## 72. Edit Distance

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.

## Rust Solution

``````struct Solution;

impl Solution {
fn min_distance(word1: String, word2: String) -> i32 {
let n = word1.len();
let m = word2.len();
let word1: Vec<char> = word1.chars().collect();
let word2: Vec<char> = word2.chars().collect();
let mut dp = vec![vec![0; m + 1]; n + 1];
for i in 0..=n {
dp[i] = i;
}
for j in 0..=m {
dp[j] = j;
}
for i in 1..=n {
for j in 1..=m {
if word1[i - 1] == word2[j - 1] {
dp[i][j] = dp[i - 1][j - 1];
} else {
dp[i][j] = dp[i - 1][j].min(dp[i][j - 1]).min(dp[i - 1][j - 1]) + 1;
}
}
}
dp[n][m] as i32
}
}

#[test]
fn test() {
let word1 = "horse".to_string();
let word2 = "ros".to_string();
let res = 3;
assert_eq!(Solution::min_distance(word1, word2), res);
let word1 = "intention".to_string();
let word2 = "execution".to_string();
let res = 5;
assert_eq!(Solution::min_distance(word1, word2), res);
}
``````

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