<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 valid(int i , int j){
        return i>=0 && i<2 && j>=0 && j<3 ;
    }
    pair<int,int> Z(vector<vector<int>>& b){
        for(int i = 0; i < 2; i++) {
        for (int j = 0; j < 3; j++) {
            if(b[i][j] == 0) {
                return {i, j};
            }
        }
    }
    return {-1,-1};
    }
    int bfs(vector<vector<int>>& b){
        queue<    pair<   vector<vector<int>>,int   >    > Q ;
        set<vector<vector<int>>> visited ;
        Q.push({b,0}); visited.insert(b) ;
        while(!Q.empty()){
            auto [B,M] = Q.front() ; Q.pop() ;
            if(B[0][0]==1&&B[0][1]==2&&B[0][2]==3&&B[1][0]==4&&B[1][1]==5)return M ;
            auto X = Z(B);
               std::vector<std::pair<int, int>> directions = {{1, 0}, {-1, 0}, {0, 1}, {0, -1}};
            for (auto [dx, dy] : directions) {
                int nx = X.first + dx, ny = X.second + dy;
                if (valid(nx, ny)) {
                    std::vector<std::vector<int>> T = B;
                    std::swap(T[X.first][X.second], T[nx][ny]);
                    if (visited.find(T) == visited.end()) {
                        visited.insert(T);
                        Q.push({T, M + 1});
                    }
                }
            }
        }
    return -1 ;
    }
    int slidingPuzzle(vector<vector<int>>& b) {
        if(b[0][0]==1&&b[0][1]==2&&b[0][2]==3&&b[1][0]==4&&b[1][1]==5)return 0 ;
        return bfs(b);
    }
};



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