<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:
    bool solved(vector<vector<int>>& a){
        if(a[0][0]==1 && a[0][1]==2 && a[0][2]==3 && a[1][0]==4 && a[1][1]==5 && a[1][2]==0)
            return true;
        return false;
    }
    int slidingPuzzle(vector<vector<int>>& board) {
        int n=2;
        int m=3;
        int u,v;
        for(int i=0;i<n;i++){
            for(int j=0;j<m;j++){
                if(board[i][j]==0){
                    u=i;
                    v=j;
                    break;
                }
            }
        }
        set<vector<vector<int>>>st;
        st.insert(board);
        int R[4]={1,-1,0,0};
        int C[4]={0,0,-1,1};
        queue<pair< pair<int, vector<vector<int>>>, pair<int,int> >>q;
        q.push({{0,board},{u,v}});
        while(!q.empty()){
            auto p=q.front();
            q.pop();
            int x=p.second.first;
            int y=p.second.second;
            int t=p.first.first;
            auto g=p.first.second;
            if(solved(g))
                return t;
            for(int k=0;k<4;k++){
                int a=x+R[k];
                int b=y+C[k];
                if(a>=0 && b>=0 && a<n && b<m){
                    swap(g[a][b],g[x][y]);
                    if(st.find(g)==st.end()){
                        q.push({{t+1,g},{a,b}});
                        st.insert(g);
                    }
                    swap(g[a][b],g[x][y]);
                }
            }
        }
        return -1;
    }
};
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