0583.Delete_Operation_for_Two_Strings.py

"""
Given two strings word1 and word2, return the minimum number of steps required to make word1 and word2 the same.

In one step, you can delete exactly one character in either string.

 

Example 1:

Input: word1 = "sea", word2 = "eat"
Output: 2
Explanation: You need one step to make "sea" to "ea" and another step to make "eat" to "ea".
Example 2:

Input: word1 = "leetcode", word2 = "etco"
Output: 4
 

Constraints:

1 <= word1.length, word2.length <= 500
word1 and word2 consist of only lowercase English letters.
"""

"""
dp[i][j] 代表最小的步骤你需要做的是的word1[:i] and word[:j]相同，不包括i,j
求dp[m][n]
"""
class Solution:
    def minDistance(self, word1: str, word2: str) -> int:
        m = len(word1)
        n = len(word2)
        
        dp = [[0]*(n+1) for _ in range(m+1)]
        
        for i in range(m+1):
            dp[i][0] = i
        for j in range(n+1):
            dp[0][j] = j
            
        for i in range(1, m+1):
            for j in range(1, n+1):
                if word1[i-1] == word2[j-1]:
                    dp[i][j] = dp[i-1][j-1]
                else:
                    dp[i][j] = 1 + min(dp[i-1][j], dp[i][j-1])
                    
        return dp[m][n]