<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 {
private:
    vector<string> calculateConditions(const string& base) {
        vector<string> result;
        vector<vector<int>> swapTable = {
            {1, 3},
            {0, 2, 4},
            {1, 5},
            {0, 4},
            {1, 3, 5},
            {2, 4}
        };
        
        const int place = find(base.begin(), base.end(), '0') - base.begin();
        for (int target : swapTable[place]) {
            result.push_back(base);
            swap(result.back()[place], result.back()[target]);
        }
        return result;
    }
    
public:
    int slidingPuzzle(vector<vector<int>>& board) {
        const string solved = "123450";
        vector<string> prev(1, solved); // As template
        set<string> visited;
        for (int i = 0; i < 2; i ++)
            for (int j = 0; j < 3; j ++)
                prev[0][i * 3 + j] = board[i][j] + '0';
        visited.insert(prev[0]);
        
        vector<string> now;
        int depth = 0;
        while (!prev.empty()) {
            now.clear();
            
            for (auto& s : prev) {
                if (s == solved) return depth;
                
                auto conditions = calculateConditions(s);
                for (auto& c : conditions) {
                    if (!visited.contains(c)) {
                        visited.insert(c);
                        now.push_back(c);
                    }
                }
            }
            
            depth ++;
            swap(prev, now);
        }
        
        return -1;
    }
};
19734