41. First Missing Positive

Cyclic sort in place. For each index i, while nums[i] is in [1, n] and nums[nums[i] - 1] != nums[i], swap nums[i] with nums[nums[i] - 1]. This puts each value v in [1, n] at index v - 1. The inner condition prevents infinite loops when duplicates would otherwise endlessly swap. Values outside [1, n] (zeros, negatives, values > n) are simply skipped — they can't be answers and don't need a home. After the placement pass, walk the array: the first index i where nums[i] != i + 1 means i + 1 is missing, so return i + 1. If every slot is correct, the answer is n + 1. The algorithm is O(n) because each swap moves a value into its correct slot, so the total number of swaps is bounded by n. O(1) extra space because we mutate in place.