<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:
// TC O(6!), SC O(6!)
    int slidingPuzzle(vector<vector<int>>& board) {
        if(board.empty() || board[0].empty()) return 0;
        int m = board.size();
        int n = board[0].size();
        string status;
        for(int i = 0; i < m; ++i)
        for(int j = 0; j < n; ++j)
            status += board[i][j] + '0';
        
        queue<string> myq;
        int res = 0;
        myq.push(status);
        
        unordered_set<string> visited;
        visited.insert(status);
        vector<vector<int>> dirs{{1, 0}, {0, 1}, {-1, 0}, {0, -1}};
        while(!myq.empty())
        {
            for(int k = myq.size() - 1; k >= 0; --k)
            {
                string cur = myq.front();
                myq.pop();
                if(cur == "123450") return res;
                size_t pos = cur.find('0');
                int i = pos / n;
                int j = pos % n;
                for(auto &d : dirs)
                {
                    int x = i + d[0];
                    int y = j + d[1];
                    if(x >= 0 && y >= 0 && x < m && y < n)
                    {
                        int index = x * n + y;
                        swap(cur[index], cur[pos]);
                        if(!visited.count(cur))
                        {
                            visited.insert(cur);
                            myq.push(cur);
                        }
                        swap(cur[index], cur[pos]);
                    }
                }
            }
            ++res;
        }
        return -1;
    }
};
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