<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>

class Solution {
public:
    int slidingPuzzle(vector<vector<int>>& board) {
        queue<vector<vector<int>>> q;
        q.push(board);
        set<vector<vector<int>>> st;
        st.insert(board);
        int moves = 0;

        vector<vector<int>> ans = {{1,2,3},{4,5,0}};
        vector<vector<int>> dir = {{1,0},{-1,0},{0,1},{0,-1}};

        while(!q.empty()){
            int s = q.size();
            while(s--){
                auto mat = q.front();
                q.pop();

                if(mat == ans){
                    return moves;
                }
                for(int i = 0; i < 2; i++){
                    for(int j = 0; j < 3; j++){
                        if(mat[i][j] == 0){
                            auto temp = mat;
                            for(int k = 0; k < 4; k++){
                                auto temp1 = temp;
                                int x = i + dir[k][0];
                                int y = j + dir[k][1];

                                if(x<0 || y<0 || x>=2 || y>=3){
                                    continue;
                                }

                                swap(temp1[i][j], temp1[x][y]);

                                if(st.find(temp1) == st.end()){
                                    st.insert(temp1);
                                    q.push(temp1);
                                }
                            }
                            break;
                        }
                    }
                }
            }
            moves++;
        }
        return -1;
    }
};
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