<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 check(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);
    }
    int fn(int r, int c, int val, vector<vector<int>>& board, int pr, int pc){
        if(val>18) return 1e9;
        if(check(board)) return val;
        int sw=1e9;
        int dr[]={-1,0,+1,0};
        int dc[]={0,+1,0,-1};
        for(int x=0;x<4;x++){
            int nr=r+dr[x];
            int nc=c+dc[x];
            if(nr>=0 && nc>=0 && nr<2 && nc<3){
                if(nr==pr && nc==pc) continue;
                swap(board[r][c],board[nr][nc]);
                sw=min(sw,fn(nr,nc,val+1,board,r,c));
                swap(board[r][c],board[nr][nc]);
            }
        }
        return sw;
    }
    int slidingPuzzle(vector<vector<int>>& board) {
        int ans;
        for(int i=0;i<2;i++){
            for(int j=0;j<3;j++){
                if(board[i][j]==0){
                    ans=fn(i,j,0,board,-1,-1);
                    if(ans==1e9) return -1;
                    return ans;
                }
            }
        }
        return -1;
    }
};
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