Edit Distance
Difficulty: Medium
Category: DSA
Topics: String, Dynamic Programming
Asked at: Amazon, Microsoft, Google, Square, Palantir Technologies
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.