leetcode 773. Sliding Puzzle

Seawolf

1. On a 2x3 board, there are 5 tiles represented by the integers 1 through 5, and an empty square represented by 0.
   
2. 
   
3. A move consists of choosing 0 and a 4-directionally adjacent number and swapping it.
   
4. 
   
5. The state of the board is solved if and only if the board is [[1,2,3],[4,5,0]].
   
6. 
   
7. 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.
   
8. 
   
9. Examples:
   
10. 
    
11. Input: board = [[1,2,3],[4,0,5]]
    
12. Output: 1
    
13. Explanation: Swap the 0 and the 5 in one move.
    
14. Input: board = [[1,2,3],[5,4,0]]
    
15. Output: -1
    
16. Explanation: No number of moves will make the board solved.
    
17. Input: board = [[4,1,2],[5,0,3]]
    
18. Output: 5
    
19. Explanation: 5 is the smallest number of moves that solves the board.
    
20. An example path:
    
21. After move 0: [[4,1,2],[5,0,3]]
    
22. After move 1: [[4,1,2],[0,5,3]]
    
23. After move 2: [[0,1,2],[4,5,3]]
    
24. After move 3: [[1,0,2],[4,5,3]]
    
25. After move 4: [[1,2,0],[4,5,3]]
    
26. After move 5: [[1,2,3],[4,5,0]]
    
27. Input: board = [[3,2,4],[1,5,0]]
    
28. Output: 14
    
29. Note:
    
30. 
    
31. board will be a 2 x 3 array as described above.
    
32. board[i][j] will be a permutation of [0, 1, 2, 3, 4, 5].

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1. class Solution:
   
2.     def slidingPuzzle(self, board: List[List[int]]) -> int:
   
3.         start, goal = "", ""
   
4.         row_len, col_len = 2, 3
   
5.         
   
6.         for i in range(len(board)):
   
7.             for j in range(len(board[0])):
   
8.                 goal += str((i * col_len + j + 1) % (row_len * col_len))
   
9.                 start += str(board[i][j])
   
10.         
    
11.         if start == goal:
    
12.             return 0
    
13.         
    
14.         directions = [[0, 1], [0, -1], [1, 0], [-1, 0]]
    
15.         queue = []
    
16.         visited = set()
    
17.         queue.append(start)
    
18.         visited.add(start)
    
19.         steps = 0
    
20.         
    
21.         while queue:
    
22.             steps += 1
    
23.             size = len(queue)
    
24.             for _ in range(size):
    
25.                 cur = queue.pop(0)
    
26.                 p = cur.find('0')
    
27.                 x = p % col_len
    
28.                 y = p // col_len
    
29. 
    
30.                 for direction in directions:
    
31.                     new_x = x + direction[0]
    
32.                     new_y = y + direction[1]
    
33. 
    
34.                     if new_x < 0 or new_x >= col_len or new_y < 0 or new_y >= row_len:
    
35.                         continue
    
36. 
    
37.                     pp = new_y * col_len + new_x
    
38.                     
    
39.                     if pp < 0 or pp >= 6:
    
40.                         continue
    
41.                     
    
42.                     new_cur = cur[:]
    
43.                     new_str = list(new_cur)
    
44.                     new_str[p], new_str[pp] = new_str[pp], new_str[p]
    
45.                     new_cur = "".join(new_str)
    
46.                     
    
47.                     if new_cur in visited:
    
48.                         continue
    
49. 
    
50.                     if new_cur == goal:
    
51.                         return steps
    
52.                     
    
53.                     visited.add(new_cur)
    
54.                     queue.append(new_cur)
    
55.         
    
56.         return -1

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