Write a program to solve a Sudoku puzzle by filling the empty cells.
A sudoku solution must satisfy all of the following rules:
- Each of the digits
1-9
must occur exactly once in each row. - Each of the digits
1-9
must occur exactly once in each column. - Each of the digits
1-9
must occur exactly once in each of the 93x3
sub-boxes of the grid.
The '.'
character indicates empty cells.
Example 1:
Input: board = [["5","3",".",".","7",".",".",".","."],["6",".",".","1","9","5",".",".","."],[".","9","8",".",".",".",".","6","."],["8",".",".",".","6",".",".",".","3"],["4",".",".","8",".","3",".",".","1"],["7",".",".",".","2",".",".",".","6"],[".","6",".",".",".",".","2","8","."],[".",".",".","4","1","9",".",".","5"],[".",".",".",".","8",".",".","7","9"]] Output: [["5","3","4","6","7","8","9","1","2"],["6","7","2","1","9","5","3","4","8"],["1","9","8","3","4","2","5","6","7"],["8","5","9","7","6","1","4","2","3"],["4","2","6","8","5","3","7","9","1"],["7","1","3","9","2","4","8","5","6"],["9","6","1","5","3","7","2","8","4"],["2","8","7","4","1","9","6","3","5"],["3","4","5","2","8","6","1","7","9"]] Explanation: The input board is shown above and the only valid solution is shown below:
Constraints:
board.length == 9
board[i].length == 9
-
board[i][j]
is a digit or'.'
. - It is guaranteed that the input board has only one solution.
Idea: 这个题目是在[LeetCode] 36. Valid Sudoku_Medium tag: Array的基础上加入了backtracking, 去将1 - 9放到空的,也就是有'.'的地方,然后不停的去弄, 每次要看行,列及相应的小正方形中有没有相应的数字, 如果有的话,那就continue, 直到所有的空都被填满, 否则的话就backtrack. 这里参考[LeetCode] 系统刷题7_Array & numbers & string中的对于每个小正方形里面的index要用newRow = (row //3) * 3 + k //3, newCol = (col //3) * 3 + k %3 for k in range(9).
Code:
class Solution: def solveSudoku(self, board: List[List[str]]) -> None: def backtrack(board): for i in range(9): for j in range(9): if board[i][j] != '.': continue for c in "123456789": if not self.isValid(board, i, j, c): continue board[i][j] = c if backtrack(board): return True board[i][j] = '.' return False return True helper(board) def isValid(self, board, i, j, c): for k in range(9): row = i //3 * 3 + k//3 col = j //3 * 3 + k%3 if c in [board[i][k], board[k][j], board[row][col]]: return False return True