Find the first missing positive

For an array of length n, the smallest missing positive must lie in 1 through n plus 1. Therefore values less than one or greater than n need no dedicated slot. Iterate through indices; while nums[i] is in range and nums[nums[i]-1] differs from nums[i], swap the current value into its home index. The inequality check prevents an infinite loop on duplicates. Once placement finishes, scan from index zero: the first place i where nums[i] is not i plus one implies i plus one is missing; if none exists, return n plus one. Explain why swapping makes progress because it places at least one value in its final home. Test empty input, all negatives, [1,2,0], duplicates, and arrays already containing 1 through n. Time is O(n) because each successful swap fixes a position, and auxiliary space is O(1) when mutation is allowed.