Spotting a repeat among values 0 to N-1

An integer array of length $N$ holds values between $0$ and $N-1$. You may overwrite the array. Determine whether some value appears more than once.

Use the array itself as the visited marker: $O(N)$ time, $O(1)$ extra space. For each position, while $a[i]\ne i$, look at $a[a[i]]$: if it already equals $a[i]$ you have a duplicate, otherwise swap to put that value in its home slot. Each swap fixes one value permanently, so total work is linear; if all slots end up home, there is no repeat. (Sorting is $O(N\log N)$; a separate seen-array is $O(N)$ space.)