HardDp
Edit Distance
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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')
Example 3:
Input: word1 = "", word2 = "abc"
Output: 3
Explanation: Insert 'a', 'b', and 'c' into the empty string.
Examples
Example 1
Input: word1 = "horse", word2 = "ros"
Output: 3
Explanation: horse -> rorse (replace 'h' with 'r') -> rose (remove second 'r') -> ros (remove 'e'). Three operations total.
Example 2
Input: word1 = "intention", word2 = "execution"
Output: 5
Explanation: Five operations: remove 't', replace 'i' with 'e', replace first 'n' with 'x', replace second 'n' with 'c', insert 'u'.
Constraints
- -0 <= word1.length, word2.length <= 500
- -word1 and word2 consist of lowercase English letters
Optimal Complexity
Time
O(m * n)
Space
O(m * n)
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