<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>> cur = {{1, 2, 3}, {4, 5, 0}};
        set<vector<vector<int>>> vis;
        vector<vector<int>> dir = {{0, 1}, {1, 0}, {-1, 0}, {0, -1}};
        priority_queue<pair<int, vector<vector<int>>>, vector<pair<int, vector<vector<int>>>>, greater<pair<int, vector<vector<int>>>>> pq;
        pq.push({0, board});
        
        while (!pq.empty()) {
            auto steps = pq.top().first;
            auto vec = pq.top().second;
            pq.pop();
            
            vis.insert(vec);
            
            if (vec == cur) return steps;
            int x = 0, y = 0;
            for (int i = 0; i < 2; i++) {
                for (int j = 0; j < 3; j++) {
                    if (vec[i][j] == 0) {
                        x = i;
                        y = j;
                        break;
                    }
                }
            }
            for (int i = 0; i < 4; i++) {
                int nx = x + dir[i][0];
                int ny = y + dir[i][1];
                
                if (nx >= 0 && ny >= 0 && nx < 2 && ny < 3) {
                    auto new_vec = vec;
                    swap(new_vec[x][y], new_vec[nx][ny]);
                    
                    if (vis.find(new_vec) == vis.end()) {
                        pq.push({steps + 1, new_vec});
                    }
                }
            }
        }
        
        return -1;
    }
};

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