<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 dx[4] = {1,0,-1,0};
    int dy[4] = {0,1,0,-1};

    int slidingPuzzle(vector<vector<int>>& board) {
        int row = board.size();
        int col = board[0].size();
        int starti = 0;
        int endi = 0;
        for(int i=0; i<row; i++){
            for(int j=0; j<col; j++){
                if(board[i][j] == 0){
                    starti = i;
                    endi = j;
                }
            }
        }
        priority_queue<tuple<int, vector<vector<int>>, int, int>, vector<tuple<int, vector<vector<int>>, int, int>>, greater<tuple<int, vector<vector<int>>, int , int>>>pq;
        set<vector<vector<int>>>s;

        pq.push({0, board, starti, endi});
        s.insert(board);

        while(!pq.empty()){
            auto [count, grid, i, j] = pq.top();
            pq.pop();
            if(grid[0][0] == 1 && grid[0][1] == 2 && grid[0][2] == 3 && grid[1][0] == 4 && grid[1][1] == 5 && grid[1][2] == 0){
                return count;
            }

            for(int k=0; k<4; k++){
                int xx = i + dx[k];
                int yy = j + dy[k];
                if(xx>=0 and xx<row and yy>=0 and yy<col){
                    swap(grid[i][j], grid[xx][yy]);
                    if(!s.count(grid)){
                        pq.push({count+1,grid, xx, yy});
                        s.insert(grid);
                    }
                    swap(grid[i][j], grid[xx][yy]);
                }
            } 
        }
        return -1;
    }
};
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