What is the time and space complexity of Permutation in String?

Time complexity: O(n). Space complexity: O(1).

Permutation in String

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Concept

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Solution Guide: Permutation in String

Approach

Build a frequency map for s1. Slide a fixed-size window of length s1.length over s2, maintaining a frequency map for the current window. At each position, compare the two frequency maps. If they match, s2 contains a permutation of s1.

Complexity Analysis

Time: O(n)
Space: O(1)

Pattern

Sliding Window (Fixed Size + Frequency)

Why It Works

Two strings are permutations of each other if and only if they have identical character frequencies. By maintaining a sliding frequency map, we check every possible substring of the correct length in O(1) amortized time per position.

Updated Feb 2026