<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:

    pair<int, int> findZero(vector<vector<int>> & board){
        pair<int, int> now;
        for (int i = 0; i < 2; ++i) {
            for (int j = 0; j < 3; ++j) {
                if(board[i][j] == 0){
                    now.first = i;
                    now.second = j;
                }
            }
        }
        return now;
    }

    bool isCorrect(vector<vector<int>> & board){
        return board[0][0] == 1 && board[0][1] == 2 && board[0][2] == 3
            && board[1][0] == 4 && board[1][1] == 5 && board[1][2] == 0;
    }

    int go(vector<vector<int>> & board){

        vector<int> dx = {-1, 0, 1, 0};
        vector<int> dy = {0, 1, 0, -1};

        int result = -1;
        set<vector<vector<int>>> sv;

        queue<pair<vector<vector<int>>, int>> q;
        q.push({board, 0});
        sv.insert(board);
        vector<vector<int>> nowBoard;
        vector<vector<int>> nextBoard;

        while(!q.empty()){
            auto p = q.front();
            nowBoard = p.first;
            int nowDepth = p.second;
            pair<int, int> now = findZero(nowBoard);

            q.pop();
            if(isCorrect(nowBoard)) {
                result = nowDepth;
                break;
            }

            for (int i = 0; i < 4; ++i) {
                pair<int, int> next = {now.first + dx[i], now.second + dy[i]};

                if(next.first < 0 || next.first > 1 || next.second < 0 || next.second > 2) continue;

                nextBoard = nowBoard;
                swap(nextBoard[now.first][now.second], nextBoard[next.first][next.second]);
                if(sv.find(nextBoard) != sv.end()) continue;

                q.push({nextBoard, nowDepth+1});
                sv.insert(nextBoard);
            }
        }
        return result;
    }

    int slidingPuzzle(vector<vector<int>>& board) {
        return go(board);
    }
};
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