<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>

import copy
class Solution:
    def slidingPuzzle(self, board: List[List[int]]) -> int:
        def flat(puzzleBoard):
            f = ""
            for i in range(len(puzzleBoard)):
                for j in range(len(puzzleBoard[0])):
                    f = f + str(puzzleBoard[i][j])
            return f
        
        def twoD(flat):
            b = []
            b.append(list(flat[:3]))
            b.append(list(flat[3:]))
            
            for i in range(len(b)):
                for j in range(len(b[0])):
                    b[i][j] = int(b[i][j])
            return b
        
        def zero(b):
            for i in range(len(b)):
                for j in range(len(b[0])):
                    if b[i][j] == 0:
                        return i, j
            return -1, -1
        
        goal = [[1,2,3],[4,5,0]]
        ADJS = [[-1, 0], [1, 0], [0, 1], [0, -1]]
        
        q = [(board, 0)]
        visited = set()
        while q:
            b, c = q.pop(0)

            if b == goal:
                return c

            visited.add(flat(b))

            x, y = zero(b)

            for dx, dy in ADJS:
                if x+dx < 0 or x+dx >= len(board) or y+dy < 0 or y+dy >= len(board[0]):
                    continue
                new = copy.deepcopy(b)
                new[x][y], new[x+dx][y+dy] = new[x+dx][y+dy], new[x][y]
                if flat(new) in visited:
                    continue
                
                q.append((new, c+1))

        return -1

16400