minDistance.cpp

class Solution {
public:
    int minDistance(string word1, string word2) {
        int n = word1.length();
        int m = word2.length();

        // if one of the strings is empty
        if (n * m == 0)
          return n + m;

        // array to store the convertion history
        int d[n+1][m+1];

        // init boundaries
        for (int i = 0; i < n + 1; i++) {
          d[i][0] = i;
        }
        for (int j = 0; j < m + 1; j++) {
          d[0][j] = j;
        }

        // DP compute 
        for (int i = 1; i < n + 1; i++) {
          for (int j = 1; j < m + 1; j++) {
            int left = d[i - 1][j] + 1;
            int down = d[i][j - 1] + 1;
            int left_down = d[i - 1][j - 1];
            if (word1[i - 1] != word2[j - 1])
              left_down += 1;
            d[i][j] = min(left, min(down, left_down));

          }
        }
        return d[n][m];
    }
};