<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:
    bool checkIndex(int i, int j) {
        if (i < 0 || j < 0 || i > 1 || j > 2) {
            return false;
        }
        return true;
    }
    int boardToInt(vector<vector<int>>& board) {
        return board[0][0] * 100000 + \
            board[0][1] * 10000 + \
            board[0][2] * 1000 + \
            board[1][0] * 100 + \
            board[1][1] * 10 + \
            board[1][2] * 1;
    }
    vector<vector<int>> intToBoard(int n) {
        vector<vector<int>> board(3, vector<int>(3));
        board[0][0] = n/100000;
        n %= 100000;
        board[0][1] = n/10000;
        n %= 10000;
        board[0][2] = n/1000;
        n %= 1000;
        board[1][0] = n/100;
        n %= 100;
        board[1][1] = n/10;
        n %= 10;
        board[1][2] = n;
        return board;
    }
    int slidingPuzzle(vector<vector<int>>& board) {
        queue<tuple<int, int, int, int>> q;
        unordered_set<int> visit;
        int goal_pos = 123450;
        vector<pair<int,int>> neighbors = {{1, 0}, {0, 1}, {-1, 0}, {0, -1}};
        for (int i = 0; i < 2; i++) {
            for (int j = 0; j < 3; j++) {
                if (board[i][j] == 0) {
                    int pos = boardToInt(board);
                    q.push({i, j, 0, pos});
                    visit.insert(pos);
                    break;
                }
            }
        }

        while (!q.empty()) {
            auto [i, j, moves, pos] = q.front();
            q.pop();

            if (pos == goal_pos) {
                return moves;
            }

            if (!checkIndex(i,j)) {
                continue;
            }

            auto cur_board = intToBoard(pos);
            for (auto nei : neighbors) {
                int r = i+nei.first;
                int c = j+nei.second;
                if (checkIndex(r,c)) {
                    swap(cur_board[i][j], cur_board[r][c]);
                    auto new_pos = boardToInt(cur_board);
                    if (visit.find(new_pos) == visit.end()) {
                        q.push({r, c, moves+1, new_pos});
                        visit.insert(new_pos);
                    }
                    swap(cur_board[i][j], cur_board[r][c]);
                }
            }
        }
        return -1;
    }
    
};
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