two-pointers

name	two-pointers
description	Solve pair-sum, sliding window, and cycle detection problems with two pointers. Use when reducing O(n²) nested loops to O(n) on sorted or sequential data.
topic	Two Pointers and Sliding Window
token_cost	100
related	["binary-search","sorting-choice","hash-vs-tree"]
keywords	["pointer","two","sliding","window","substring","subarray","pair","sum","target","sorted","left","right","fast","slow","cycle","linked","list","contiguous","consecutive","squeeze"]

When to use

Two pointers on a sorted array: start left=0, right=n-1, move inward based on comparison.

Rules

• Solves pair-sum, three-sum, container problems in O(n)
• Sliding window: expand right boundary, shrink left when constraint violated
• Solves "longest/shortest substring with property" in O(n)
• Fast/slow pointers: detect cycles in linked lists (Floyd's), find middle element
• If brute force is O(n^2) nested loops over a sorted or sequential structure, two pointers likely reduces it to O(n)
• ALWAYS prefer two pointers over nested loops when data is sorted
• NEVER use nested loops when two pointers would work

Complexity

Two pointers: O(n). Sliding window: O(n). Fast/slow: O(n).

Example

"Two sum on sorted" → left=0, right=n-1; if arr[left]+arr[right] < target: left++, else right--. "Longest substring without repeats" → expand right, shrink left when duplicate found.