<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:
    // 012345 -> id:0
    // 012354 -> id:1 
    // 012435
    // 012453
    // 012534
    // 012543
    // 102543
    // 512043
    
    int bfs(string node, unordered_set<string> &visited, string &target) {
        queue<string> q;
        q.push(node);
        int count = 0;
        while (!q.empty()) {
            size_t s = q.size();
            for (size_t i = 0; i < s; ++i) {
                string t = q.front();
                q.pop();
                if (t == target) {
                    return count;
                }
                if (visited.count(t))
                    continue;
                visited.insert(t);
                int zero = t.find('0');
                cout << zero << ' ' << t << '\n';
                if (zero != 0 && zero != 3) {
                    string tmp = t;
                    swap(tmp[zero], tmp[zero - 1]);
                    cout << "push " << tmp << '\n';
                    q.push(tmp);
                }
                if (zero != 2 && zero != 5) {
                    string tmp = t;
                    swap(tmp[zero], tmp[zero + 1]);
                    cout << "push " << tmp << '\n';
                    q.push(tmp);
                }
                if (zero >= 3) {
                    string tmp = t;
                    swap(tmp[zero], tmp[zero - 3]);
                    cout << "push " << tmp << '\n';
                    q.push(tmp);
                }
                if (zero < 3) {
                    string tmp = t;
                    swap(tmp[zero], tmp[zero + 3]);
                    cout << "push " << tmp << '\n';
                    q.push(tmp);
                }
            }
            count++;
        }
        return -1;
    }
    
    int slidingPuzzle(vector<vector<int>>& board) {
        string node = "";
        for (int i = 0; i < board.size(); ++i) {
            for (int j = 0; j < board[i].size(); ++j) {
                node += (board[i][j] + '0');
            }
        }
        string target = "123450";
        unordered_set<string> visited;
        cout << "node " << node << "\n";
        return bfs(node, visited, target);
    }
};
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