79. Edit Distance

class Solution:
    def minDistance(self, word1: str, word2: str) -> int:
        m, n = len(word1), len(word2)
        dp = [[0] * (n + 1) for _ in range(m + 1)]   # dp[i][j]: edits for word1[:i] -> word2[:j]
        for i in range(m + 1): dp[i][0] = i          # delete everything
        for j in range(n + 1): dp[0][j] = j          # insert everything
        for i in range(1, m + 1):
            for j in range(1, n + 1):
                if word1[i - 1] == word2[j - 1]:
                    dp[i][j] = dp[i - 1][j - 1]
                else:
                    dp[i][j] = 1 + min(dp[i - 1][j],      # delete
                                       dp[i][j - 1],      # insert
                                       dp[i - 1][j - 1])  # replace
        return dp[m][n]

class Solution {
    public int minDistance(String word1, String word2) {
        int m = word1.length(), n = word2.length();
        int[][] dp = new int[m + 1][n + 1];
        for (int i = 0; i <= m; i++) dp[i][0] = i;
        for (int j = 0; j <= n; j++) dp[0][j] = j;
        for (int i = 1; i <= m; i++)
            for (int j = 1; j <= n; j++)
                dp[i][j] = word1.charAt(i - 1) == word2.charAt(j - 1) ? dp[i - 1][j - 1]
                         : 1 + Math.min(dp[i - 1][j - 1], Math.min(dp[i - 1][j], dp[i][j - 1]));
        return dp[m][n];
    }
}

class Solution {
public:
    int minDistance(string word1, string word2) {
        int m = word1.size(), n = word2.size();
        vector<vector<int>> dp(m + 1, vector<int>(n + 1));
        for (int i = 0; i <= m; i++) dp[i][0] = i;
        for (int j = 0; j <= n; j++) dp[0][j] = j;
        for (int i = 1; i <= m; i++)
            for (int j = 1; j <= n; j++)
                dp[i][j] = word1[i - 1] == word2[j - 1] ? dp[i - 1][j - 1]
                         : 1 + min({dp[i - 1][j - 1], dp[i - 1][j], dp[i][j - 1]});
        return dp[m][n];
    }
};

function minDistance(word1, word2) {
  const m = word1.length, n = word2.length;
  const dp = Array.from({ length: m + 1 }, (_, i) => Array.from({ length: n + 1 }, (_, j) => (i === 0 ? j : j === 0 ? i : 0)));
  for (let i = 1; i <= m; i++)
    for (let j = 1; j <= n; j++)
      dp[i][j] = word1[i - 1] === word2[j - 1] ? dp[i - 1][j - 1]
        : 1 + Math.min(dp[i - 1][j - 1], dp[i - 1][j], dp[i][j - 1]);
  return dp[m][n];
}