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

<p>The state of the board is solved if and only if the board is <code>[[1,2,3],[4,5,0]]</code>.</p>

<p>Given the puzzle board <code>board</code>, return <em>the least number of moves required so that the state of the board is solved</em>. If it is impossible for the state of the board to be solved, return <code>-1</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/06/29/slide1-grid.jpg" style="width: 244px; height: 165px;" />
<pre>
<strong>Input:</strong> board = [[1,2,3],[4,0,5]]
<strong>Output:</strong> 1
<strong>Explanation:</strong> Swap the 0 and the 5 in one move.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/06/29/slide2-grid.jpg" style="width: 244px; height: 165px;" />
<pre>
<strong>Input:</strong> board = [[1,2,3],[5,4,0]]
<strong>Output:</strong> -1
<strong>Explanation:</strong> No number of moves will make the board solved.
</pre>

<p><strong class="example">Example 3:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/06/29/slide3-grid.jpg" style="width: 244px; height: 165px;" />
<pre>
<strong>Input:</strong> board = [[4,1,2],[5,0,3]]
<strong>Output:</strong> 5
<strong>Explanation:</strong> 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]]
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>board.length == 2</code></li>
	<li><code>board[i].length == 3</code></li>
	<li><code>0 &lt;= board[i][j] &lt;= 5</code></li>
	<li>Each value <code>board[i][j]</code> is <strong>unique</strong>.</li>
</ul>

#include <vector>
#include <unordered_map>
#include <queue>
#include <algorithm>
using namespace std;

class Solution {
public:
    struct vector_hash {
        size_t operator()(const vector<vector<int>>& v) const {
            size_t hash = 0;
            for (const auto& row : v) {
                for (int num : row) {
                    hash = hash * 31 + num;
                }
            }
            return hash;
        }
    };
    
    unordered_map<vector<vector<int>>, int, vector_hash> m;

    bool check(vector<vector<int>>& t) {
        vector<int> temp;
        for (int i = 0; i < 2; i++) {
            for (int j = 0; j < 3; j++) {
                temp.push_back(t[i][j]);
            }
        }
        for (int i = 0; i < 5; i++) if (temp[i] != i + 1) return false;
        return true;
    }

    int bfs(vector<vector<int>>& board, int x, int y) {
        int moves = 0;
        queue<pair<vector<vector<int>>, pair<int, int>>> q;
        q.push({board, {x, y}});
        m[board] = 1;

        while (!q.empty()) {
            int sz = q.size();

            while (sz--) {
                auto [curBoard, pos] = q.front();
                int i = pos.first;
                int j = pos.second;
                q.pop();

                for (int p = -1; p <= 1; p++) {
                    for (int r = -1; r <= 1; r++) {  // renamed loop variable q to r
                        if ((abs(p) + abs(r)) == 2) continue;

                        int nx = i + p;
                        int ny = j + r;

                        if (nx >= 0 && nx < 2 && ny >= 0 && ny < 3) {
                            swap(curBoard[i][j], curBoard[nx][ny]);
                            if (m.find(curBoard) == m.end()) {
                                if (check(curBoard)) return moves + 1;
                                q.push({curBoard, {nx, ny}});
                                m[curBoard] = 1;
                            }
                            swap(curBoard[i][j], curBoard[nx][ny]);  // restore the original state
                        }
                    }
                }
            }
            moves++;
        }
        return -1;
    }

    int slidingPuzzle(vector<vector<int>>& board) {
        if (check(board)) return 0;
        for (int i = 0; i < 2; i++) {
            for (int j = 0; j < 3; j++) {
                if (board[i][j] == 0) {
                    return bfs(board, i, j);
                }
            }
        }
        return -1;
    }
};

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