<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:
    def slidingPuzzle(self, board: List[List[int]]) -> int:
        m = len(board)
        n = len(board[0])
        curr_state = ''
        for r in range(m):
            for c in range(n):
                curr_state += str(board[r][c])
        queue = deque([curr_state])
        seen = {curr_state}
        target = ''
        for i in range(1, m * n):
            target += str(i)
        target += '0'
        neighbors = self.generateNeighbors(m, n)
        steps = 0

        while queue:
            size = len(queue)
            for _ in range(size):
                curr_state = queue.popleft()
                if curr_state == target:
                    return steps
                idx = 0
                while curr_state[idx] != '0':
                    idx += 1
                for n_id in neighbors[idx]:
                    new_state = list(curr_state)
                    new_state[idx], new_state[n_id] = new_state[n_id], new_state[idx]
                    new_state = ''.join(new_state)
                    if new_state not in seen:
                        seen.add(new_state)
                        queue.append(new_state)
            steps += 1
        return -1
    
    def generateNeighbors(self, m, n):
        neighbors = []
        for i in range(m * n):
            curr_neighbors = []
            row, col = divmod(i, n)
            if row > 0:
                curr_neighbors.append(i - n)
            if row < m - 1:
                curr_neighbors.append(i + n)
            if col > 0:
                curr_neighbors.append(i - 1)
            if col < n - 1:
                curr_neighbors.append(i + 1)
            neighbors.append(curr_neighbors)
        return neighbors

16600