轉載于: www.jianshu.com/p/1b2ee6539…

• python3、numpy的學習
• 遞歸算法

世界最難數獨

芬蘭數學家因卡拉，花費3個月時間設計出了世界上迄今難度最大的數獨游戲，而且它只有一個答案。因卡拉說只有思考能力最快、頭腦最聰明的人才能破解這個游戲

數獨解法

有很多，這里練習用排除+遞歸回溯法。

排除法很直觀

• 根據已知的數字，排除同一行、同一列、同一九宮格內相同的數字
• 同一九宮格內，如果存在某一行/列上猜測有兩個同一數字，那大數獨同一行/列也能排除
• 新解出的數字，加入到先進先出隊列(棧) - FIFO Queue

猜測+回溯法

• 如果已經沒有任何已知的數字，那就只能猜測了
• 把猜測數字加入到后進先出（LastInFirstOut）隊列 - LIFO Queue
• 遞歸寫法，畫流程圖會比較容易理解！！

根據流程圖寫代碼，會很輕松，邏輯也不會亂：

def sudo_solve_iter(self):# 排除法解題self.sudo_exclude()# logger.debug(f'excluded, current result:\n{self.value}')if self.verify_value():if self.get_num_count() == 81:# solve successreturnelse:logger.info(f'current no. of fixed answers: {self.get_num_count()}')point = self.get_best_point()index = 0items = 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 += 1return 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 rollbackrecord = self.record_queue.get()point = record.pointindex = record.point_index + 1items = record.value[point]self.value = record.valuelogger.info(f'Recall! Pop previous point, {items} @{point}')# 判斷索引是否超出范圍# if not exceed，則再回溯一次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 += 1return self.sudo_solve_iter() 復制代碼

實戰

最難數獨，需要猜測109次？！確實很變態啊！不過就算i3級別的舊電腦，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]] 復制代碼

源碼：github.com/kevinqqnj/s…

參考：Python秒解最難數獨?-?楊仕航的博客 http://yshblog.com/blog/74

預告1：會寫一個小網站，秒解任何你輸入的數獨題目 mysudo.herokuapp.com/

• 預告2：添加掃一掃功能，人工智能識別拍攝的數獨題目，Opencv抓圖 + CNN卷積網絡識別。
• 預告3：集成到微信小程序

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