<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) {
        vector<vector<int>> finalb = {{1,2,3},{4,5,0}};
        if(board == finalb)
            return 0;

        vector<vector<int>> moves = {{1,3},{0,2,4},{1,5},{0,4},{1,3,5},{2,4}};
        
        vector<int> loc;
        int m = 2, n = 3;
        for(int i = 0;i<m;i++){
            for(int j = 0;j<n;j++){
                if(board[i][j] == 0){
                    loc.push_back(i); loc.push_back(j);
                    break;
                }
            }
        }

        queue<vector<vector<int>>> bq;
        queue<vector<int>> q;
        set<vector<vector<int>>> visit;
        bq.push(board);
        q.push(loc);
        int step = 0;
        while(!q.empty()){
            int sz = q.size();
            step++;
            for(int i = 0;i<sz;i++){
                vector<int> p = q.front(); q.pop();
                vector<vector<int>> b = bq.front(); bq.pop();
                if(visit.count(b))
                    continue;

                visit.insert(b);
                int id = p[0]*3+p[1];



                for(int nid: moves[id]){
                    int x = nid/3;
                    int y = nid%3;
                    vector<vector<int>> newb(b.begin(), b.end());
                    swap(newb[p[0]][p[1]], newb[x][y]);
                    if(!visit.count(newb)){
                        if(x==1&&y==2 && newb == finalb){
                            return step;
                        }

                        q.push({x, y});
                        bq.push(newb);
                    }
                }
            }
            
        }
        return -1;
    }
};
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