> ## 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.

# Sliding Puzzle Python Solution with Tests

> Tested Python solution for LeetCode 773 with 12 pytest cases. Generate a practice environment with lcpy.

LeetCode 773, [Hard](/catalog/hard). Topics: [Array](/catalog/topics/array), [Breadth-First Search](/catalog/topics/breadth-first-search), [Matrix](/catalog/topics/matrix). [View on LeetCode](https://leetcode.com/problems/sliding-puzzle/description/).

Generate this problem as a practice environment: tested reference solution, 12 [parametrized pytest cases](/practice/testing), and a playground notebook:

```bash theme={"theme":{"light":"github-light","dark":"github-dark"}}
lcpy gen -n 773   # by problem number
lcpy gen -s sliding_puzzle   # by problem name
```

## Problem

On an `2 x 3` board, there are five tiles labeled from `1` to `5`, and an empty square represented by `0`. A move consists of choosing `0` and a 4-directionally adjacent number and swapping it.

The state of the board is solved if and only if the board is `[[1,2,3],[4,5,0]]`.

Given the puzzle board `board`, return *the least number of moves required so that the state of the board is solved*. If it is impossible for the state of the board to be solved, return `-1`.

### Examples

![Example 1](https://assets.leetcode.com/uploads/2021/06/29/slide1-grid.jpg)

```
Input: board = [[1,2,3],[4,0,5]]
Output: 1
Explanation: Swap the 0 and the 5 in one move.
```

![Example 2](https://assets.leetcode.com/uploads/2021/06/29/slide2-grid.jpg)

```
Input: board = [[1,2,3],[5,4,0]]
Output: -1
Explanation: No number of moves will make the board solved.
```

![Example 3](https://assets.leetcode.com/uploads/2021/06/29/slide3-grid.jpg)

```
Input: board = [[4,1,2],[5,0,3]]
Output: 5
Explanation: 5 is the smallest number of moves that solves the board.
An example path:
After move 0: [[4,1,2],[5,0,3]]
After move 1: [[4,1,2],[0,5,3]]
After move 2: [[0,1,2],[4,5,3]]
After move 3: [[1,0,2],[4,5,3]]
After move 4: [[1,2,0],[4,5,3]]
After move 5: [[1,2,3],[4,5,0]]
```

### Constraints

* board.length == 2
* board\[i].length == 3
* 0 \<= board\[i]\[j] \<= 5
* Each value board\[i]\[j] is unique.

## Solution

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

```python theme={"theme":{"light":"github-light","dark":"github-dark"}}
from collections import deque


class Solution:
    # Time: O((n * m)!) states, each expanded once
    # Space: O((n * m)!)
    def sliding_puzzle(self, board: list[list[int]]) -> int:
        target = (1, 2, 3, 4, 5, 0)
        start = tuple(x for row in board for x in row)
        neighbors = ((1, 3), (0, 2, 4), (1, 5), (0, 4), (1, 3, 5), (2, 4))

        queue = deque([(start, start.index(0), 0)])
        seen = {start}
        while queue:
            state, zero, moves = queue.popleft()
            if state == target:
                return moves
            for nz in neighbors[zero]:
                nxt = list(state)
                nxt[zero], nxt[nz] = nxt[nz], nxt[zero]
                ns = tuple(nxt)
                if ns not in seen:
                    seen.add(ns)
                    queue.append((ns, nz, moves + 1))
        return -1
```

## Complexity

| Time | Space |
| - | - |
| O((n \* m)!) states, each expanded once | O((n \* m)!) |

## Tags

[NeetCode All](/catalog/neetcode).


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