<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:
        zero_index = [0,0]
        foundZero = False
        for i in range(len(board)):
            if foundZero:
                break
            for j in range(len(board[i])):
                if board[i][j] == 0:
                    zero_index = [i, j]
                    foundZero = True
                    break
        expected = [[1,2,3],[4,5,0]]
        targetStr = self.getHash(expected)

        hashStr = self.getHash(board)
        q = [[copy.deepcopy(board), zero_index,hashStr, 0]]
        visited = set()
        ans = math.inf
        # steps = 0
        visited.add(hashStr)
        while len(q) > 0:
            size = len(q)
            while size > 0:
                size-=1
                board, zero_index, hashStr, steps = q.pop(0)
                if hashStr == targetStr:
                    return steps
                for state, new_zero_index, hashStr in self.nextStates(board, zero_index):
                    if hashStr not in visited:
                        q.append([state, new_zero_index, hashStr, steps+1])
                        visited.add(hashStr)
            # steps+=1
        return -1
    
    # def isTerminal(self, board):
    #     for i in range(len(board)):
    #         for j in range(len(board[i])):
    #             if board[i][j]!=expected[i][j]:
    #                 return False
    #     return True
    
    def nextStates(self, board, zeroIndex):
        # print('original board', board)
        states = []
        moves = [[-1,0],[1,0],[0,-1],[0,1]]
        for move in moves:
            x = zeroIndex[0] + move[0]
            y = zeroIndex[1] + move[1]
            if x < 0 or x>=len(board) or y < 0 or y >=len(board[0]):
                continue
            newState = copy.deepcopy(board) 
            temp = newState[x][y]
            newState[x][y] = 0
            newState[zeroIndex[0]][zeroIndex[1]] = temp
            hashStr = self.getHash(newState)
            states.append([newState , [x,y], hashStr])
        # print(states)
        return states
    
    # def isNotVisited(self, visited, board):
    #     hashStr = self.getHash(board)
    #     return True if hashStr not in visited else False
    
    def getHash(self, board):
        hashStr = ""
        for i in range(len(board)):
            for j in range(len(board[i])):
                hashStr+=str(board[i][j])
        return hashStr
16700