<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 hash(vector<vector<int>>& board)
    {
        int ans = 0;
        for (int i = 0; i < board.size(); i++)
        {
            for (int j = 0; j < board[0].size(); j++)
            {
                ans = ans * 10 + board[i][j];
            }
        }
        return ans;
    }

    pair<int, int> findZero(vector<vector<int>>& board)
    {
        for (int i = 0; i < board.size(); i++)
        {
            for (int j = 0; j < board[0].size(); j++)
            {
                if (board[i][j] == 0)
                {
                    return {i, j};
                }
            }
        }
        return {-1, -1};
    }
    int slidingPuzzle(vector<vector<int>>& board) 
    {
        int target = 123450;
        unordered_set<int> visit;
        queue<vector<vector<int>>> que;
        que.push(board);
        visit.insert(hash(board));
        int output = 0;
        int dirs[4][2] = {{0, 1}, {0, -1}, {1, 0}, {-1, 0}};
        while (!que.empty())
        {
            int size = que.size();
            while(size--)
            {
                auto curr = que.front();
                if (hash(curr) == target)
                {
                    return output;
                }
                que.pop();
                auto pos = findZero(curr);
                for (auto dir: dirs)
                {
                    int x = pos.first + dir[0];
                    int y = pos.second + dir[1];
                    if (x >= board.size() || y >= board[0].size() || x < 0 || y < 0)
                    {
                        continue;
                    }
                    auto next = curr;
                    swap(next[x][y], next[pos.first][pos.second]);
                    int hash_val = hash(next);
                    if (visit.count(hash_val) == 0)
                    {
                        que.push(next);
                        visit.insert(hash_val);
                    } 
                }
            }
            output++;
        }
        return -1;
    }
};
15665