Edit Distance

Medium

Strings Dynamic Programming Dynamic Programming

Problem

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

Constraints

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

Examples

Input: word1 = "horse", word2 = "ros"

Output: 3

horse -> rorse (replace 'h' with 'r'), rorse -> rose (remove 'r'), rose -> ros (remove 'e')

Input: word1 = "intention", word2 = "execution"

Output: 5

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')

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