最难数独的快速解法 - python
2018-07-21 本文已影响118人
非梦nj
python3、numpy的学习
递归算法
参考：Python秒解最难数独 - 杨仕航的博客
http://yshblog.com/blog/74
世界最难数独
image.png
芬兰数学家因卡拉，花费3个月时间设计出了世界上迄今难度最大的数独游戏，而且它只有一个答案。因卡拉说只有思考能力最快、头脑最聪明的人才能破解这个游戏
数独解法
有很多，这里练习用排除+递归回溯法。
- 排除法很直观
- 根据已知的数字，排除同一行、同一列、同一九宫格内相同的数字
- 同一九宫格内，如果存在某一行/列上猜测有两个同一数字，那大数独同一行/列也能排除
- 新解出的数字，加入到先进先出队列(栈) - FIFO Queue
- 猜测+回溯法
- 如果已经没有任何已知的数字，那就只能猜测了
- 把猜测数字加入到后进先出（LastInFirstOut）队列 - LIFO Queue
- 递归写法，画流程图会比较容易理解！！
image.png
根据流程图写代码，会很轻松，逻辑也不会乱：
def sudo_solve_iter(self):
# 排除法解题
self.sudo_exclude()
# logger.debug(f'excluded, current result:\n{self.value}')
if self.verify_value():
if self.get_num_count() == 81:
# solve success
return
else:
logger.info(f'current no. of fixed answers: {self.get_num_count()}')
point = self.get_best_point()
index = 0
items = self.add_to_queue(point, index)
logger.info(f'add to LIFO queue and guessing {items[index]}/{items}: '
f'{[x.point for x in self.record_queue.queue]}')
self.guess_times += 1
return self.sudo_solve_iter()
while True:
if self.record_queue.empty():
# raise Exception('Sudo is wrong, no answer!')
logger.error(f'Guessed {self.guess_times} times. Sudo is wrong, no answer!')
exit()
# check value ERROR, need to try next index or rollback
record = self.record_queue.get()
point = record.point
index = record.point_index + 1
items = record.value[point]
self.value = record.value
logger.info(f'Recall! Pop previous point, {items} @{point}')
# 判断索引是否超出范围
# if not exceed，则再回溯一次
if index < len(items):
items = self.add_to_queue(point, index)
logger.info(f'guessing next index: answer={items[index]}/{items} @{point}')
self.guess_times += 1
return self.sudo_solve_iter()
实战
最难数独，需要猜测109次？！确实很变态啊！不过就算i3级别的旧电脑，也只要0.3s左右。
/home/kevinqq/git/sudo-py3/venv/bin/python /home/kevinqq/git/sudo-py3/sudo-recur.py
DEBUG:__main__:current no. of fixed answers: 21
DEBUG:__main__:add to LIFO queue and guessing 3/[3, 9]: [(7, 6)]
DEBUG:__main__:current no. of fixed answers: 22
DEBUG:__main__:add to LIFO queue and guessing 5/[5, 9]: [(7, 6), (6, 6)]
DEBUG:__main__:current no. of fixed answers: 25
DEBUG:__main__:add to LIFO queue and guessing 6/[6, 8, 9]: [(7, 6), (6, 6), (5, 6)]
DEBUG:__main__:verify failed. dup in col 0
DEBUG:__main__:Recall! Pop previous point, [6, 8, 9] @(5, 6)
DEBUG:__main__:guessing next index: answer=8/[6, 8, 9] @(5, 6)
DEBUG:__main__:current no. of fixed answers: 29
DEBUG:__main__:add to LIFO queue and guessing 2/[2, 4, 6]: [(7, 6), (6, 6), (5, 6), (5, 1)]
DEBUG:__main__:verify failed. dup in col 0
...
DEBUG:__main__:guessing next index: answer=3/[2, 3, 8] @(4, 3)
DEBUG:__main__:current no. of fixed answers: 41
DEBUG:__main__:add to LIFO queue and guessing 1/[1, 4]: [(7, 6), (6, 6), (6, 1), (6, 3), (4, 3), (1, 1)]
DEBUG:__main__:verify failed. dup in row 0
DEBUG:__main__:Recall! Pop previous point, [1, 4] @(1, 1)
DEBUG:__main__:guessing next index: answer=4/[1, 4] @(1, 1)
DEBUG:__main__:current no. of fixed answers: 42
DEBUG:__main__:add to LIFO queue and guessing 1/[1, 6, 8]: [(7, 6), (6, 6), (6, 1), (6, 3), (4, 3), (1, 1), (4, 1)]
DEBUG:__main__:verify failed. dup in row 4
DEBUG:__main__:Recall! Pop previous point, [1, 6, 8] @(4, 1)
DEBUG:__main__:guessing next index: answer=6/[1, 6, 8] @(4, 1)
DEBUG:__main__:verify failed. dup in row 0
DEBUG:__main__:Recall! Pop previous point, [1, 6, 8] @(4, 1)
DEBUG:__main__:guessing next index: answer=8/[1, 6, 8] @(4, 1)
DEBUG:__main__:verify failed. dup in row 0
DEBUG:__main__:Recall! Pop previous point, [1, 6, 8] @(4, 1)
DEBUG:__main__:Recall! Pop previous point, [1, 4] @(1, 1)
DEBUG:__main__:Recall! Pop previous point, [2, 3, 8] @(4, 3)
DEBUG:__main__:guessing next index: answer=8/[2, 3, 8] @(4, 3)
DEBUG:__main__:current no. of fixed answers: 33
DEBUG:__main__:add to LIFO queue and guessing 2/[2, 3]: [(7, 6), (6, 6), (6, 1), (6, 3), (4, 3), (3, 3)]
DEBUG:__main__:current no. of fixed answers: 42
DEBUG:__main__:add to LIFO queue and guessing 3/[3, 4]: [(7, 6), (6, 6), (6, 1), (6, 3), (4, 3), (3, 3), (7, 1)]
DEBUG:__main__:current no. of fixed answers: 45
DEBUG:__main__:add to LIFO queue and guessing 1/[1, 6]: [(7, 6), (6, 6), (6, 1), (6, 3), (4, 3), (3, 3), (7, 1), (4, 1)]
DEBUG:__main__:verify failed. dup in row 0
DEBUG:__main__:Recall! Pop previous point, [1, 6] @(4, 1)
DEBUG:__main__:guessing next index: answer=6/[1, 6] @(4, 1)
INFO:__main__:Done! guessed 109 times, in 0.540sec
INFO:__main__:Puzzle:
[[8 0 0 0 0 0 0 0 0]
[0 0 3 6 0 0 0 0 0]
[0 7 0 0 9 0 2 0 0]
[0 5 0 0 0 7 0 0 0]
[0 0 0 0 4 5 7 0 0]
[0 0 0 1 0 0 0 3 0]
[0 0 1 0 0 0 0 6 8]
[0 0 8 5 0 0 0 1 0]
[0 9 0 0 0 0 4 0 0]]
INFO:__main__:Answer:
[[8 1 2 7 5 3 6 4 9]
[9 4 3 6 8 2 1 7 5]
[6 7 5 4 9 1 2 8 3]
[1 5 4 2 3 7 8 9 6]
[3 6 9 8 4 5 7 2 1]
[2 8 7 1 6 9 5 3 4]
[5 2 1 9 7 4 3 6 8]
[4 3 8 5 2 6 9 1 7]
[7 9 6 3 1 8 4 5 2]]
源码：https://github.com/kevinqqnj/sudo-py3/
预告1：会写一个小网站，秒解任何你输入的数独题目 https://mysudo.herokuapp.com/
image.png
预告2：添加扫一扫功能，人工智能识别拍摄的数独题目，Opencv抓图 + CNN卷积网络识别。
预告3：集成到微信小程序
