<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) {
        
        const string target = "123450";
        string start;
        for (int i = 0; i < 2; ++i) {
            for (int j = 0; j < 3; ++j) {
                start += '0' + board[i][j];
            }
        }

       
        auto get_neighbors = [&](const string& board) -> vector<string>
        {
            static const pair<int,int> dirs[4] = {{0,1}, {1,0}, {-1, 0}, {0,-1}}; 
            auto zero_pos = board.find_first_of('0');
            int zero_row = zero_pos/3, zero_col = zero_pos%3;
            vector<string> neighbors;
            for (auto& [drow,dcol] : dirs) {
                 auto nrow = zero_row + drow,  ncol = zero_col + dcol;
                 if (nrow >= 0 && nrow < 2 && ncol >= 0 && ncol < 3) {
                    auto nbr = board;
                    swap(nbr[zero_pos], nbr[3*nrow + ncol]);
                    neighbors.emplace_back(move(nbr));
                 }
            }
            return neighbors;
        };

       

        queue<string> q;
        unordered_set<string> visited;
        q.push(start);
        visited.insert(start);
        int distance = 0;
        while (!q.empty()) {
            for (int i = 0, qsize = q.size(); i < qsize; ++i) {
                auto b = q.front(); q.pop();
                if (b == target) return distance;
                for (auto&& nbr : get_neighbors(b)) if (!visited.contains(nbr)) {
                    visited.insert(nbr);
                    q.push(move(nbr));
                }
            } 
            ++distance;
        }

        return -1;
    }
};
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