<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 {
    const vector<int> di{1,-1, 0, 0};
    const vector<int> dj{0, 0, 1,-1};

    bool valid(int i, int j) {
        return (i >= 0 && i < 2) and (j >= 0 && j < 3);
    }

public:
    int slidingPuzzle(vector<vector<int>>& board) {
        const vector<vector<int>> target{{1,2,3}, {4,5,0}};                

        set<vector<vector<int>>> visited;
        visited.insert(board);

        queue<vector<vector<int>>> states;
        states.push(board);

        for(int level{}, size = states.size(); !states.empty(); ++level, size = states.size())
            while(size--) {
                auto current = states.front();
                states.pop();
                
                if(current == target) {
                    return level;
                }

                int zero_i,zero_j;
                for(int i{}; i < 2; ++i)
                    for(int j{}; j < 3; ++j)
                        if(current[i][j] == 0) {
                            zero_i = i;
                            zero_j = j; 
                        }

                for(int dir{}; dir < 4; ++dir) {
                    int i = zero_i + di[dir];
                    int j = zero_j + dj[dir];

                    auto state = current;

                    if(valid(i, j)) {
                        swap(state[zero_i][zero_j], state[i][j]);

                        if(visited.insert(state).second == true) {
                            states.push(state);
                        }
                    }
                }
            }
        return -1;
    }
};
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