python 数独游戏

网上看到一个python写的数独，很好玩：

import random
import itertools
from copy import deepcopy

def make_board(m = 3):
  numbers = list(range(1, m**2 + 1))
  board = None

  while board is None:
    board = attempt_board(m, numbers)
  return board

def attempt_board(m, numbers):
  n = m**2
  board = [[None for _ in range(n)] for _ in range(n)]
  for i, j in itertools.product(range(n), repeat = 2):
    i0, j0 = i - i % m, j - j % m
    random.shuffle(numbers)
    for x in numbers:
      if(x not in board[i]) and all(row[j] != x for row in board) and all(x not in row[j0:j0+m] for row in board[i0:i]):
        board[i][j] = x
        break
    else:
      return None
  return board

def print_board(board, m = 3):
  numbers = list(range(1, m**2 + 1))
  omit = 5
  challange = deepcopy(board)
  for i, j in itertools.product(range(omit), range(m ** 2)):
    x = random.choice(numbers) - 1
    challange[x][j] = None
    spacer = "++---+---+---++---+---+---++---+---+---++"
  print (spacer.replace('-', '='))
  for i, line in enumerate(challange):
    print("|| {0} | {1} | {2} || {3} | {4} | {5} || {6} | {7} | {8} ||".format(*(cell or ' ' for cell in line)))
    if(i + 1) % 3 == 0:
      print(spacer.replace('-', '='))
    else:
      print(spacer)
  return challange

def print_answer(board):
  spacer = "++---+---+---++---+---+---++---+---+---++"
  print(spacer.replace('-','='))
  for i, line in enumerate(board):
    print("|| {0} | {1} | {2} || {3} | {4} | {5} || {6} | {7} | {8} ||".format(*(cell or ' ' for cell in line)))
    if(i + 1) % 3 == 0:
      print(spacer.replace('-','='))
    else:
      print(spacer)

def is_full(challange, m = 3):
  for i, j in itertools.product(range(m**2), repeat = 2):
    if challange[i][j] is None:
      return False
  return True

def cal_candidate(challange, x, y, m = 3):
  candidate = range(1, m ** 2 + 1)
  for i in range(m ** 2):
    if challange[x][i] in candidate:
      candidate.remove(challange[x][i])
    if challange[i][y] in candidate:
      candidate.remove(challange[i][y])
  for i, j in itertools.product(range(m), repeat = 2):
    x0, y0 = x - x % m, y - y % m
    if challange[x0 + i][y0 + j] in candidate:
      candidate.remove(challange[x0 + i][y0 + j])
  return candidate

def least_candidate(challange, m = 3):
  least, x, y = m ** 2, -1, -1
  for i, j in itertools.product(range(m ** 2), repeat = 2):
    if not challange[i][j]:
      num = len(cal_candidate(challange, i, j))
      if num < least:
        least = num
        x, y = i, j
  return x, y

def solving_soduku(challange, m = 3):
  if is_full(challange):
    return challange
  x, y = least_candidate(challange)
  id = x * (m ** 2) + y
  result = try_candidate(challange, id)
  return result

def try_candidate(challange, id, m = 3):
  if is_full(challange):
    return challange
  x = id / (m ** 2)
  y = id % (m ** 2)
  while challange[x][y]:
    id = (id + 1) % m ** 4
    x = id / (m ** 2)
    y = id % (m ** 2)
  candidate = cal_candidate(challange, x, y)
  if len(candidate) == 0:
    return False
  for i in range(len(candidate)):
    challange[x][y] = candidate[i]
    result_r = try_candidate(challange, (id + 1) % m ** 4)
    if not result_r:
      pass
    else:
      return challange
  challange[x][y] = None
  return False


#Board = make_board()
#print Board
#challange = print_board(Board)
#print_answer(Board)

#result = solving_soduku(challange) 
#print_answer(result)   


testing = [[8, None, None, None, None, None, None, None, None],
           [None, None, 3, 6, None, None, None, None, None],
           [None, 7, None, None, 9, None, 2, None, None],
           [None,5 , None, None, None, 7, None, None, None ],
           [None, None, None, None, 4, 6, 7, None, None],
           [None, None, None, 1, None, None, None, 3, None],
           [None, None, 1, None, None, None, None, 6, 8],
           [None, None, 8, 5, None, None, None, 1, None],
           [None, 9, None, None, None, None, 4, None, None]]
result = solving_soduku(testing)
print_answer(result)