<transcript><audio_22>then do the aggregation and there's another uh simple optimization if i square root of n is over the n log n which means the set is very large we can just choose to open all proofs</transcript><transcript><audio_23>instead of to get each single proof which means that we don't need to consider uh to get each single proof one</transcript><transcript><audio_24>actually now we can try some amortization technique to improve the worst case since i want to amortize the unlogan time algorithm i want to do it separately so</transcript><transcript><audio_25>the method is to extend the size of the record list to 2 square root of n so if we have square root of n records we can just divide the n log and time computation in to</transcript><transcript><audio_26>square root of n parts and we do the computation in the next square root of an update and if we have two square root of records we can clear the first square root of a record since the first</transcript><transcript><audio_27>unlogan time open or algorithm is finished now and so in this case the record list is at most two square eleven and uh generally it has at least square root</transcript> then do the aggregation and there's another uh simple optimization if i square root of n is over the n log n which means the set is very large we can just choose to open all proofs instead of to get each single proof which means that we don't need to consider uh to get each single proof one actually now we can try some amortization technique to improve the worst case since i want to amortize the unlogan time algorithm i want to do it separately so the method is to extend the size of the record list to 2 square root of n so if we have square root of n records we can just divide the n log and time computation in to square root of n parts and we do the computation in the next square root of an update and if we have two square root of records we can clear the first square root of a record since the first unlogan time open or algorithm is finished now and so in this case the record list is at most two square eleven and uh generally it has at least square root
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