712. Minimum ASCII Delete Sum for Two Strings

// Approach: LCS-variant DP where the cost is the sum of ASCII values deleted;
// dp[i][j] = min total ASCII cost to equalize s1[0..i) and s2[0..j).
// Time: O(m*n) Space: O(m*n)

public class Solution
{
    public int MinimumDeleteSum(string s1, string s2)
    {
        int m = s1.Length;
        int n = s2.Length;
        // dp[i,j] := the minimum cost to make s1[0..i) and s2[0..j) equal
        int[,] dp = new int[m + 1, n + 1];

        // Delete s1[i - 1].
        for (int i = 1; i <= m; ++i)
            dp[i, 0] = dp[i - 1, 0] + s1[i - 1];

        // Delete s2[j - 1].
        for (int j = 1; j <= n; ++j)
            dp[0, j] = dp[0, j - 1] + s2[j - 1];

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

        return dp[m, n];
    }
}