, { "text": "AUDIENCE: [INAUDIBLE].", "start": 3299.344, "duration": 0.916 }, { "text": "SPEAKER 1: OK.", "start": 3303.197, "duration": 0.583 }, { "text": "So if you have a like guessing\nalgorithm-- yes, this is sorted.", "start": 3303.78, "duration": 4.4 }, { "text": "That's constant time.", "start": 3308.18, "duration": 1.009 }, { "text": "You're just not always correct.", "start": 3309.189, "duration": 1.291 }, { "text": "So I should clarify, can you\nsort correctly n elements", "start": 3310.48, "duration": 3.86 }, { "text": "without necessarily looking at\nall n-- the short answer is no.", "start": 3314.34, "duration": 3.24 }, { "text": "There is like a fundamental\nlimit of computation.", "start": 3317.58, "duration": 2.3 }, { "text": "And also, just human intuition here.", "start": 3319.88, "duration": 1.89 }, { "text": "You can't possibly claim to me and\nconvince me, in a court of law even,", "start": 3321.77, "duration": 4.53 }, { "text": "that these n elements are\nsorted if you can't even", "start": 3326.3, "duration": 2.48 }, { "text": "testify to having looked\nat all n of those elements.", "start": 3328.78, "duration": 2.88 }, { "text": "It's just not possible given\nthe computational model", "start": 3331.66, "duration": 2.47 }, { "text": "we've been discussing where a computer\ncan only look at one element at a time.", "start": 3334.13, "duration": 3.89 }, { "text": "So sorting is out of the question.", "start": 3338.02, "duration": 1.85 }, { "text": "But an algorithm that\ntakes omega of one step?", "start": 3339.87, "duration": 4.85 }, { "text": "For instance in the best case, when\nmight an algorithm need only one step?", "start": 3344.72, "duration": 5.64 }, { "text": "How about something like linear\nsearch or even binary search?", "start": 3350.36, "duration": 3.93 }, { "text": "The running time of those algorithms\nwas big O of n and big O of log n", "start": 3354.29, "duration": 4.98 }, { "text": "respectively.", "start": 3359.27, "duration": 0.95 }, { "text": "Linear search, binary search.", "start": 3360.22, "duration": 2.8 }, { "text": "What's the lower bound on those\ntwo algorithms' running times?", "start": 3363.02, "duration": 2.91 }, { "text": "AUDIENCE: [INAUDIBLE].", "start": 3370.407, "duration": 0.933 }, { "text": "SPEAKER 1: Yeah, it's omega of 1.", "start": 3371.34, "duration": 1.6 }, { "text": "But why?", "start": 3372.94, "duration": 1.99 }, { "text": "Derek wasn't so lucky.", "start": 3374.93, "duration": 1.08 }, { "text": "But AJ, last year, touched\nthe number 50-- voila, 1 step.", "start": 3376.01, "duration": 3.87 }, { "text": "And that was actually, while\nsort of bad pedagogy for us,", "start": 3379.88, "duration": 3.42 }, { "text": "was a perfect manifestation\nof yes, in the best", "start": 3383.3, "duration": 2.78 }, { "text": "case the lower bound on your running\ntime might indeed just be one step.", "start": 3386.08, "duration": 3.43 }, { "text": "Or two steps, but some\nconstant number of steps.", "start": 3389.51, "duration": 2.54 }, { "text": "So we have a range of these options.", "start": 3392.05, "duration": 2.05 }, { "text": "Now, sometimes these ranges coincide.", "start": 3394.1, "duration": 2.73 }, { "text": "If your big O notation, so to speak,\nand your omega notation, so to speak,", "start": 3396.83, "duration": 4.16 }, { "text": "are one in the same values, you\ncan claim that the algorithm", "start": 3400.99, "duration": 2.95 }, { "text": "has a running time in capital Theta.", "start": 3403.94, "duration": 2.77 }, { "text": "So theta just means when big\nO and omega are the same,", "start": 3406.71, "duration": 3.35 }, { "text": "you can instead use this formula and\nsort of convey two thoughts at once.", "start": 3410.06, "duration": 3.69 }, { "text": "But for now, the takeaway\nis that as best we've", "start": 3413.75, "duration": 2.48 }, { "text": "seen for something like sorting,\nthe best we've done so far, at least", "start": 3416.23, "duration": 4.64 }, { "text": "in the worst case, is\nbig O of n squared.", "start": 3420.87, "duration": 2.022 }, { "text": "And this doesn't feel very good,\nespecially since sorting and searching", "start": 3422.892, "duration": 2.958 }, { "text": "is all around us.", "start": 3425.85, "duration": 0.84 }, { "text": "Anyone with an iPhone or an Android.", "start": 3426.69, "duration": 1.714 }, { "text": "I mean, there's so much data that\nwe're carrying around in our pockets", "start": 3428.404, "duration": 2.916 }, { "text": "these days, let alone in the cloud\nand on our laptops and desktops,", "start": 3431.32, "duration": 3.08 }, { "text": "that it's just generally\ngood practice to keep sorted.", "start": 3434.4, "duration": 2.65 }, { "text": "In your phone book, it\nwould be pretty tedious", "start": 3437.05, "duration": 2.08 }, { "text": "if all of your friends and family were\nin random order in the contacts list.", "start": 3439.13, "duration": 3.77 }, { "text": "And you had to like scroll through\nthe whole darn list, big O of n,", "start": 3442.9, "duration": 3.31 }, { "text": "to find someone.", "start": 3446.21, "duration": 1.43 }, { "text": "No, instead we have a\nsearch box, of course.", "start": 3447.64, "duration": 1.952 }, { "text": "And most of us probably wouldn't\nblindly scroll through the whole list.", "start": 3449.592, "duration": 2.958 }, { "text": "But even that search box, if you start\ntyping in D-E-R to look up Derek,", "start": 3452.55, "duration": 4.36 }, { "text": "or S-M-I-T-H to find Smith.", "start": 3456.91, "duration": 2.58 }, { "text": "Well, how is iOS?", "start": 3459.49, "duration": 1.35 }, { "text": "How is Android finding Mike\nSmith or finding Derek?", "start": 3460.84, "duration": 3.54 }, { "text": "Those pieces of software themselves\nhave algorithms that underneath the hood", "start": 3464.38, "duration": 5.92 }, { "text": "are hopefully leveraging smarter\nalgorithms than we've even seen here.", "start": 3470.3, "duration": 4.277 }, { "text": "Because especially as you have more\nand more friends, more and more family", "start": 3474.577, "duration": 3.083 }, { "text": "members, even big O of n squared\nstarts to feel kind of slow", "start": 3477.66, "duration": 3.92 }, { "text": "as we can see here.", "start": 3481.58, "duration": 1.37 }, { "text": "Let me go ahead and open up an example.", "start": 3482.95, "duration": 4.384 }, { "text": "So let's take a look at a demonstration.", "start": 3487.334, "duration": 1.666 }, { "text": "Here is a visualization that someone\non the internet kindly put together.", "start": 3489.0, "duration": 3.31 }, { "text": "And it focuses on sorting numbers.", "start": 3492.31, "duration": 1.96 }, { "text": "But rather than just show the numbers\ntextually as 1, 2, 3, 4, 5, 6, 7, 8,", "start": 3494.27, "duration": 3.56 }, { "text": "it instead shows them as bar.", "start": 3497.83, "duration": 1.36 }, { "text": "So the shorter the bar,\nthe smaller the number.", "start": 3499.19, "duration": 2.05 }, { "text": "The taller the bar,\nthe taller the number.", "start": 3501.24, "duration": 1.956 }, { "text": "And let me go ahead and\nincrease the speed of this,", "start": 3503.196, "duration": 2.124 }, { "text": "just so it doesn't get too tedious.", "start": 3505.32, "duration": 1.61 }, { "text": "And let's take a quick\nlook at bubble sort.", "start": 3506.93, "duration": 3.39 }, { "text": "Now, notice what's happening.", "start": 3510.32, "duration": 1.69 }, { "text": "The two red bars adjacently\nare the ones that are", "start": 3512.01, "duration": 3.21 }, { "text": "being compared and potentially swapped.", "start": 3515.22, "duration": 1.9 }, { "text": "And you'll notice that just like in\nour human demo, what is happening over", "start": 3517.12, "duration": 3.13 }, { "text": "there on the right-hand side?", "start": 3520.25, "duration": 3.525 }, { "text": "AUDIENCE: [INAUDIBLE].", "start": 3523.775, "duration": 1.059 }, { "text": "SPEAKER 1: Yeah.", "start": 3524.834, "duration": 0.666 }, { "text": "So the biggest elements seem to be\nbubbling up, if you will, to the top.", "start": 3525.5, "duration": 4.71 }, { "text": "Even though there's still a lot of\nwork to be done to the left of those,", "start": 3530.21, "duration": 3.64 }, { "text": "we indeed have the ability here to see\nthe list getting sorted progressively.", "start": 3533.85, "duration": 7.394 }, { "text": "But you know, I'm already getting bored.", "start": 3541.244, "duration": 1.666 }, { "text": "This algorithm doesn't feel very fast.", "start": 3542.91, "duration": 1.583 }, { "text": "It's very pretty.", "start": 3544.493, "duration": 0.907 }, { "text": "It's very correct, it would\nseem, but it's a little slow.", "start": 3545.4, "duration": 3.09 }, { "text": "Let's try another one to see\nif it's any better than that.", "start": 3548.49, "duration": 3.67 }, { "text": "That's the spoiler.", "start": 3552.16, "duration": 0.84 }, { "text": "That's what it should look like.", "start": 3553.0, "duration": 1.333 }, { "text": "Let's try our friend selection\nsort, which is already sorted.", "start": 3554.333, "duration": 3.477 }, { "text": "Let me stop this.", "start": 3557.81, "duration": 2.71 }, { "text": "Let me click on Randomize Array.", "start": 3560.52, "duration": 3.86 }, { "text": "And now click Selection Sort.", "start": 3564.38, "duration": 1.7 }, { "text": "And what's happening here?", "start": 3566.08, "duration": 1.29 }, { "text": "This is like me walking across\nthe audience again and again", "start": 3567.37, "duration": 4.0 }, { "text": "and again and again.", "start": 3571.37, "duration": 1.27 }, { "text": "You don't see any of\nthis bubbling effect,", "start": 3572.64, "duration": 2.02 }, { "text": "but you do see the smallest\nelement being selected again", "start": 3574.66, "duration": 4.03 }, { "text": "and again and again.", "start": 3578.69, "duration": 1.59 }, { "text": "So we're kind of cleaning up\nthat mess one step at a time.", "start": 3580.28, "duration": 3.65 }, { "text": "It's still going to take some\nsteps, but you can perhaps", "start": 3583.93, "duration": 2.35 }, { "text": "see it a little better\nand a little faster here.", "start": 3586.28, "duration": 2.42 }, { "text": "And spoiler alert, when we skip forward\nto the end, that's what it looks like.", "start": 3588.7, "duration": 3.95 }, { "text": "If we now randomize it one last\ntime and do insertion sort,", "start": 3592.65, "duration": 4.35 }, { "text": "this one kind of feels\nand looks different.", "start": 3597.0, "duration": 3.97 }, { "text": "It's kind of mostly\nfixing things, but then it", "start": 3600.97, "duration": 2.487 }, { "text": "kind of goes in and fills in the gaps.", "start": 3603.457, "duration": 1.583 }, { "text": "Because indeed, it's moving forward\none at a time, grabbing the element,", "start": 3605.04, "duration": 3.35 }, { "text": "and then shifting the element as\nneeded to make room for whatever number", "start": 3608.39, "duration": 3.22 }, { "text": "it's encountered.", "start": 3611.61, "duration": 1.22 }, { "text": "So that's why sometimes\nit only takes a few steps", "start": 3612.83, "duration": 2.054 }, { "text": "because you find where it belongs.", "start": 3614.884, "duration": 1.416 }, { "text": "That time it took a while to\nfind the space that it belongs.", "start": 3616.3, "duration": 4.3 }, { "text": "But generally, the list is\ngetting more and more sorted.", "start": 3620.6, "duration": 2.71 }, { "text": "And once we do get to\nthe very end, this one", "start": 3623.31, "duration": 2.81 }, { "text": "we can actually feel\nbeing a little faster.", "start": 3626.12, "duration": 1.98 }, { "text": "Which isn't necessarily a testament\nto it being fundamentally better.", "start": 3628.1, "duration": 2.874 }, { "text": "All of these remain on the\norder of n squared steps.", "start": 3630.974, "duration": 3.296 }, { "text": "And now indeed, it's starting to\ndrag, kind of like our blue books.", "start": 3634.27, "duration": 2.83 }, { "text": "And now we're actually complete.", "start": 3637.1, "duration": 1.8 }, { "text": "But what if we were to\ncompare these things?", "start": 3638.9, "duration": 3.19 }, { "text": "Bubble sort on the left,\nselection sort in the middle,", "start": 3642.09, "duration": 2.63 }, { "text": "and then a third algorithm that we've\nnot seen this time called merge sort.", "start": 3644.72, "duration": 4.06 }, { "text": "So insertion sort is roughly\nthe same as all of these.", "start": 3648.78, "duration": 2.39 }, { "text": "So this visualization lets us try three.", "start": 3651.17, "duration": 2.295 }, { "text": "To start this, I have to click on them.", "start": 3653.465, "duration": 1.625 }, { "text": "So there's a little\nbit of a fudge factor", "start": 3655.09, "duration": 1.708 }, { "text": "here where I have to click on all\nthree programs quickly in succession", "start": 3656.798, "duration": 2.972 }, { "text": "to see them.", "start": 3659.77, "duration": 0.72 }, { "text": "But let's see if we can't\ndo fundamentally better.", "start": 3660.49, "duration": 3.63 }, { "text": "Merge sort is our new\nfriend on the right.", "start": 3664.12, "duration": 4.78 }, { "text": "Oh my god.", "start": 3668.9, "duration": 0.65 }, { "text": "And these are different visualizations,\nbut they're the same algorithms.", "start": 3672.97, "duration": 3.9 }, { "text": "And it's not that they're\njust poorly implemented.", "start": 3676.87, "duration": 2.14 }, { "text": "It's arguably that\nthey're poorly designed.", "start": 3679.01, "duration": 2.49 }, { "text": "They are all correct,\nbut merge sort clearly", "start": 3681.5, "duration": 3.81 }, { "text": "seems to have some upsides\nover selection sort.", "start": 3685.31, "duration": 2.307 }, { "text": "And if you'll take it on faith for\nnow, just because we can only fit three", "start": 3687.617, "duration": 3.083 }, { "text": "on the screen, insertion sort, too.", "start": 3690.7, "duration": 2.39 }, { "text": "You see the bigger elements\nbubbling up to the top.", "start": 3693.09, "duration": 2.21 }, { "text": "You see us selecting.", "start": 3695.3, "duration": 1.78 }, { "text": "Again, it turns out this person\nimplemented selection sort", "start": 3697.08, "duration": 3.285 }, { "text": "by selecting the biggest element.", "start": 3700.365, "duration": 1.375 }, { "text": "But that's fundamentally equivalent\nto selecting the smallest element.", "start": 3701.74, "duration": 2.916 }, { "text": "And that's because you can see\nthem all stacking here in this way.", "start": 3704.656, "duration": 3.594 }, { "text": "But my god, I wonder,\ncan me start this again?", "start": 3708.25, "duration": 4.26 }, { "text": "Let's try.", "start": 3712.51, "duration": 0.5 }, { "text": "Let's see if we can lap it.", "start": 3713.01, "duration": 1.11 }, { "text": "Come on.", "start": 3714.12, "duration": 0.29 }, { "text": "Come on.", "start": 3714.41, "duration": 0.5 }, { "text": "Come on.", "start": 3714.91, "duration": 0.93 }, { "text": "Come on.", "start": 3715.84, "duration": 2.27 }, { "text": "Oh, so close.", "start": 3718.11, "duration": 0.96 }, { "text": "All right.", "start": 3719.07, "duration": 0.5 }, { "text": "Had I not talked as much.", "start": 3719.57, "duration": 1.041 }, { "text": "So merge sort.", "start": 3720.611, "duration": 0.759 }, { "text": "Where is this magical algorithm?", "start": 3721.37, "duration": 2.08 }, { "text": "What are we actually doing wasting\ntime on these other things?", "start": 3723.45, "duration": 3.96 }, { "text": "Well, let's consider exactly that, but\nwe need sort of a secret ingredient.", "start": 3727.41, "duration": 3.86 }, { "text": "And let me revisit Mike\nSmith for just a moment.", "start": 3731.27, "duration": 2.292 }, { "text": "So you'll recall, this\nwas the pseudocode", "start": 3733.562, "duration": 1.708 }, { "text": "that we had from Mike Smith in week 0.", "start": 3735.27, "duration": 2.17 }, { "text": "And we decided when Mike\nis earlier in the book", "start": 3737.44, "duration": 3.98 }, { "text": "or when Mike is later in the book,\nto just go to an earlier step.", "start": 3741.42, "duration": 3.87 }, { "text": "Thereby, inducing some kind of loop.", "start": 3745.29, "duration": 2.27 }, { "text": "But suppose we changed that\nlanguage to be this instead.", "start": 3747.56, "duration": 3.18 }, { "text": "Don't go to a specific line number.", "start": 3750.74, "duration": 1.85 }, { "text": "Don't go to some earlier step.", "start": 3752.59, "duration": 2.21 }, { "text": "But just more generally,\nsay, search for Mike", "start": 3754.8, "duration": 2.46 }, { "text": "in the left half of the book or search\nfor Mike in the right half of the book.", "start": 3757.26, "duration": 3.25 }, { "text": "This is borrowing an idea that\nI proposed a moment ago when", "start": 3760.51, "duration": 3.45 }, { "text": "we were searching for something else.", "start": 3763.96, "duration": 2.28 }, { "text": "And what word did we\nascribe to this kind", "start": 3766.24, "duration": 2.14 }, { "text": "of approach of this cyclical\nuse of your own definition?", "start": 3768.38, "duration": 5.5 }, { "text": "Yeah.", "start": 3773.88, "duration": 0.69 }, { "text": "AUDIENCE: [INAUDIBLE].", "start": 3774.57, "duration": 0.38 }, { "text": "SPEAKER 1: Recursion.", "start": 3774.95, "duration": 0.99 }, { "text": "So recursion is actually\nthis secret ingredient", "start": 3775.94, "duration": 2.86 }, { "text": "that we can leverage, both\nintuitively and in code,", "start": 3778.8, "duration": 2.75 }, { "text": "to implement this new and improved\nfourth algorithm, merge sort.", "start": 3781.55, "duration": 4.27 }, { "text": "And indeed, this we'll use\ndemonstrative of a class of algorithms", "start": 3785.82, "duration": 3.117 }, { "text": "that doesn't behave in quite the\nsame way fundamentally as selection", "start": 3788.937, "duration": 2.833 }, { "text": "sort, insertion sort, and bubble sort.", "start": 3791.77, "duration": 1.583 }, { "text": "Indeed, you can do better\nthan big O of n squared.", "start": 3793.353, "duration": 2.477 }, { "text": "You can do much better, as you felt\na moment ago with visualization.", "start": 3795.83, "duration": 3.76 }, { "text": "And merge sort is one such\nalgorithm with which we can do that.", "start": 3799.59, "duration": 3.25 }, { "text": "And amazingly, the pseudocode\ncode is this simple.", "start": 3802.84, "duration": 3.16 }, { "text": "When you're given n elements, if\nn is less than 2, just return.", "start": 3806.0, "duration": 4.17 }, { "text": "If you have fewer than 2 elements, the\nlist is of size 1, which is sorted,", "start": 3810.17, "duration": 3.44 }, { "text": "or size 0, which is also\nmeaninglessly sorted.", "start": 3813.61, "duration": 2.65 }, { "text": "So you're done.", "start": 3816.26, "duration": 1.199 }, { "text": "So that's kind of a base\ncase, like a default scenario.", "start": 3817.459, "duration": 2.291 }, { "text": "Let's just make sure that no\nmatter what, we eventually", "start": 3819.75, "duration": 2.291 }, { "text": "quit, even if the list is super-small.", "start": 3822.041, "duration": 2.399 }, { "text": "But then, the magic is hidden\nin those last three lines.", "start": 3824.44, "duration": 2.84 }, { "text": "Else, sort the left\nhalf of the elements,", "start": 3827.28, "duration": 2.93 }, { "text": "then sort the right\nhalf of the elements,", "start": 3830.21, "duration": 1.76 }, { "text": "which is completely punting so to speak.", "start": 3831.97, "duration": 2.13 }, { "text": "Just kind of recursively\ncalling yourself.", "start": 3834.1, "duration": 2.04 }, { "text": "But the key detail here is that then\nyou have to merge the sorted halves.", "start": 3836.14, "duration": 4.72 }, { "text": "You're not just looking for Mike to the\nleft and looking for Mike to the right.", "start": 3840.86, "duration": 3.312 }, { "text": "You're doing something on the\nleft, something on the right,", "start": 3844.172, "duration": 2.458 }, { "text": "sorting each half, but then you have\nto kind of weave things together.", "start": 3846.63, "duration": 3.43 }, { "text": "And we'll see how\nexpensive that actually is.", "start": 3850.06, "duration": 2.85 }, { "text": "So let's take an example.", "start": 3852.91, "duration": 1.3 }, { "text": "And I mocked this up with some\nvery simple animation so we", "start": 3854.21, "duration": 3.82 }, { "text": "could walk through it step-by-step.", "start": 3858.03, "duration": 1.585 }, { "text": "But consider the following.", "start": 3859.615, "duration": 1.125 }, { "text": "So here is that same\nlist from before where", "start": 3860.74, "duration": 1.791 }, { "text": "we had a whole bunch of volunteers.", "start": 3862.531, "duration": 1.699 }, { "text": "But rather than call up humans,\nwe'll just do this visually.", "start": 3864.23, "duration": 2.58 }, { "text": "Let me consider the fact that\nthis is really just an array.", "start": 3866.81, "duration": 3.245 }, { "text": "So I'm just going to box\neverything like this.", "start": 3870.055, "duration": 2.015 }, { "text": "And this is actually key that we\nhave random access to these elements.", "start": 3872.07, "duration": 3.28 }, { "text": "We can jump right to\nthe elements we want", "start": 3875.35, "duration": 1.82 }, { "text": "and code ultimately, too, if we cared.", "start": 3877.17, "duration": 2.16 }, { "text": "And now, let's focus\non the left-hand side.", "start": 3879.33, "duration": 2.35 }, { "text": "So I've wrapped 4, 8,\n6, 2 in a solid line", "start": 3881.68, "duration": 4.682 }, { "text": "and left everything else\ndash because I want to focus", "start": 3886.362, "duration": 2.208 }, { "text": "our attention on sorting the left half.", "start": 3888.57, "duration": 2.23 }, { "text": "So again, to rewind\nthis is the algorithm.", "start": 3890.8, "duration": 2.51 }, { "text": "And the goal at hand is\nto walk through visually", "start": 3893.31, "duration": 2.0 }, { "text": "an example whereby we sort 8 elements.", "start": 3895.31, "duration": 2.684 }, { "text": "And we do that by sorting the\nleft half, sorting the right half,", "start": 3897.994, "duration": 2.666 }, { "text": "and then somehow merging\nthese things together.", "start": 3900.66, "duration": 3.16 }, { "text": "So how do we do this?", "start": 3903.82, "duration": 1.14 }, { "text": "Well, let's consider the left half.", "start": 3904.96, "duration": 2.23 }, { "text": "All right.", "start": 3907.19, "duration": 0.95 }, { "text": "How do I sort a list of 4 elements?", "start": 3908.14, "duration": 2.07 }, { "text": "What does it mean to sort the left half?", "start": 3910.21, "duration": 1.78 }, { "text": "Well, what algorithms do I have in\nmy toolkit for sorting elements?", "start": 3911.99, "duration": 2.9 }, { "text": "Yeah, selection sort, insertion\nsort, bubble sort, but-- merge sort.", "start": 3917.64, "duration": 4.68 }, { "text": "And that's where this\ngets weird quickly.", "start": 3922.32, "duration": 2.29 }, { "text": "You want to use your same algorithm to\nsort the left-hand side of this list.", "start": 3924.61, "duration": 4.324 }, { "text": "And yet, we haven't even\nfinished defining this algorithm,", "start": 3928.934, "duration": 2.416 }, { "text": "but that's going to be OK we'll see.", "start": 3931.35, "duration": 2.13 }, { "text": "So let's sort the left half.", "start": 3933.48, "duration": 1.19 }, { "text": "How do you sort the left half of a list?", "start": 3934.67, "duration": 1.666 }, { "text": "Well, you sort a list of size 4.", "start": 3936.336, "duration": 1.494 }, { "text": "What does that mean?", "start": 3937.83, "duration": 0.85 }, { "text": "How do you sort a list of size 4?", "start": 3938.68, "duration": 2.66 }, { "text": "Sort the left half of that.", "start": 3941.34, "duration": 2.19 }, { "text": "So let's focus on 4 and 8.", "start": 3943.53, "duration": 2.19 }, { "text": "How do you sort a list of size 2?", "start": 3945.72, "duration": 1.96 }, { "text": "Merge sort it.", "start": 3947.68, "duration": 1.25 }, { "text": "So how do you sort a list of size 2?", "start": 3948.93, "duration": 1.98 }, { "text": "Sort the left half.", "start": 3950.91, "duration": 1.86 }, { "text": "OK, beautifully.", "start": 3952.77, "duration": 1.16 }, { "text": "Done.", "start": 3953.93, "duration": 1.72 }, { "text": "Done.", "start": 3955.65, "duration": 1.29 }, { "text": "Sort the right half.", "start": 3956.94, "duration": 1.51 }, { "text": "Nice, done.", "start": 3958.45, "duration": 1.56 }, { "text": "I mean, I'm doing real\nwork, or claiming to.", "start": 3960.01, "duration": 2.57 }, { "text": "But now I have to do something more.", "start": 3962.58, "duration": 1.69 }, { "text": "Now I have to merge the two halves.", "start": 3964.27, "duration": 1.46 }, { "text": "So I'm taking a step back.", "start": 3965.73, "duration": 1.33 }, { "text": "I have two lists now, one\nof size 1, one of size 1.", "start": 3967.06, "duration": 3.579 }, { "text": "I have to merge these\nthings, two together.", "start": 3970.639, "duration": 1.791 }, { "text": "Which comes first, 4 or 8?", "start": 3972.43, "duration": 2.69 }, { "text": "4.", "start": 3975.12, "duration": 0.67 }, { "text": "So let's create some extra space for it.", "start": 3975.79, "duration": 2.03 }, { "text": "Let's put 4 here and let's put 8 here.", "start": 3977.82, "duration": 3.53 }, { "text": "So here's a key detail\nwith merge sort, kind", "start": 3981.35, "duration": 2.394 }, { "text": "of cheating, at least at the\nmoment, I'm using some extra space.", "start": 3983.744, "duration": 2.666 }, { "text": "So I hope you won't mind.", "start": 3986.41, "duration": 1.23 }, { "text": "To achieve this, I'm using\nmore memory, more RAM,", "start": 3987.64, "duration": 2.76 }, { "text": "that I wasn't allowing myself\nfor selection sort, bubble", "start": 3990.4, "duration": 2.53 }, { "text": "sort, or insertion sort.", "start": 3992.93, "duration": 1.011 }, { "text": "OK.", "start": 3993.941, "duration": 0.499 }, { "text": "So now it's going to be\neasy to get lost quickly.", "start": 3994.44, "duration": 2.041 }, { "text": "So what have I just done?", "start": 3996.481, "duration": 1.239 }, { "text": "I have sorted a list of size 2\nby sorting the left half, done.", "start": 3997.72, "duration": 4.06 }, { "text": "Right half, done.", "start": 4001.78, "duration": 1.27 }, { "text": "Merging it together.", "start": 4003.05, "duration": 1.4 }, { "text": "So now I have a sorted list of size 2.", "start": 4004.45, "duration": 3.69 }, { "text": "Rewind the story.", "start": 4008.14, "duration": 0.87 }, { "text": "What step comes next?", "start": 4009.01, "duration": 2.76 }, { "text": "Sort the right half.", "start": 4011.77, "duration": 2.06 }, { "text": "That was of size 2.", "start": 4013.83, "duration": 1.2 }, { "text": "So if you kind of mentally buffer\nall of the to-dos that we're doing,", "start": 4015.03, "duration": 3.5 }, { "text": "and then pluck them off as we go,\nyou'll see where the story goes.", "start": 4018.53, "duration": 3.68 }, { "text": "Now I want to sort the right\nhalf of the original list.", "start": 4022.21, "duration": 2.31 }, { "text": "Sorry, the right half of the\nleft half of the original list.", "start": 4024.52, "duration": 4.32 }, { "text": "How do I do that?", "start": 4028.84, "duration": 0.94 }, { "text": "Sort of left half, done.", "start": 4029.78, "duration": 1.7 }, { "text": "Sort the right half, done.", "start": 4031.48, "duration": 1.77 }, { "text": "Merge them together.", "start": 4033.25, "duration": 1.21 }, { "text": "What comes first, 6 or 2?", "start": 4034.46, "duration": 1.86 }, { "text": "OK.", "start": 4036.32, "duration": 0.5 }, { "text": "So let's give ourselves a\nlittle more memory for that", "start": 4036.82, "duration": 1.76 }, { "text": "so we have a place to put it.", "start": 4038.58, "duration": 1.33 }, { "text": "2.", "start": 4039.91, "duration": 0.97 }, { "text": "And then 6.", "start": 4040.88, "duration": 1.271 }, { "text": "All right.", "start": 4042.151, "duration": 0.499 }, { "text": "So it doesn't look like all\nthat much progress, frankly.", "start": 4042.65, "duration": 2.93 }, { "text": "My left half of the list is now 4,\n8, 2, 6, which is not really sorted.", "start": 4045.58, "duration": 3.74 }, { "text": "But we'll get there.", "start": 4049.32, "duration": 1.21 }, { "text": "What step comes next?", "start": 4050.53, "duration": 1.55 }, { "text": "I've just sorted the right half of\nthe left half of my original list.", "start": 4052.08, "duration": 4.701 }, { "text": "AUDIENCE: [INAUDIBLE].", "start": 4056.781, "duration": 2.409 }, { "text": "SPEAKER 1: You're missing a step.", "start": 4059.19, "duration": 1.47 }, { "text": "AUDIENCE: [INAUDIBLE].", "start": 4060.66, "duration": 0.97 }, { "text": "SPEAKER 1: Merge, that third step.", "start": 4061.63, "duration": 1.98 }, { "text": "Once you've sorted the\nleft half of something,", "start": 4063.61, "duration": 2.0 }, { "text": "then you've sorted the\nright half of something.", "start": 4065.61, "duration": 1.958 }, { "text": "Now you have to merge them or\nweave them together somehow.", "start": 4067.568, "duration": 2.942 }, { "text": "So the left half of the list in\nthe story at the moment is 4 and 8.", "start": 4070.51, "duration": 3.25 }, { "text": "The right half is 2 and 6.", "start": 4073.76, "duration": 1.75 }, { "text": "So here's where mentally\nyou can kind of bring out", "start": 4075.51, "duration": 2.309 }, { "text": "your fingers to think through this sort\nof conceptually, or in pseudocode code.", "start": 4077.819, "duration": 3.291 }, { "text": "Here's the left list.", "start": 4081.11, "duration": 1.69 }, { "text": "Here's the right list,\nor the right half.", "start": 4082.8, "duration": 2.13 }, { "text": "So how do I merge these two together?", "start": 4084.93, "duration": 1.577 }, { "text": "Well, it turns out--\nand you can see it now.", "start": 4086.507, "duration": 1.833 }, { "text": "Before it was idiotic that we\njust were merging lists of size 1.", "start": 4088.34, "duration": 2.85 }, { "text": "It's pretty easy.", "start": 4091.19, "duration": 0.89 }, { "text": "Here now, we have something\nsubstantive to talk about.", "start": 4092.08, "duration": 2.51 }, { "text": "So I have one list here, one list here.", "start": 4094.59, "duration": 2.33 }, { "text": "Which element from these two\nlists obviously comes first?", "start": 4096.92, "duration": 4.67 }, { "text": "So 2.", "start": 4101.59, "duration": 1.11 }, { "text": "And so what I'm going to do is then\n2 is going to have to come down here.", "start": 4102.7, "duration": 3.369 }, { "text": "And then I can advance my\nright hand so to speak.", "start": 4106.069, "duration": 2.491 }, { "text": "And now, compare 4 and 6.", "start": 4108.56, "duration": 1.379 }, { "text": "What's going to come next?", "start": 4109.939, "duration": 1.641 }, { "text": "4.", "start": 4111.58, "duration": 0.72 }, { "text": "Now I can advance my left hand.", "start": 4112.3, "duration": 1.389 }, { "text": "I compare 8 and 6.", "start": 4113.689, "duration": 1.311 }, { "text": "Which comes next?", "start": 4115.0, "duration": 1.29 }, { "text": "6.", "start": 4116.29, "duration": 0.63 }, { "text": "Now, my right hand, its job is done.", "start": 4116.92, "duration": 1.93 }, { "text": "I have only one more to do.", "start": 4118.85, "duration": 2.31 }, { "text": "And this.", "start": 4121.16, "duration": 0.54 }, { "text": "So what's key in the merging\nis that you essentially", "start": 4121.7, "duration": 2.6 }, { "text": "have this left hand and\nthis right hand concept.", "start": 4124.3, "duration": 2.49 }, { "text": "Each of them kind of steps forward\nover time, but you never go back.", "start": 4126.79, "duration": 3.77 }, { "text": "You never double back.", "start": 4130.56, "duration": 1.29 }, { "text": "So it's this sort of linear relationship\nwith your left and right hand", "start": 4131.85, "duration": 2.968 }, { "text": "as you're merging the lists together.", "start": 4134.818, "duration": 1.541 }, { "text": "So pictorially, let's see that.", "start": 4136.359, "duration": 1.5 }, { "text": "We compare 4 and 2.", "start": 4137.859, "duration": 2.091 }, { "text": "2 goes first.", "start": 4139.95, "duration": 1.09 }, { "text": "Then, 4.", "start": 4141.04, "duration": 1.04 }, { "text": "Then, 6.", "start": 4142.08, "duration": 0.92 }, { "text": "Then, 8.", "start": 4143.0, "duration": 0.649 }, { "text": "Where am I in the story?", "start": 4143.649, "duration": 1.33 }, { "text": "I mean, we've been droning\non for some time now.", "start": 4144.979, "duration": 3.09 }, { "text": "I have just successfully sorted what?", "start": 4148.069, "duration": 3.511 }, { "text": "The left half of the original\nlist, which means the next step is?", "start": 4151.58, "duration": 3.568 }, { "text": "AUDIENCE: Sort the right.", "start": 4155.148, "duration": 1.041 }, { "text": "SPEAKER 1: Sort the right\nhalf of the original list.", "start": 4156.189, "duration": 2.29 }, { "text": "So I can box that in to\ndraw attention to it.", "start": 4158.479, "duration": 2.181 }, { "text": "How do I sort a list of size 4?", "start": 4160.66, "duration": 1.52 }, { "text": "Well, that's really\njust 2 lists of size 2.", "start": 4162.18, "duration": 2.13 }, { "text": "Let's sort the left half.", "start": 4164.31, "duration": 1.21 }, { "text": "How do I sort a list of size 2?", "start": 4165.52, "duration": 1.5 }, { "text": "Well, that's really just a\nlist of-- 2 lists of size 1.", "start": 4167.02, "duration": 4.28 }, { "text": "Done.", "start": 4171.3, "duration": 0.5 }, { "text": "1 is sorted.", "start": 4171.8, "duration": 0.929 }, { "text": "Done.", "start": 4172.729, "duration": 0.5 }, { "text": "7 is sorted.", "start": 4173.229, "duration": 0.851 }, { "text": "Now I have to merge them together.", "start": 4174.08, "duration": 1.48 }, { "text": "1 comes first, then 7.", "start": 4175.56, "duration": 3.009 }, { "text": "OK, now sort the right half of the\nright half of the original list.", "start": 4178.569, "duration": 4.071 }, { "text": "OK.", "start": 4182.64, "duration": 0.85 }, { "text": "Sort the left half.", "start": 4183.49, "duration": 1.0 }, { "text": "Done.", "start": 4184.49, "duration": 0.55 }, { "text": "Right half.", "start": 4185.04, "duration": 0.6 }, { "text": "Done.", "start": 4185.64, "duration": 0.67 }, { "text": "Merge them together\ninto some extra space.", "start": 4186.31, "duration": 2.629 }, { "text": "3, and then 5.", "start": 4188.939, "duration": 2.271 }, { "text": "Now where am I in the story?", "start": 4191.21, "duration": 1.939 }, { "text": "Now I have sorted the left\nhalf of the original right half", "start": 4193.149, "duration": 4.085 }, { "text": "and the right half of\nthe original right half,", "start": 4197.234, "duration": 1.916 }, { "text": "so now I have to merge them together.", "start": 4199.15, "duration": 2.81 }, { "text": "So 1, 3, 5, 7.", "start": 4201.96, "duration": 5.24 }, { "text": "Almost there.", "start": 4207.2, "duration": 0.94 }, { "text": "Now we're sort of rewinding in time.", "start": 4208.14, "duration": 1.94 }, { "text": "Now we're at the very first\nchapter in the story--", "start": 4210.08, "duration": 2.49 }, { "text": "sort left half, sort right half, merge.", "start": 4212.57, "duration": 2.37 }, { "text": "I have that one final merge step.", "start": 4214.94, "duration": 1.64 }, { "text": "So what comes first from the\nleft half and the right half?", "start": 4216.58, "duration": 3.96 }, { "text": "1, 2-- even if you've\nlost track of the story,", "start": 4220.54, "duration": 3.43 }, { "text": "the answer's going to be\n1, 2, 3, 4, 5, 6, 7, 8.", "start": 4223.97, "duration": 2.0 }, { "text": "But 1, 2, 3.", "start": 4225.97, "duration": 2.24 }, { "text": "But notice what's\nhappening here in effect.", "start": 4228.21, "duration": 1.97 }, { "text": "Whatever code is implementing this,\nit's as though my right and left", "start": 4230.18, "duration": 3.67 }, { "text": "fingers are just moving from left to\nright, plucking off the element that", "start": 4233.85, "duration": 4.72 }, { "text": "is indeed then the smallest.", "start": 4238.57, "duration": 3.61 }, { "text": "That was a heck of a lot of work.", "start": 4242.18, "duration": 1.42 }, { "text": "And frankly, that story seemed to take\nlonger to tell than any of the others.", "start": 4243.6, "duration": 5.64 }, { "text": "But what happened?", "start": 4249.24, "duration": 1.156 }, { "text": "And in fact, I've left deliberately,\nwith this little animation", "start": 4250.396, "duration": 2.624 }, { "text": "of sorts, on the screen the\nremnants of where we came.", "start": 4253.02, "duration": 2.7 }, { "text": "And it looks like I\nreally cheated, though.", "start": 4255.72, "duration": 1.88 }, { "text": "I seemed to first say,\nhey, I need some extra RAM.", "start": 4257.6, "duration": 2.68 }, { "text": "And I took it.", "start": 4260.28, "duration": 0.94 }, { "text": "And then I didn't\nmention I need more RAM.", "start": 4261.22, "duration": 1.83 }, { "text": "I didn't mention I needed even more RAM.", "start": 4263.05, "duration": 1.666 }, { "text": "So this seems to have taken like four\ntimes as much total memory than any", "start": 4264.716, "duration": 3.863 }, { "text": "of our previous algorithms, but\nthat's not actually the case.", "start": 4268.579, "duration": 2.541 }, { "text": "I left this here pictorially\nso we could see the history.", "start": 4271.12, "duration": 2.71 }, { "text": "Technically, you do need more RAM to\nimplement this algorithm, merge sort.", "start": 4273.83, "duration": 3.741 }, { "text": "But we could have cut corners.", "start": 4277.571, "duration": 1.249 }, { "text": "Instead of merging down\nhere, we could have just", "start": 4278.82, "duration": 2.24 }, { "text": "merged back into our original chunk.", "start": 4281.06, "duration": 1.68 }, { "text": "And so we could have just bounced\nbetween two separate arrays,", "start": 4282.74, "duration": 2.77 }, { "text": "but this is just a little more\nclear in terms of remnants.", "start": 4285.51, "duration": 3.51 }, { "text": "So how many steps did this take?", "start": 4289.02, "duration": 2.04 }, { "text": "Well, how many times did I\ndivide my original list in half,", "start": 4291.06, "duration": 4.39 }, { "text": "in half, in half effectively?", "start": 4295.45, "duration": 1.325 }, { "text": "I had 8 elements here.", "start": 4299.45, "duration": 1.58 }, { "text": "And that was really like, if\nyou divide it up differently,", "start": 4301.03, "duration": 2.74 }, { "text": "two bigger halves and two bigger halves.", "start": 4303.77, "duration": 1.78 }, { "text": "But if you divide it again,\nthat's like two really big halves,", "start": 4305.55, "duration": 3.17 }, { "text": "and then you get one big list.", "start": 4308.72, "duration": 2.03 }, { "text": "So it would seem that starting\nhere, I divided it 1, 2, 3 times.", "start": 4310.75, "duration": 4.69 }, { "text": "I did some splitting.", "start": 4315.44, "duration": 0.916 }, { "text": "Left half, right half,\nleft half, right half.", "start": 4316.356, "duration": 1.874 }, { "text": "And any time you split something\nin half, in half, in half,", "start": 4318.23, "duration": 2.26 }, { "text": "in half, what's the running time of\nanything involving like halving again", "start": 4320.49, "duration": 3.16 }, { "text": "and again and again?", "start": 4323.65, "duration": 0.833 }, { "text": "It's like binary search.", "start": 4327.687, "duration": 2.743 }, { "text": "Log n.", "start": 4330.43, "duration": 0.66 }, { "text": "Log n.", "start": 4331.09, "duration": 0.78 }, { "text": "So any time you see in\ncomputer science more", "start": 4331.87, "duration": 2.76 }, { "text": "generally, certainly CS50 in\nupcoming weeks, this division", "start": 4334.63, "duration": 2.894 }, { "text": "and conquering again and\nagain and again where", "start": 4337.524, "duration": 1.916 }, { "text": "you're dividing something in half,\nodds are logarithmic running time", "start": 4339.44, "duration": 3.4 }, { "text": "is somehow at play.", "start": 4342.84, "duration": 1.34 }, { "text": "But this algorithm, merge sort, surely\ncannot run in big O of log n time.", "start": 4344.18, "duration": 5.93 }, { "text": "Because again, you can't sort n\nelements in less than linear time", "start": 4350.11, "duration": 5.14 }, { "text": "because you'd be guessing\nthat everything is sorted.", "start": 4355.25, "duration": 3.08 }, { "text": "So log n is not the final\nanswer here, but there", "start": 4358.33, "duration": 2.54 }, { "text": "is something logarithmic happening.", "start": 4360.87, "duration": 2.19 }, { "text": "However, even though we did\na left half/right half thing,", "start": 4363.06, "duration": 4.17 }, { "text": "a left half/right half thing,\na left half/right hand,", "start": 4367.23, "duration": 2.56 }, { "text": "thing sort of a total of three\ntimes, from here to here to here", "start": 4369.79, "duration": 2.98 }, { "text": "to here, at which point we were done.", "start": 4372.77, "duration": 2.47 }, { "text": "On every row that's on\nthe screen if you will,", "start": 4375.24, "duration": 3.92 }, { "text": "what did I do with my\nleft and right hand?", "start": 4379.16, "duration": 2.66 }, { "text": "I sort of always did n steps.", "start": 4381.82, "duration": 5.01 }, { "text": "You can really see it up here.", "start": 4386.83, "duration": 1.39 }, { "text": "How did I merge this last thing?", "start": 4388.22, "duration": 1.594 }, { "text": "I had to touch all 8 elements\nby walking through the list.", "start": 4389.814, "duration": 2.416 }, { "text": "How did I merge these two left halves?", "start": 4392.23, "duration": 2.21 }, { "text": "Well, I had to do this.", "start": 4394.44, "duration": 1.3 }, { "text": "And then I had to do this.", "start": 4395.74, "duration": 1.76 }, { "text": "So if you kind of consider the remnants\nof my finger touching the screen,", "start": 4397.5, "duration": 4.24 }, { "text": "every time I did a divide and conquer,\nI had to touch every element in order", "start": 4401.74, "duration": 3.6 }, { "text": "to merge them together.", "start": 4405.34, "duration": 1.48 }, { "text": "So I did log n things.", "start": 4406.82, "duration": 2.36 }, { "text": "And every time I did that, I\nincurred n steps of merging.", "start": 4409.18, "duration": 5.13 }, { "text": "So log n things times n is going\nto give me big O of n log n.", "start": 4414.31, "duration": 8.05 }, { "text": "So this was among the options on our\nsort of menu of possible running times,", "start": 4422.36, "duration": 3.49 }, { "text": "at least that we'll focus on right now.", "start": 4425.85, "duration": 1.9 }, { "text": "This is bigger than log n, of course.", "start": 4427.75, "duration": 1.845 }, { "text": "Because you're multiplying it by n but.", "start": 4429.595, "duration": 1.625 }, { "text": "It's smaller than n squared.", "start": 4431.22, "duration": 1.32 }, { "text": "Because if log n is less than n, then\nsurely n times log n is less than n.", "start": 4432.54, "duration": 3.9 }, { "text": "And so the running\ntime here of merge sort", "start": 4436.44, "duration": 2.12 }, { "text": "is indeed going to be big O of log n.", "start": 4438.56, "duration": 5.07 }, { "text": "Any questions on this here?", "start": 4443.63, "duration": 3.31 }, { "text": "If I may, let me point\nout one other approach", "start": 4446.94, "duration": 2.55 }, { "text": "for seeing this same thing as follows.", "start": 4449.49, "duration": 2.28 }, { "text": "You can actually glean\nthis kind of detail", "start": 4451.77, "duration": 2.5 }, { "text": "more formally, especially if you're the\nmathy type, from the pseudocode itself.", "start": 4454.27, "duration": 3.64 }, { "text": "We didn't have to walk through this\nwhole verbal exercise or visualization", "start": 4457.91, "duration": 3.29 }, { "text": "thereof.", "start": 4461.2, "duration": 0.5 }, { "text": "What if we just go back to basics and\njust analyze our own pseudocode code,", "start": 4461.7, "duration": 3.44 }, { "text": "or our own C code\neventually, line by line?", "start": 4465.14, "duration": 2.97 }, { "text": "So here's the original algorithm.", "start": 4468.11, "duration": 1.66 }, { "text": "How many steps does this take to\njust check if n is less than 2?", "start": 4469.77, "duration": 3.58 }, { "text": "Return.", "start": 4473.35, "duration": 0.56 }, { "text": "We're done.", "start": 4473.91, "duration": 1.6 }, { "text": "Big O of what?", "start": 4475.51, "duration": 1.676 }, { "text": "There's just one step.", "start": 4477.186, "duration": 0.938 }, { "text": "Or maybe, it's two, like\nthe if and then the return.", "start": 4478.124, "duration": 2.166 }, { "text": "But it's constant.", "start": 4480.29, "duration": 0.77 }, { "text": "It's one or two.", "start": 4481.06, "duration": 0.79 }, { "text": "We can debate that, but it's constant.", "start": 4481.85, "duration": 1.61 }, { "text": "It has nothing to do with the size of n.", "start": 4483.46, "duration": 1.98 }, { "text": "You're just making a finite\nnumber of decisions there, 1.", "start": 4485.44, "duration": 3.33 }, { "text": "So you know what?", "start": 4488.77, "duration": 1.61 }, { "text": "The running time, which I'm going\nto formulaically say is t of n.", "start": 4490.38, "duration": 3.61 }, { "text": "So the running time when\nyour input is of size n,", "start": 4493.99, "duration": 2.86 }, { "text": "is just going to be like on the\norder of constant time, big O of 1,", "start": 4496.85, "duration": 2.95 }, { "text": "whenever n is less than 2.", "start": 4499.8, "duration": 2.12 }, { "text": "This is not a very bold claim.", "start": 4501.92, "duration": 1.29 }, { "text": "It's sort of like I'm plucking off\nthe easiest part of the question,", "start": 4503.21, "duration": 2.48 }, { "text": "but it's at least correct.", "start": 4505.69, "duration": 1.22 }, { "text": "If you have a small\nlist, it's constant time.", "start": 4506.91, "duration": 2.11 }, { "text": "The harder question is when we\nanalyze the rest of the algorithm.", "start": 4509.02, "duration": 3.48 }, { "text": "How many steps does it take to\nsort the left half of elements?", "start": 4512.5, "duration": 3.59 }, { "text": "How many steps does it take to\nsort the right half of elements?", "start": 4516.09, "duration": 2.95 }, { "text": "And how many steps does\nit take to sort-- rather,", "start": 4519.04, "duration": 5.12 }, { "text": "to merge the sorted halves?", "start": 4524.16, "duration": 1.56 }, { "text": "So we have three questions to answer.", "start": 4525.72, "duration": 2.96 }, { "text": "And let me propose this.", "start": 4528.68, "duration": 1.385 }, { "text": "You can kind of punt.", "start": 4530.065, "duration": 0.875 }, { "text": "And this is the beauty of recursion.", "start": 4530.94, "duration": 1.18 }, { "text": "You can sort of answer the\nquestion with the question.", "start": 4532.12, "duration": 2.249 }, { "text": "The running time to sort n\nelements is really the running time", "start": 4534.369, "duration": 3.531 }, { "text": "to sort n over 2 elements, the left\nhalf, plus the running time to sort n", "start": 4537.9, "duration": 4.37 }, { "text": "over 2 elements, the right\nhalf, plus the merging step,", "start": 4542.27, "duration": 3.12 }, { "text": "which I claimed per my sort\nof left/right finger intuition", "start": 4545.39, "duration": 4.7 }, { "text": "is big O of n steps linear.", "start": 4550.09, "duration": 2.08 }, { "text": "And now this holds if n is\ngreater than or equal to 2.", "start": 4552.17, "duration": 3.68 }, { "text": "Now, unfortunately, this is like a\nrecurrence if you will, mathematically.", "start": 4555.85, "duration": 3.96 }, { "text": "This really is a cyclical definition.", "start": 4559.81, "duration": 2.0 }, { "text": "We really need to be able to\ngeneralize this and explain", "start": 4561.81, "duration": 3.53 }, { "text": "it a little more formulaically.", "start": 4565.34, "duration": 2.4 }, { "text": "But indeed, take a guess.", "start": 4567.74, "duration": 1.45 }, { "text": "If you have your old physics\ntextbook or your math textbook,", "start": 4569.19, "duration": 2.73 }, { "text": "what does this recurrence actually\nequal if you multiply it all out", "start": 4571.92, "duration": 3.09 }, { "text": "and prove it mathematically?", "start": 4575.01, "duration": 1.33 }, { "text": "What's the running\ntime total of something", "start": 4578.74, "duration": 1.75 }, { "text": "where you do some function of n over\n2 plus some function of n over 2", "start": 4580.49, "duration": 4.2 }, { "text": "plus some number of linear steps where\neach of those inner running times", "start": 4584.69, "duration": 5.0 }, { "text": "is recursively defined?", "start": 4589.69, "duration": 2.03 }, { "text": "And just to be clear, the\nreason this is like non-obvious", "start": 4591.72, "duration": 3.61 }, { "text": "and should be kind of over\nmost heads, at least if you're", "start": 4595.33, "duration": 2.75 }, { "text": "less familiar with this world, is that\nI'm saying that the running time, t, is", "start": 4598.08, "duration": 4.15 }, { "text": "a function of the running time, t.", "start": 4602.23, "duration": 1.5 }, { "text": "Like again, that's defining\na word with the word itself.", "start": 4603.73, "duration": 4.63 }, { "text": "But it turns out there are ways to\nprove this inductively, mathematically.", "start": 4608.36, "duration": 3.24 }, { "text": "And indeed, if you actually multiply\nthis all out in your textbook,", "start": 4611.6, "duration": 2.791 }, { "text": "you will get something on\nthe order of n times log n.", "start": 4614.391, "duration": 4.449 }, { "text": "So where has that left us?", "start": 4618.84, "duration": 1.204 }, { "text": "We've introduced a whole number of\nalgorithms here, the last of which,", "start": 4620.044, "duration": 2.916 }, { "text": "merge sort, gives us this ability\nto actually solve problems", "start": 4622.96, "duration": 3.66 }, { "text": "much faster than any of the others.", "start": 4626.62, "duration": 2.01 }, { "text": "But in each case, are we able to\napply some general formulaic analysis,", "start": 4628.63, "duration": 4.34 }, { "text": "asymptotic notation so to speak--\nbig O, big Omega, and big Theta, that", "start": 4632.97, "duration": 5.35 }, { "text": "describes in general terms how much\ntime these kinds of things take.", "start": 4638.32, "duration": 5.2 }, { "text": "So let's now translate one of today's\nkey ingredients to actual C code", "start": 4643.52, "duration": 4.36 }, { "text": "so that we can see how we can\nleverage this programmatically.", "start": 4647.88, "duration": 2.97 }, { "text": "So here in CS50 IDE, I've got\nan example, sigma 0 and sigma 1.", "start": 4650.85, "duration": 5.0 }, { "text": "Both of which at the end of\nthe day do the same thing,", "start": 4655.85, "duration": 2.6 }, { "text": "but they do it differently.", "start": 4658.45, "duration": 1.22 }, { "text": "And in sigma 0 here, we\nhave the following code.", "start": 4659.67, "duration": 2.26 }, { "text": "A sigma function that takes as input\nan integer m as its sole argument", "start": 4661.93, "duration": 4.96 }, { "text": "and it has a return value of type int.", "start": 4666.89, "duration": 1.59 }, { "text": "So it's going to return a number.", "start": 4668.48, "duration": 1.375 }, { "text": "Main takes no command line arguments.", "start": 4669.855, "duration": 1.545 }, { "text": "So no arg v, no arg c this time.", "start": 4671.4, "duration": 1.84 }, { "text": "But inside of main is code that's going\nto pester the user again and again", "start": 4673.24, "duration": 3.72 }, { "text": "until he or she gives us a positive\ninteger as per this condition", "start": 4676.96, "duration": 4.43 }, { "text": "down here.", "start": 4681.39, "duration": 0.94 }, { "text": "And then, notice down here I'm\ngoing to call a function sigma,", "start": 4682.33, "duration": 3.51 }, { "text": "passing in whatever\nthe user's input was.", "start": 4685.84, "duration": 1.85 }, { "text": "10, for instance.", "start": 4687.69, "duration": 1.08 }, { "text": "Or 11.", "start": 4688.77, "duration": 0.76 }, { "text": "Or some other value.", "start": 4689.53, "duration": 1.15 }, { "text": "Storing the answer in answer,\nand then just printing it out.", "start": 4690.68, "duration": 3.67 }, { "text": "And what's nice about\nthe fact that frankly you", "start": 4694.35, "duration": 2.12 }, { "text": "can't see anything else on the screen\nis that for all intents and purposes,", "start": 4696.47, "duration": 3.21 }, { "text": "sigma, the function at the\nmoment, is a black box.", "start": 4699.68, "duration": 2.72 }, { "text": "It is a function whose purpose in life\nis to add all of the numbers from 1 up", "start": 4702.4, "duration": 3.23 }, { "text": "until the user's input and return it.", "start": 4705.63, "duration": 1.96 }, { "text": "And we don't know yet or need to\ncare how it's actually implemented.", "start": 4707.59, "duration": 3.99 }, { "text": "If we do take a look inside that\nblack box down lower in the file,", "start": 4711.58, "duration": 4.76 }, { "text": "you'll see this code here.", "start": 4716.34, "duration": 1.62 }, { "text": "Sigma takes an input, m, as an int.", "start": 4717.96, "duration": 3.08 }, { "text": "Returns an int.", "start": 4721.04, "duration": 0.84 }, { "text": "And what does it do inside?", "start": 4721.88, "duration": 1.22 }, { "text": "Well, I've got what I'll\ncall a counter-variable.", "start": 4723.1, "duration": 2.51 }, { "text": "Called it sum.", "start": 4725.61, "duration": 0.9 }, { "text": "Initialized it to 0.", "start": 4726.51, "duration": 1.38 }, { "text": "And then using a for loop,\niterating from 1 up to m,", "start": 4727.89, "duration": 4.01 }, { "text": "because I want to sum all the\nnumbers from 1 up through the value", "start": 4731.9, "duration": 3.63 }, { "text": "the human has typed in.", "start": 4735.53, "duration": 1.48 }, { "text": "I just want to keep adding\nto the sum that value.", "start": 4737.01, "duration": 2.73 }, { "text": "So it's not just sum plus plus.", "start": 4739.74, "duration": 1.59 }, { "text": "If I did sum plus plus as we keep\nseeing syntactically in examples,", "start": 4741.33, "duration": 3.684 }, { "text": "that would just add 1.", "start": 4745.014, "duration": 0.916 }, { "text": "I want to add in whatever i is.", "start": 4745.93, "duration": 2.33 }, { "text": "Whether it's 1, or 2, or 3,\nas I'm counting all the way", "start": 4748.26, "duration": 4.16 }, { "text": "up through the user's input.", "start": 4752.42, "duration": 1.52 }, { "text": "And then I return sum.", "start": 4753.94, "duration": 1.95 }, { "text": "But the neat thing\nabout sigma is that it", "start": 4755.89, "duration": 2.76 }, { "text": "affords an opportunity for recursion.", "start": 4758.65, "duration": 2.13 }, { "text": "This isn't necessarily a better\nopportunity or more correct,", "start": 4760.78, "duration": 3.66 }, { "text": "but we could view the\nworld a little differently.", "start": 4764.44, "duration": 2.35 }, { "text": "Sigma1.c is identical code in main,\nbut the implementation of sigma", "start": 4766.79, "duration": 6.29 }, { "text": "is fundamentally different.", "start": 4773.08, "duration": 1.58 }, { "text": "And here's where it's kind of\nmind-blowing, at least at first glance.", "start": 4774.66, "duration": 3.21 }, { "text": "You can implement a\nfunction, like sigma,", "start": 4777.87, "duration": 2.9 }, { "text": "in such a way that the\nfunction calls itself.", "start": 4780.77, "duration": 3.53 }, { "text": "Much like the running time for merge\nsort is defined in terms of itself.", "start": 4784.3, "duration": 3.76 }, { "text": "Much like searching\nor sorting a list, it", "start": 4788.06, "duration": 2.756 }, { "text": "can be recursively defined as\nsearching or sorting a smaller list,", "start": 4790.816, "duration": 4.664 }, { "text": "but with the same steps.", "start": 4795.48, "duration": 1.43 }, { "text": "We implement this code in C as follows.", "start": 4796.91, "duration": 1.97 }, { "text": "On this line here, if m is\nless than or equal to 0,", "start": 4798.88, "duration": 4.06 }, { "text": "it's really just a sanity check.", "start": 4802.94, "duration": 1.55 }, { "text": "If the human was messing\nwith me and somehow", "start": 4804.49, "duration": 3.15 }, { "text": "was able to inject a negative value\nor a 0 value into this function,", "start": 4807.64, "duration": 4.609 }, { "text": "I don't want to get stuck in\nsome random, like infinite loop.", "start": 4812.249, "duration": 2.541 }, { "text": "I want to catch that.", "start": 4814.79, "duration": 1.02 }, { "text": "So I'm just going to say less than or\nequal to 0 just to be super-defensive", "start": 4815.81, "duration": 3.124 }, { "text": "when programming return 0.", "start": 4818.934, "duration": 1.926 }, { "text": "It's not correct to say\nthat, but I just want--", "start": 4820.86, "duration": 2.31 }, { "text": "and I'll document this in\nmy comments, for instance.", "start": 4823.17, "duration": 2.65 }, { "text": "Return 0 if the user does not cooperate.", "start": 4825.82, "duration": 1.96 }, { "text": "I need that base case so\nthat stuff stops eventually.", "start": 4827.78, "duration": 3.94 }, { "text": "And then, here's kind\nof the amazing thing.", "start": 4831.72, "duration": 2.12 }, { "text": "In my \"else\" condition,\nis one line of code", "start": 4833.84, "duration": 2.84 }, { "text": "that implements the\nentirety of this function.", "start": 4836.68, "duration": 3.7 }, { "text": "The result of asking me the\nquestion, what is sigma of m,", "start": 4840.38, "duration": 3.39 }, { "text": "is really the same thing as\nsaying m plus sigma of m minus 1.", "start": 4843.77, "duration": 8.07 }, { "text": "In other words, if the goal is to count\nup all of the numbers between 1 and m,", "start": 4851.84, "duration": 4.28 }, { "text": "logically that's the same as counting\nup all the numbers from m to 1.", "start": 4856.12, "duration": 4.12 }, { "text": "And so if I view it that\nway, if you give me m,", "start": 4860.24, "duration": 4.48 }, { "text": "I am going to sort of on my cheat\nsheet write down the number m,", "start": 4864.72, "duration": 3.35 }, { "text": "and then say plus whatever the\nsummation is from m minus 1", "start": 4868.07, "duration": 4.05 }, { "text": "all the way down to 1.", "start": 4872.12, "duration": 1.11 }, { "text": "And you know what?", "start": 4873.23, "duration": 0.75 }, { "text": "I have a function, a piece of code, that\ngives me exactly that answer if I just", "start": 4873.98, "duration": 3.88 }, { "text": "pass-in that slightly smaller value.", "start": 4877.86, "duration": 2.7 }, { "text": "So on first glance, it might\nlook like sigma calls sigma.", "start": 4880.56, "duration": 3.81 }, { "text": "That can't possibly be a good thing.", "start": 4884.37, "duration": 2.19 }, { "text": "But it doesn't do it forever.", "start": 4886.56, "duration": 1.48 }, { "text": "Sigma might call sigma might\ncall sigma might call sigma.", "start": 4888.04, "duration": 2.54 }, { "text": "But at what point in the story\ndoes sigma stop calling sigma?", "start": 4890.58, "duration": 4.67 }, { "text": "AUDIENCE: [INAUDIBLE].", "start": 4895.25, "duration": 1.5 }, { "text": "SPEAKER 1: When it's counted.", "start": 4896.75, "duration": 1.32 }, { "text": "When m, the input, is what?", "start": 4898.07, "duration": 3.01 }, { "text": "Negative.", "start": 4901.08, "duration": 0.53 }, { "text": "Or we shouldn't hit negative ever.", "start": 4901.61, "duration": 1.46 }, { "text": "We should first hit?", "start": 4903.07, "duration": 1.231 }, { "text": "AUDIENCE: 0.", "start": 4904.301, "duration": 0.499 }, { "text": "SPEAKER 1: 0.", "start": 4904.8, "duration": 1.01 }, { "text": "So once m minus 1 gets so small, 1 minus\n1, that it equals 0, this line of code", "start": 4905.81, "duration": 6.507 }, { "text": "is going to kick in.", "start": 4912.317, "duration": 0.833 }, { "text": "And it's going to say return 0.", "start": 4913.15, "duration": 1.92 }, { "text": "Thereby, short circuiting\nthis seemingly infinite loop,", "start": 4915.07, "duration": 3.82 }, { "text": "which does, in fact, terminate\neventually once the input", "start": 4918.89, "duration": 3.74 }, { "text": "gets small enough.", "start": 4922.63, "duration": 1.41 }, { "text": "Now, probably you shouldn't bother\nimplementing code like this.", "start": 4924.04, "duration": 3.195 }, { "text": "If anything, we'll talk\nabout this in future weeks.", "start": 4927.235, "duration": 2.125 }, { "text": "Calling function after function after\nfunction after function after actually", "start": 4929.36, "duration": 3.66 }, { "text": "can take up a lot of memory.", "start": 4933.02, "duration": 1.352 }, { "text": "It can actually cause your\ncomputer to crash in some cases.", "start": 4934.372, "duration": 2.458 }, { "text": "And we'll talk about when and why.", "start": 4936.83, "duration": 1.82 }, { "text": "So this isn't necessarily\nthe best technical decision,", "start": 4938.65, "duration": 2.95 }, { "text": "but it's illustrative of the capability\nwe have in programming to map intuition", "start": 4941.6, "duration": 4.48 }, { "text": "from our binary search or our\nmerge sort into actual code.", "start": 4946.08, "duration": 5.301 }, { "text": "And indeed, there's going to\nbe data structures that we soon", "start": 4951.381, "duration": 2.499 }, { "text": "see far fancier than arrays.", "start": 4953.88, "duration": 2.11 }, { "text": "We're going to see things\nlike link lists, and trees,", "start": 4955.99, "duration": 2.39 }, { "text": "and tries, and hash tables.", "start": 4958.38, "duration": 1.46 }, { "text": "And other data structures\nstill that are going", "start": 4959.84, "duration": 2.71 }, { "text": "to allow us opportunities to implement\nalgorithms on top of those data", "start": 4962.55, "duration": 5.22 }, { "text": "structures so to speak,\nto answer questions", "start": 4967.77, "duration": 2.45 }, { "text": "using an ingredient like this one here.", "start": 4970.22, "duration": 2.96 }, { "text": "But of course, we're left then\nfortunately with a better algorithm", "start": 4973.18, "duration": 3.51 }, { "text": "than something like bubble sort.", "start": 4976.69, "duration": 1.5 }, { "text": "And indeed, this is fairly\nwell-known now it would seem.", "start": 4978.19, "duration": 2.75 }, { "text": "And I thought we'd conclude with\na look at this interview that", "start": 4980.94, "duration": 3.13 }, { "text": "was conducted with a certain senator\nsome years ago who was running", "start": 4984.07, "duration": 3.71 }, { "text": "for the presidency and was asked\nby Google's own Eric Schmidt,", "start": 4987.78, "duration": 4.03 }, { "text": "the CEO at the time, a set\nof interview questions.", "start": 4991.81, "duration": 3.06 }, { "text": "One of which we thought was\nappropriate note to end on here.", "start": 4994.87, "duration": 4.45 }, { "text": "[AUDIO PLAYBACK]", "start": 4999.32, "duration": 3.666 }, { "text": "[APPLAUSE]", "start": 5002.986, "duration": 2.334 }, { "text": "-Now, Senator.", "start": 5005.32, "duration": 1.86 }, { "text": "You're here at Google.", "start": 5007.18, "duration": 1.01 }, { "text": "And I like to think of the\npresidency as a job interview.", "start": 5008.19, "duration": 5.71 }, { "text": "Now, it's hard to get\na job as president.", "start": 5013.9, "duration": 3.142 }, { "text": "You're going [INAUDIBLE] now.", "start": 5017.042, "duration": 1.208 }, { "text": "It's also hard to get a job at Google.", "start": 5018.25, "duration": 2.17 }, { "text": "We have questions.", "start": 5020.42, "duration": 2.67 }, { "text": "And we ask our candidates questions.", "start": 5023.09, "duration": 2.58 }, { "text": "And this one is from Larry Schwimmer.", "start": 5025.67, "duration": 3.676 }, { "text": "[LAUGHTER]", "start": 5029.346, "duration": 1.969 }, { "text": "You guys think I'm kidding?", "start": 5031.315, "duration": 1.125 }, { "text": "It's right here.", "start": 5032.44, "duration": 2.46 }, { "text": "What is the most efficient way to\nsort a million 32-bit integers?", "start": 5034.9, "duration": 4.148 }, { "text": "[LAUGHTER]", "start": 5039.048, "duration": 2.922 }, { "text": "-Well--", "start": 5041.97, "duration": 2.4 }, { "text": "-I'm sorry.", "start": 5044.37, "duration": 0.591 }, { "text": "Maybe--", "start": 5044.961, "duration": 0.499 }, { "text": "-No, no, no, no.", "start": 5045.46, "duration": 0.75 }, { "text": "I think the bubble sort\nwould be the wrong way to go.", "start": 5046.21, "duration": 4.98 }, { "text": "-Come on.", "start": 5054.19, "duration": 0.745 }, { "text": "Who told him this?", "start": 5054.935, "duration": 1.565 }, { "text": "OK.", "start": 5056.5, "duration": 1.84 }, { "text": "I didn't see computer\nscience in your background.", "start": 5058.34, "duration": 2.352 }, { "text": "-We've got our spies in there.", "start": 5060.692, "duration": 2.878 }, { "text": "[END PLAYBACK]", "start": 5063.57, "duration": 1.32 }, { "text": "SPEAKER 1: All right,\nso that's it for week 3.", "start": 5064.89, "duration": 2.23 }, { "text": "We will see you next time.", "start": 5067.12, "duration": 1.6 }, { "text": "SPEAKER 2: So you want\nto know the full story?", "start": 5076.94, "duration": 2.352 }, { "text": "SPEAKER 3: As far back\nas you can remember.", "start": 5079.292, "duration": 3.013 }, { "text": "SPEAKER 2: All right.", "start": 5082.305, "duration": 0.875 }, { "text": "Well, let me tell you.", "start": 5083.18, "duration": 2.64 }, { "text": "The first time I met David Malan,\nI knew he was nothing but trouble.", "start": 5085.82, "duration": 4.06 }, { "text": "SPEAKER 4: There's a David\nJ. Malan here for you.", "start": 5097.779, "duration": 2.041 }, { "text": "SPEAKER 5: Who?", "start": 5099.82, "duration": 1.534 }, { "text": "SPEAKER 4: He says he's in\nyour Computer Science 50 class.", "start": 5101.354, "duration": 2.416 }, { "text": "Wants to talk about his grade.", "start": 5103.77, "duration": 2.04 }, { "text": "SPEAKER 5: Are you kidding me?", "start": 5105.81, "duration": 1.44 }, { "text": "I mean, who does he\nthink he is, Bill Gates?", "start": 5107.25, "duration": 3.67 }, { "text": "All right.", "start": 5110.92, "duration": 0.82 }, { "text": "send him in.", "start": 5111.74, "duration": 2.02 } ]