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.
SOLUTION:
class Solution:
def getPos(self, board, i, j):
pos = set(map(str, range(1, 10)))
ci, cj = i - i % 3, j - j % 3
for a in range(3):
for b in range(3):
if board[ci + a][cj + b] != "." and board[ci + a][cj + b] in pos:
pos.remove(board[ci + a][cj + b])
for a in range(9):
if board[i][a] in pos:
pos.remove(board[i][a])
if board[a][j] in pos:
pos.remove(board[a][j])
return pos
def solve(self, board, spi):
if spi >= len(self.spaces):
return True
if spi < len(self.spaces):
i, j = self.spaces[spi]
pos = self.getPos(board, i, j)
for p in pos:
board[i][j] = p
currsolution = self.solve(board, spi + 1)
if currsolution:
return True
else:
board[i][j] = "."
return False
def solveSudoku(self, board: List[List[str]]) -> None:
self.spaces = []
for i in range(9):
for j in range(9):
if board[i][j] == ".":
self.spaces.append((i, j))
self.solve(board, 0)
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