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.
A sudoku puzzle...
...and its solution numbers marked in red.
题意分析：
本题是要解决一个数独问题。输入一个部分数独，将空白的格子填上正确的数字，只需要找到一个正确的解即可。
解答：
关于数独的规则，在上一篇文章里面有讲【LeetCode题意分析&解答】36. Valid Sudoku，这里不再赘述。
填入的数字是在1~9之间，我们先将当前节点置为某个要填入的数，并判断是否符合数独的规则。如果符合则继续循环，如果不符合则退回来填入其他的数。如果按照这个思路去做，就是一个典型的深度优先搜索的回溯算法。
AC代码：
class Solution(object):
def solveSudoku(self, board):
def backtracing():
for i in xrange(9):
for j in xrange(9):
if board[i][j] != '.':
continue
for v in [str(c) for c in xrange(1, 10)]:
# judge if against to the rule
if v in board[i] or v in [board[k][j] for k in xrange(9)] or v in \
[board[i / 3 * 3 + m][j / 3 * 3 + n] for m in xrange(3) for n in xrange(3)]:
continue
board[i][j] = v
if backtracing():
return True
else:
board[i][j] = '.'
return False
return True
backtracing()