int minDistance(string word1, string word2) {

int n = word1.length();

int m = word2.length();

// 有一个字符串为空串

if (n * m == 0) return n + m;

// DP 数组

int D[n + 1][m + 1];

// 边界状态初始化

for (int i = 0; i < n + 1; i++) {

D[i][0] = i;

}

for (int j = 0; j < m + 1; j++) {

D[0][j] = j;

}

// 计算所有 DP 值

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];

}