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Two Pointers
Two indices moving through a sequence — from opposite ends or in lockstep — to cut brute-force O(n²) scans to O(n).
Study first: Arrays & Hashing
What it is
Two pointers is a technique for scanning a sequence (usually sorted, or with a monotonic property) using two indices that move according to a rule, instead of nested loops.
Common shapes
- Opposite ends closing in — e.g. finding a pair that sums to a target in a sorted array: move the low pointer up or the high pointer down based on the comparison.
- Fast/slow pointers — one pointer advances twice as fast as the other; used for cycle detection and finding the middle element.
- Read/write pointers — one pointer scans, the other marks where the next valid element should be written, useful for in-place array modification (removing duplicates, partitioning).
Why it beats brute force
A nested loop comparing every pair is O(n²). Two pointers exploit a monotonic property (sortedness, or "moving one pointer can only help, never hurt") to guarantee each pointer moves at most n times, giving O(n).
Prerequisite for
Binary search (pointers bounding a search space), sliding window (a variable-size two-pointer window), and the linked list fast/slow pattern all specialize this idea.