72. Edit Distance

Problem #72 (Edit Distance | Dynamic Programming, String)

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.

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Solutions

Approach: Dynamic Programming

• Levenshtein Distance