712. Minimum ASCII Delete Sum for Two Strings 

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class Solution {
    public int minimumDeleteSum(String s1, String s2) {
        int m = s1.length(), n = s2.length();

        // 定义 dp[i][j] 为使 s1 前 i 个字符组成的字符串与 s2 前 j 个字符组成的字符串相等所需删除字符的 ASCII 值的最小和
        int[][] dp = new int[m + 1][n + 1];
        int sum = 0;
        for (int i = 1; i <= m; i++) {
            sum += s1.charAt(i - 1);
            dp[i][0] = sum;
        }
        sum = 0;
        for (int j = 1; j <= n; j++) {
            sum += s2.charAt(j - 1);
            dp[0][j] = sum;
        }

        for (int i = 1; i <= m; i++) {
            char a = s1.charAt(i - 1);
            for (int j = 1; j <= n; j++) {
                char b = s2.charAt(j - 1);
                if (a == b) {
                    dp[i][j] = dp[i - 1][j - 1];
                } else {
                    dp[i][j] = Math.min(dp[i - 1][j] + a, dp[i][j - 1] + b);
                }
            }
        }

        return dp[m][n];
    }
}

References

712. Minimum ASCII Delete Sum for Two Strings