Algorithm to find a duplicate entry in constant space and O(n) time

Question

Given an array of N integer such that only one integer is repeated. Find the repeated integer in O(n) time and constant space. There is no range for the value of integers or

Answer 1

If the range of the integers is bounded, you can perform a counting sort variant in O(n) time. The space complexity is O(k) where k is the upper bound on the integers(*), but that's a constant, so it's O(1).

If the range of the integers is unbounded, then I don't think there's any way to do this, but I'm not an expert at complexity puzzles.

(*) It's O(k) since there's also a constant upper bound on the number of occurrences of each integer, namely 2.

Answer 2

In the case where the entries are bounded by the length of the array, then you can check out Find any one of multiple possible repeated integers in a list and the O(N) time and O(1) space solution.

The generalization you mention is discussed in this follow up question: Algorithm to find a repeated number in a list that may contain any number of repeats and the O(n log^2 n) time and O(1) space solution.