<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 {
    
    
    
private: 
    vector<vector<int>> neigh={{1,3},{0,2,4}, {1,5},{0,4},{1,3,5},{2,4} };
public:
    
    
    
    // 0,1,2
    // 3,4,5
    
    // 0-1,0-3,1-2,1-4,3-4,4-5,2-5
    
    
    int bfs_helper(string board){
        set<string> vis;
        queue<string> q;
        q.push(board);
        int sz=1,nx=0;
        int ans=0;
        while(q.size()){
            string x=q.front();q.pop();
            --sz;
            if(x=="123450"){
                return ans;
            }
            int hole=0;
            for(int i=0;i<6;++i){
                if(x[i]=='0'){
                    hole=i;
                }
            }
            for(auto& y: neigh[hole]){
                string tmp=x;
                swap(tmp[hole],tmp[y]);
                if(vis.find(tmp)==vis.end()){
                    vis.insert(tmp);
                    q.push(tmp);
                    ++nx;
                }
            }
            if(sz==0){
                ++ans;
                sz=nx;
                nx=0;
            }
            
        }
        return -1;
        
    }
    
    
    int slidingPuzzle(vector<vector<int>>& board) {
        string s;
        for(int j=0;j<2;++j){
            for(int i=0;i<3;++i){
                s+=('0'+board[j][i]);
            }
        }
        return bfs_helper(s);
        
    }
};
11015