Edit distance

String Dynamic Programming

60.2% acceptance

Jan 12, 2026

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Given two strings word1 and word2, return the minimum number of operations required to convert word1 to word2. You have the following three operations permitted on a word: Insert a character Delete a character Replace a character

Solution

Rust

Time O(n²)

Space O(n)

LeetCode

solution.rs

impl Solution {
  pub fn min_distance(word1: String, word2: String) -> i32 {
    let (m, n) = (word1.len(), word2.len());
    let (word1, word2) = (word1.as_bytes(), word2.as_bytes());
    
    // Space-optimized DP: O(n) instead of O(m*n)
    let mut dp = (0..=n as i32).collect::<Vec<_>>();
    
    for i in 1..=m {
      let mut prev = dp[0];
      dp[0] = i as i32;
      
      for j in 1..=n {
        let temp = dp[j];
        dp[j] = if word1[i-1] == word2[j-1] {
          prev
        } else {
          1 + prev.min(dp[j]).min(dp[j-1])
        };
        prev = temp;
      }
    }
    
    dp[n]
  }
}