> ## Documentation Index
> Fetch the complete documentation index at: https://leetcode-py.wisl.dev/llms.txt
> Use this file to discover all available pages before exploring further.

> ## Agent Instructions
> leetcode-py is a Python LeetCode practice environment generator with one CLI: lcpy. It is not a service or platform.
> Each problem is a directory under leetcode/ with README.md, solution.py, test_solution.py, helpers.py, and playground.ipynb. lcpy gen creates them from JSON templates bundled with the package.
> Examples are backed by tests; copy them verbatim.

# Edit Distance Python Solution with Tests

> Tested Python solution for LeetCode 72 with 14 pytest cases. Generate a practice environment with lcpy.

LeetCode 72, Hard. Topics: String, Dynamic Programming. [View on LeetCode](https://leetcode.com/problems/edit-distance/description/).

Generate this problem as a practice environment: tested reference solution, 14 [parametrized pytest cases](/practice/testing), and a playground notebook:

```bash theme={"theme":{"light":"github-light","dark":"github-dark"}}
lcpy gen -n 72   # by problem number
lcpy gen -s edit_distance   # by problem name
```

## Problem

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

### Examples

```
Input: word1 = "horse", word2 = "ros"
Output: 3
Explanation:
horse -> rorse (replace 'h' with 'r')
rorse -> rose (remove 'r')
rose -> ros (remove 'e')
```

```
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.

## Solution

Reference implementation from [solution.py on GitHub](https://github.com/wislertt/leetcode-py/blob/main/leetcode/edit_distance/solution.py), full suite in [test\_solution.py](https://github.com/wislertt/leetcode-py/blob/main/leetcode/edit_distance/test_solution.py):

```python theme={"theme":{"light":"github-light","dark":"github-dark"}}
class Solution:
    # Time: O(m * n)
    # Space: O(n) using a single rolling row
    def min_distance(self, word1: str, word2: str) -> int:
        m, n = len(word1), len(word2)
        # dp[j] = edit distance between word1 prefix (current row) and word2[:j]
        prev = list(range(n + 1))
        for i in range(1, m + 1):
            curr = [i] + [0] * n
            for j in range(1, n + 1):
                if word1[i - 1] == word2[j - 1]:
                    curr[j] = prev[j - 1]
                else:
                    curr[j] = 1 + min(prev[j], curr[j - 1], prev[j - 1])
            prev = curr
        return prev[n]
```

## Complexity

| Time      | Space                           |
| --------- | ------------------------------- |
| O(m \* n) | O(n) using a single rolling row |

## Tags

[NeetCode 150](/catalog/neetcode-150), [NeetCode 250](/catalog/neetcode-250), [NeetCode All](/catalog/neetcode).