Find Two Numbers Adding Up to a Target

For the common unsorted, original-index version, scan once with a hash map from seen value to index. At value x, compute complement target-x and check whether it was seen; if yes, return that stored index and the current index, otherwise store x. Checking before storing avoids using the same element twice when target equals twice x. If the array is sorted and only values matter, inward two pointers use O(1) extra space, but sorting an unsorted array loses indices unless you store pairs. Ask whether all unique pairs are needed because duplicate handling then changes. Test a pair involving index zero, duplicate values, negative numbers, no solution, and arithmetic overflow in target-x for fixed-width types. The hash-map version is O(n) expected time and O(n) space; sorted two pointers are O(n) time after sorting, or O(n log n) including sort.