<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:
    typedef vector<vector<int>> vvi;
    int slidingPuzzle(vector<vector<int>>& board) {
        int ret = 0;
        queue<vvi> q;
        set<vvi> vis;

        q.push(board);
        while (!q.empty()) {
            int ari = q.size();
            for (int ariel = 0; ariel < ari; ariel++) {
                vvi node = q.front(); q.pop();
                if (node[0][0] == 1 && node[0][1] == 2 && node[0][2] == 3 && node[1][0] == 4 && node[1][1] == 5) {
                    return ret;
                }
                // cout << node[0][0] << " " << node[0][1] << " " << node[0][2] << "\n";
                // cout << node[1][0] << " " << node[1][1] << " " << node[1][2] << "\n"; 
                for (int i = 0; i < 2; i++) {
                    for (int j = 0; j < 3; j++) {
                        if (node[i][j] != 0) continue;
                        // up
                        for (int addi = -1; addi <= 1; addi++) {
                            for (int addj = -1; addj <= 1; addj++) {
                                if (addi*addj != 0) continue;
                                if (i+addi >= 0 && i+addi < 2 && j+addj >= 0 && j+addj < 3) {
                                    vvi next = node;
                                    swap(next[i][j], next[i+addi][j+addj]);
                                    if (!vis.count(next)) {
                                        vis.insert(next);
                                        q.push(next);
                                    }
                                }
                            }
                        }
                    }
                }
            }
            ret++;
            cout << "\n";
        }
        return -1;
    }
};
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