First Missing Positive

The constrained solution uses the array itself as an indexable presence table. With n elements, the first missing positive is in [1,n+1]. While scanning, repeatedly swap a value x into index x-1 whenever x is in [1,n] and that home does not already contain x. Once no more placements are possible, the first index i not containing i+1 identifies the missing positive; otherwise the answer is n+1. The swap guard is essential for duplicates such as [1,1], where blindly swapping equal values never progresses. Explain that each successful swap places a distinct correct value, so total swaps are O(n). Test empty input, only negatives, zero, duplicates, and a fully complete range. This is O(n) time and O(1) auxiliary space but mutates input. A hash-set alternative is simpler and O(n) expected time with O(n) space when mutation is forbidden.