Leetcode 712. Minimum ASCII Delete Sum for Two Strings

Problem

Given two strings s1 and s2, return the lowest ASCII sum of deleted characters to make two strings equal.

Algorithm

Dynamic Programming (DP): similar as Longest Common Subsequence (LCS).

• If s1[i] != s2[j]:
  $$F(i,j)=\min \left(F(i-1,j)+\text{cost}(s1[i]),F(i,j-1)+\text{cost}(s2[j])\right)$$

• If s1[i] == s2[j]:
  $$F(i,j)=F(i-1,j-1)$$

Code

class Solution:
    def minimumDeleteSum(self, s1: str, s2: str) -> int:
        l1, l2 = len(s1) + 1, len(s2) + 1
        dp = [[0] * l2 for _ in range(l1)] 

        for i in range(1, l1):
            dp[i][0] = dp[i-1][0] + ord(s1[i-1])
        for j in range(1, l2):
            dp[0][j] = dp[0][j-1] + ord(s2[j-1])
        
        for i in range(1, l1):
            for j in range(1, l2):
                if s1[i-1] == s2[j-1]:
                    dp[i][j] = dp[i-1][j-1]
                else:
                    dp[i][j] = min(dp[i-1][j] + ord(s1[i-1]), dp[i][j-1] + ord(s2[j-1]))
        
        return dp[l1-1][l2-1]