# What is the time complexity of this randomized algorithm? [closed]

given an array of length $n$ with numbers $1$ through $n$ (inclusive), consider the following steps:

1. Select a random number $k$ in range $[1, n]$.
2. Set $a[k] = q$.
3. If there exists element $p$ in $a$ such that $p \ne q$, go to step 1, otherwise end.

So, basically we are going to randomly pick elements in the array and set them to some predefined value until every element in the array is set to this value. What is the time complexity of such algorithm? please explain your answer.

## closed as unclear what you're asking by Juho, Evil, Yuval Filmus, David Richerby, Rick DeckerDec 2 '16 at 3:19

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• This is a well-known problem that comes up in different guises. Where did you get stuck in solving the problem? – Juho Nov 30 '16 at 17:25
• makes sense to think about Average-case complexity – Billiska Nov 30 '16 at 19:32