What is the time and space complexity of Edit Distance?

Time complexity: O(m * n). Space complexity: O(m * n).

Edit Distance

Hard

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Solution Guide: Edit Distance

Approach

Use 2D DP where each state compares prefixes. If current chars match, carry diagonal value; otherwise take min of insert/delete/replace transitions plus one.

Complexity Analysis

Time: O(m * n)
Space: O(m * n)

Pattern

2D Dynamic Programming

Why It Works

Optimal edit sequence has optimal substructure over smaller prefix pairs, which DP enumerates exhaustively.

Updated Mar 2026