Two-Pointer Technique Explained: Cut Algorithm Time from O(n²) to O(n)

The two-pointer technique is a programming pattern that reduces time complexity by placing one pointer at each end of a sorted array and moving them inward based on defined conditions. Instead of comparing every possible pair in nested loops, each step eliminates an entire region of impossible solutions, achieving linear time. The approach applies to classic problems such as finding the maximum water container area and identifying all triplets in an array that sum to zero. For the container problem, pointers move from the shorter side inward, preserving the invariant that no better solution exists in the discarded region. For the three-sum problem, fixing one element reduces the search to a two-pointer scan, keeping overall complexity at O(n²) while duplicate-skipping logic prevents repeated results.