<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:
    static int slidingPuzzle(const std::vector<std::vector<int>>& board) {
        static auto get_key = [] (const std::vector<std::vector<int>>& board) {
            int ret = 0;
            ret |= board[0][0];
            ret <<= 5;
            ret |= board[0][1];
            ret <<= 5;
            ret |= board[0][2];
            ret <<= 5;
            ret |= board[1][0];
            ret <<= 5;
            ret |= board[1][1];
            ret <<= 5;
            ret |= board[1][2];
            return ret;
        };
        static std::unordered_map<int, int> res;

        if (res.empty()) {
            std::vector<std::vector<int>> a = {{1, 2, 3}, {4, 5, 0}};
            res[get_key(a)] = 0;
            std::queue<std::vector<std::vector<int>>> q;
            q.push(a);
            while (!q.empty()) {
                std::vector<std::vector<int>> b = q.front();
                q.pop();
                int i = 0;
                while (b[i / 3][i % 3] != 0)
                    ++i;
                int row = i / 3;
                int col = i % 3;
                int c = res[get_key(b)];
                std::swap(b[row][col], b[row ^ 1][col]);
                if (auto it = res.find(get_key(b)); it == res.end()) {
                    res[get_key(b)] = c + 1;
                    q.push(b);
                }
                std::swap(b[row][col], b[row ^ 1][col]);
                if (col > 0) {
                    std::swap(b[row][col], b[row][col - 1]);
                    if (auto it = res.find(get_key(b)); it == res.end()) {
                        res[get_key(b)] = c + 1;
                        q.push(b);
                    }
                    std::swap(b[row][col], b[row][col - 1]);
                }
                if (col < 2) {
                    std::swap(b[row][col], b[row][col + 1]);
                    if (auto it = res.find(get_key(b)); it == res.end()) {
                        res[get_key(b)] = c + 1;
                        q.push(b);
                    }
                    std::swap(b[row][col], b[row][col + 1]);
                }
            }
        }

        auto it = res.find(get_key(board));
        return it != res.end() ? it->second : -1;
    }
};
8690