# -*- coding: utf8 -*-
'''
__author__ = '[email protected]'
37: Sudoku Solver
https://oj.leetcode.com/problems/sudoku-solver/
Write a program to solve a Sudoku puzzle by filling the empty cells.
Empty cells are indicated by the character '.'.
You may assume that there will be only one unique solution.
===Comments by Dabay===
逐行扫描，当遇到“.”的时候，尝试每一个可能的valid_num。
如果能DFS到底，就return True；否则，把这个位置重置为“.”，进行下一次尝试。
'''
class Solution:
# @param board, a 9x9 2D array
# Solve the Sudoku by modifying the input board in-place.
# Do not return any value.
def solveSudoku(self, board):
def next_position(position):
i, j = position
j += 1
if j >= 9:
j -= 9
i += 1
return (i, j)
def valid_nums(board, position):
i, j = position
s = [str(n) for n in xrange(1, 10)]
for row in xrange(9):
if board[row][j] != '.' and board[row][j] in s:
s.remove(board[row][j])
for col in xrange(9):
if board[i][col] != '.' and board[i][col] in s:
s.remove(board[i][col])
ii = i / 3
jj = j / 3
for row in xrange(3):
for col in xrange(3):
if board[ii*3+row][jj*3+col] != '.' and board[ii*3+row][jj*3+col] in s:
s.remove(board[ii*3+row][jj*3+col])
return s
def solveSudoku2(board, position):
i, j = position
if i == 9:
return True
if board[i][j] == '.':
nums = valid_nums(board, position)
for n in nums:
board[i][j] = n
if solveSudoku2(board, next_position(position)) is True:
return True
board[i][j] = '.'
else:
return solveSudoku2(board, next_position(position))
solveSudoku2(board, (0, 0))
def print_board(board):
print "-" * 30
for row in board:
for x in row:
print "%s " % x,
print
print "-" * 30
def main():
s = 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"]
]
print_board(board)
s.solveSudoku(board)
print_board(board)
if __name__ == "__main__":
import time
start = time.clock()
main()
print "%s sec" % (time.clock() - start)
