leetcode 773. Sliding Puzzle

Seawolf

On a 2x3 board, there are 5 tiles represented by the integers 1 through 5, and an empty square represented by 0.

A move consists of choosing 0 and a 4-directionally adjacent number and swapping it.

The state of the board is solved if and only if the board is [[1,2,3],[4,5,0]].

Given a puzzle board, return the least number of moves required so that the state of the board is solved. If it is impossible for the state of the board to be solved, return -1.

Examples:

Input: board = [[1,2,3],[4,0,5]]
Output: 1
Explanation: Swap the 0 and the 5 in one move.
Input: board = [[1,2,3],[5,4,0]]
Output: -1
Explanation: No number of moves will make the board solved.
Input: board = [[4,1,2],[5,0,3]]
Output: 5
Explanation: 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]]
Input: board = [[3,2,4],[1,5,0]]
Output: 14
Note:

board will be a 2 x 3 array as described above.
board[i][j] will be a permutation of [0, 1, 2, 3, 4, 5].

class Solution:
    def slidingPuzzle(self, board: List[List[int]]) -> int:
        start, goal = "", ""
        row_len, col_len = 2, 3
        
        for i in range(len(board)):
            for j in range(len(board[0])):
                goal += str((i * col_len + j + 1) % (row_len * col_len))
                start += str(board[i][j])
        
        if start == goal:
            return 0
        
        directions = [[0, 1], [0, -1], [1, 0], [-1, 0]]
        queue = []
        visited = set()
        queue.append(start)
        visited.add(start)
        steps = 0
        
        while queue:
            steps += 1
            size = len(queue)
            for _ in range(size):
                cur = queue.pop(0)
                p = cur.find('0')
                x = p % col_len
                y = p // col_len

                for direction in directions:
                    new_x = x + direction[0]
                    new_y = y + direction[1]

                    if new_x < 0 or new_x >= col_len or new_y < 0 or new_y >= row_len:
                        continue

                    pp = new_y * col_len + new_x
                    
                    if pp < 0 or pp >= 6:
                        continue
                    
                    new_cur = cur[:]
                    new_str = list(new_cur)
                    new_str[p], new_str[pp] = new_str[pp], new_str[p]
                    new_cur = "".join(new_str)
                    
                    if new_cur in visited:
                        continue

                    if new_cur == goal:
                        return steps
                    
                    visited.add(new_cur)
                    queue.append(new_cur)
        
        return -1