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# 37. Sudoku Solver
"""
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, and each of the digits '1-9' must occur exactly
once in each of the 9 3x3 sub-boxes of the grid. the '.' character indicates
empty cells.
"""
class Solution(object):
def solveSudoku(self, board):
"""
:type board: List[List[str]]
:rtype: None Do not return anything, modify board in-place instead.
"""
n = 9
def valid(row, col, idx):
row, col = int(row), int(col)
for i in range(9):
if board[i][col] == idx:
return False
if board[row][i] == idx:
return False
if board[3 * (row // 3) + i // 3][3 * (col // 3) + i % 3] == idx:
return False
return True
def solve(row, col):
if row == n:
return True
if col == n:
return solve(row + 1, 0)
if board[row][col] == ".":
for i in range(1, 10):
if valid(row, col, str(i)):
board[row][col] = str(i)
if solve(row, col + 1):
return True
else:
board[row][col] = "."
return False
else:
return solve(row, col + 1)
solve(0, 0)
if __name__ == "__main__":
obj = Solution()
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"],
]
obj.solveSudoku(board)
print(board)
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