Create 72_Edit_Distance.md

Author: koji

72_Edit_Distance.md

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+## 72. Edit Distance
+
+```
+Given two strings word1 and word2, return the minimum number of operations required to convert word1 to word2.
+
+You have the following three operations permitted on a word:
+
+Insert a character
+Delete a character
+Replace a character
+ 
+
+Example 1:
+
+Input: word1 = "horse", word2 = "ros"
+Output: 3
+Explanation: 
+horse -> rorse (replace 'h' with 'r')
+rorse -> rose (remove 'r')
+rose -> ros (remove 'e')
+Example 2:
+
+Input: word1 = "intention", word2 = "execution"
+Output: 5
+Explanation: 
+intention -> inention (remove 't')
+inention -> enention (replace 'i' with 'e')
+enention -> exention (replace 'n' with 'x')
+exention -> exection (replace 'n' with 'c')
+exection -> execution (insert 'u')
+ 
+
+Constraints:
+
+0 <= word1.length, word2.length <= 500
+word1 and word2 consist of lowercase English letters.
+
+```
+
+
+```python
+class Solution:
+ def minDistance(self, word1: str, word2: str) -> int:
+ m = len(word1)
+ n = len(word2)
+ dp = [[float('inf')]*(n+1) for i in range(m+1)]
+ # print(dp)
+ dp[0][0]= 0
+ 
+ for i in range(0, m+1):
+ for j in range(0, n+1):
+ if i > 0 and j>0:
+ # word1[i] == word2[j]
+ if word1[i-1] == word2[j-1]:
+ dp[i][j] = min(dp[i][j], dp[i-1][j-1])
+ else:
+ dp[i][j] = min(dp[i][j], dp[i-1][j-1]+1)
+
+
+ # remove word1[i]
+ if i>0:
+ dp[i][j] = min(dp[i][j], dp[i-1][j]+1)
+
+ # remove word2[j]
+ if j>0:
+ dp[i][j] = min(dp[i][j], dp[i][j-1]+1)
+ 
+ return dp[-1][-1]
+```
+
+
+```
+Runtime: 432 ms, faster than 5.22% of Python3 online submissions for Edit Distance.
+Memory Usage: 17.8 MB, less than 41.17% of Python3 online submissions for Edit Distance.
+```