<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) {
        unordered_set<string> been;
        queue<pair<vector<vector<int>>, int>> q;
        q.push({board, 0});

        while (q.size()) {
            pair<vector<vector<int>>, int> p = q.front();
            q.pop();
            string s = serialise(p.first);
            if (s == "123450") return p.second;
            if (been.count(s)) continue;
            been.insert(s);

            pair<int, int> zero = findzero(p.first);

            if (zero.first > 0) {
                vector<vector<int>> temp(p.first);
                temp[zero.first][zero.second] = temp[zero.first - 1][zero.second];
                temp[zero.first - 1][zero.second] = 0;
                q.push({temp, p.second + 1});
            } if (zero.first < 1) {
                vector<vector<int>> temp(p.first);
                temp[zero.first][zero.second] = temp[zero.first + 1][zero.second];
                temp[zero.first + 1][zero.second] = 0;
                q.push({temp, p.second + 1});
            } if (zero.second > 0) {
                vector<vector<int>> temp(p.first);
                temp[zero.first][zero.second] = temp[zero.first][zero.second - 1];
                temp[zero.first][zero.second - 1] = 0;
                q.push({temp, p.second + 1});
            } if (zero.second < 2) {
                vector<vector<int>> temp(p.first);
                temp[zero.first][zero.second] = temp[zero.first][zero.second + 1];
                temp[zero.first][zero.second + 1] = 0;
                q.push({temp, p.second + 1});
            }
        }

        return -1;
    }

    string serialise(vector<vector<int>>& board) {
        string res = "";
        for (int i = 0; i < board.size(); i++) {
            for (int j = 0; j < board[0].size(); j++) {
                res += to_string(board[i][j]);
            }
        }
        return res;
    }

    pair<int, int> findzero(vector<vector<int>>& board) {
        for (int i = 0; i < board.size(); i++) {
            for (int j = 0; j < board[0].size(); j++) {
                if (!board[i][j]) {
                    return {i, j};
                }
            }
        }
        return {0, 0};
    }
};
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