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Edit Distance

Problem​

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 Approach​

Expected Time complexity: O(n2)O(n^2)

Click - to see solution code
class Solution {
   public:
    int minDistance(string word1, string word2) {
        int m = word1.size();
        int n = word2.size();
        vector<vector<int>> dp(n + 1, vector<int>(m + 1, INT_MAX));

        for (int i = 0; i <= n; i++) dp[i][0] = i;
        for (int i = 0; i <= m; i++) dp[0][i] = i;

        for (int i = 1; i <= n; i++) {
            for (int j = 1; j <= m; j++) {
                dp[i][j] = min(dp[i][j], dp[i - 1][j] + 1);
                if (word1[j - 1] == word2[i - 1])
                    dp[i][j] = min(dp[i][j], dp[i - 1][j - 1]);
                dp[i][j] = min(dp[i][j], dp[i - 1][j - 1] + 1);
                dp[i][j] = min(dp[i][j], dp[i][j - 1] + 1);
            }
        }
        return dp[n][m];
    }
};