Given two strings word1 and word2, return the minimum number of operations needed to transform word1 into word2.

The following three operations are allowed on any character of a word:

• Insert a character

• Delete a character

• Replace a character

Constraints:

• $0 \leq$ word1.length, word2.length $\leq 500$

• word1 and word2 consist of lowercase English letters

The key insight behind this problem is that we can break the transformation of word1 into word2 into smaller overlapping subproblems. If we know the minimum edit distance for shorter prefixes, we can use those results to build the answer for longer prefixes.

We use a 2D dynamic programming table dp, where dp[i][j] represents the minimum number of operations required to convert the first i characters of word1 into the first j characters of word2.

At each cell, we either carry forward the value from a matching pair of characters or take the minimum cost among three possible operations: replace, delete, or insert.

Now, let’s look at the solution steps:

1. Compute the lengths m and n of word1 and word2.

2. Create a 2D dp table of size (m + 1) × (n + 1), initialized with 0. ...