<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:
    string target = "123450";

    int BFS(vector<string> board) {
        unordered_map<string, bool> vis;
        queue<vector<string>> q;
        q.push(board);
        vis[board[0] + board[1]] = true;
        vector<pair<int, int>> dir = {{-1, 0}, {0, 1}, {0, -1}, {1, 0}};
        for (int sz = q.size(), level = 0; !q.empty(); ++level, sz = q.size())
            while (sz--) {
                vector<string> curr = q.front(), tmp = curr;
                q.pop();
                if (curr[0] == target.substr(0, 3) &&
                    curr[1] == target.substr(3, 3))
                    return level;

                bool found = false;
                int r, c;
                for (int i = 0; i < 3 && !found; ++i)
                    for (int j = 0; j < 3 && !found; ++j)
                        if (curr[i][j] == '0')
                            r = i, c = j, found = true;

                for (int i = 0; i < 4; ++i) {
                    int newX = r + dir[i].first;
                    int newY = c + dir[i].second;
                    if (newX > 1 || newX < 0 || newY > 2 || newY < 0)
                        continue;
                    swap(tmp[r][c], tmp[newX][newY]);
                    string state = tmp[0] + tmp[1];
                    if (!vis[state])
                        q.push(tmp), vis[state] = true;
                    swap(tmp[r][c], tmp[newX][newY]);
                }
            }
        return -1;
    }
    int slidingPuzzle(vector<vector<int>>& board) {
        vector<string> boardStr(2);
        for (auto i : board[0])
            boardStr[0].push_back(i + '0');
        for (auto i : board[1])
            boardStr[1].push_back(i + '0');

        return BFS(boardStr);
    }
};

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