<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 dx [4] = {0,0,1,-1};
    int dy [4] = {-1,1,0,0};
    unordered_set<string> visited ;
    string board_string (vector<vector<int>>& board)
    {
        string strboard ;
        for(int i = 0 ; i < 2 ; i++)
            for(int j = 0 ; j < 3 ; j++)
                strboard.push_back(char(board[i][j]+48));
    return strboard ;
    }
    bool isvisit_board (vector<vector<int>>& board)
    {
        string strboard = board_string(board);
        return (visited.count(strboard));
    }
    void visit_board (vector<vector<int>>& board)
    {
        string strboard = board_string(board);
        visited.insert(strboard);
    }
    bool isvalid_board (vector<vector<int>>& board)
    {
    return (board[0][0]== 1 &&
           board[0][1]== 2 &&
           board[0][2]== 3 &&
           board[1][0]== 4 &&
           board[1][1]== 5 &&
           board[1][2]== 0 );
    }
    bool isvaild_pos (int x , int y)
    {
    return x >= 0 && x < 2 && y >= 0 && y < 3 ;
    }
    int slidingPuzzle(vector<vector<int>>& board) {
       queue<vector<vector<int>>>qu ;
       qu.push(board);
       visit_board(board);
       for(int level = 0 , sz = 1 ; !qu.empty();level++,sz=qu.size())
       {
            while(sz--)
            {
                vector<vector<int>>board2 = qu.front();
                qu.pop();
                if(isvalid_board(board2))return level ;
                int x_axis , y_axis ;
                for (int i=0 ; i < 2 ; i++)
                    for(int j = 0 ; j < 3 ; j++)
                        if(board2[i][j]==0)  x_axis = i , y_axis =j;
                for (int i = 0 ; i < 4 ; i++)
                {
                    if (isvaild_pos(x_axis+dx[i],y_axis+dy[i])==0)continue ;
                    vector<vector<int>>board3 (2,vector<int>(3));
                    copy(board2.begin(),board2.end(),board3.begin());
                    board3[x_axis][y_axis] = board3[x_axis+dx[i]][y_axis+dy[i]];
                    board3[x_axis+dx[i]][y_axis+dy[i]] = 0 ;
                    if (isvisit_board(board3))continue ;
                    qu.push(board3);
                    visit_board(board3);
                }
            }
       } 
    return -1 ; 
    }
};
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