<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) {
        map<vector<vector<int>>,int> mp;
        priority_queue<pair<int,vector<vector<int>>>, vector<pair<int,vector<vector<int>>>>, greater<pair<int,vector<vector<int>>>>>pq;
        pq.push({0,board});
        while(!pq.empty()){
            int val = pq.top().first;
            vector<vector<int>> b = pq.top().second;
            mp[b]=val;
            // if(val > 20){break;}
            pq.pop();
            if(b == vector<vector<int>>{{1,2,3},{4,5,0}}){return val;}
            for(int i=0; i<2;i++){
                for(int j=0;j<3;j++){
                    if(b[i][j]==0){
                        if(i-1 == 0){
                            swap(b[i-1][j],b[i][j]);
                            if(!mp[b])pq.push({val+1,b});
                            swap(b[i-1][j],b[i][j]);
                        }
                        if(i+1 == 1){
                            swap(b[i+1][j],b[i][j]);
                            if(!mp[b])pq.push({val+1,b});
                            swap(b[i+1][j],b[i][j]);
                        }
                        if(j-1>=0){
                            swap(b[i][j-1],b[i][j]);
                            if(!mp[b])pq.push({val+1,b});
                            swap(b[i][j-1],b[i][j]);
                        }
                        if(j+1<3){
                            swap(b[i][j+1],b[i][j]);
                            if(!mp[b])pq.push({val+1,b});
                            swap(b[i][j+1],b[i][j]);
                        }
                    }
                }
            }
        }
        return -1;
    }
};
20121