Edit Distance LeetCode solution in C++

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