<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) {
    int origin{ Encode(board) };
    if (origin == 123450) {
      return 0;
    }
    
    reachable_combinations_.insert( {123450, 0} ); // target
    std::queue<int> combinations_queue;
    combinations_queue.push(123450);
    while (!combinations_queue.empty()) {
      int combination{ combinations_queue.front() };
      combinations_queue.pop();
      int moves{ reachable_combinations_[combination] };

      vector<int> ngb_combinations{ FindNgbCombinations(combination) };
      for (int comb : ngb_combinations) {
        if (comb == origin) {
          return moves + 1;
        }

        auto [iter, success]{ reachable_combinations_.insert( {comb, moves+1} ) };
        if (success) {
          // new combination
          combinations_queue.push(comb);
        }
      }
    }

    // could not build origin
    return -1;
  }

private:
  int Encode(vector<vector<int>>& board) {
    return board[0][0] * 100'000 + board[0][1] * 10'000 + board[0][2] * 1'000
                  + board[1][0] * 100 + board[1][1] * 10 + board[1][2];
  }

  vector<vector<int>> Decode(int comb) {
    vector<vector<int>> board(3, vector<int>(3));
    board[1][2] = comb % 10;
    comb /= 10;
    board[1][1] = comb % 10;
    comb /= 10;
    board[1][0] = comb % 10;
    comb /= 10;
    board[0][2] = comb % 10;
    comb /= 10;
    board[0][1] = comb % 10;
    comb /= 10;
    board[0][0] = comb % 10;

    return board;
  }

  vector<int> FindNgbCombinations(int comb) {
    vector<int> result;
    vector<vector<int>> board(Decode(comb));
    if (board[0][0] == 0 || board[0][1] == 0) {
      std::swap(board[0][0], board[0][1]);
      result.push_back(Encode(board));
      std::swap(board[0][0], board[0][1]);
    }
    if (board[0][1] == 0 || board[0][2] == 0) {
      std::swap(board[0][1], board[0][2]);
      result.push_back(Encode(board));
      std::swap(board[0][1], board[0][2]);
    }    
    if (board[1][0] == 0 || board[1][1] == 0) {
      std::swap(board[1][0], board[1][1]);
      result.push_back(Encode(board));
      std::swap(board[1][0], board[1][1]);
    }
    if (board[1][1] == 0 || board[1][2] == 0) {
      std::swap(board[1][1], board[1][2]);
      result.push_back(Encode(board));
      std::swap(board[1][1], board[1][2]);
    }
    if (board[0][0] == 0 || board[1][0] == 0) {
      std::swap(board[0][0], board[1][0]);
      result.push_back(Encode(board));
      std::swap(board[0][0], board[1][0]);
    }
    if (board[0][1] == 0 || board[1][1] == 0) {
      std::swap(board[0][1], board[1][1]);
      result.push_back(Encode(board));
      std::swap(board[0][1], board[1][1]);
    }
    if (board[0][2] == 0 || board[1][2] == 0) {
      std::swap(board[0][2], board[1][2]);
      result.push_back(Encode(board));
      std::swap(board[0][2], board[1][2]);
    }
    return result;    
  }

  std::unordered_map<int, int> reachable_combinations_;
};

15665