Edit Distance

Problem Statement: Given two strings word1 and word2, return the minimum number of operations required to convert word1 to word2. We can use the following three operations on the string:

1.    Insert a character.

2.    Delete a character.

3.    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')

Solution:

To solve this problem, we use dynamic programming. We define a 2D array dp where dp[i][j] represents the minimum number of operations required to convert the first i characters of word1 to the first j characters of word2.

Time Complexity: O(m x n)

Space Complexity: O(m x n)