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) + 1dp = [[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]