Why is に used in a sentence like this?

> 若者が元気 **に** 溢れている

I thought it was:

> 若者に元気 **が** 溢れている

I know に is used as an indirect object marker. Could someone tell me the
difference between direct and indirect object?

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I already understand this usage of the particle:

It is used to show destination of an action

> 本を彼に上げた

To show an action in a place with semi-permanent or permanent consequences

> 山に雪が積もった

To show existence in a place

> 部屋にいる

To show a specific time when something happens

> 来た時に林檎を食べた

To show the agent in passive or verbs of receiving

> ペンを彼に貰った  
>  林檎が彼に食べられた
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grammar syntax particle-に
Why is に used in 若者が元気に溢れている?
You are understanding `に` correctly. This is actually a quirk of the verb 溢れる.
It can be used with either a subject (〜が) or with an object (〜に/〜で).

### 元気 as subject

> 若者に元気 **が** 溢れている  
>  _元気 is overflowing in the 若者_

### 元気 as object

> 若者が元気 **に** 溢れている  
>  _若者 is overflowing with 元気_

Just remember that when you are talking about something that is overflowing
_literally_ and not figuratively, you should put it as a subject:

  * コップから水 **が** 溢れている _Water is overflowing from the cup_
  * コップが水 **に** 溢れている ← unnatural

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There are other verbs like this that can be used both ways, for example:

  * 満ちる → 月 **が** 満ちる / (心が)喜び **に** 満ちる
  * 欠ける → 歯 **が** 欠ける / (彼は)常識 **に** 欠ける
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