Two-Pointer Based

A two-pointer-based solution should begin with the property that permits it. For sorted values and a target relation, use endpoints and preserve the invariant that every unexamined answer lies between them. Compare the current pair, then eliminate an entire row or column of candidates by moving the endpoint whose change can improve the comparison. For a lead-lag list problem, create a fixed gap first and move both pointers so their gap remains invariant. In either form, each pointer advances monotonically, giving O(n) time and usually O(1) extra space. If input ordering is absent, decide whether sorting is acceptable or whether a hash-based method better preserves indices. Cover no solution, duplicate values, empty and one-element inputs, and arithmetic overflow. Do not present the technique as universal: its correctness comes from monotonic structure.