Edit Distance

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

Examples

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'.

Constraints

• 0 <= word1.length, word2.length <= 500
• word1 and word2 consist of lowercase English letters.

Expected Complexity

• Time: O(m * n) where m and n are the lengths of the two strings
• Space: O(m * n) for the DP table, or O(n) with space optimization