#python# 来做奥数题

# encoding=utf8

import itertools

class DataGenerator(object):
   """
   DataGenerator:数生成器
   """   def __init__(self, count=6, digitals=[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]):
       super(DataGenerator, self).__init__()
       self._count = count
       self._digitals = digitals    

    def get_digitals(self):
       return self._digitals    
    
    def generate_numbers(self):
       """
       获取定长的由数字组成的数，例如：
       _count = 6, 返回所有的可能数字组合，对应的数，对应的逆序数
       5 -> [([1, 2, 3, 4, 5], 12345, 54321), [1, 2, 3, 4, 6], 12346, 64321), ...]
       """
       all = list(itertools.permutations(self._digitals, self._count))        
        return [(x,
                self._generate_numbers_from_digit_list(x),
                self._generate_numbers_from_digit_list(x, True)) 
                 for x in all if len(set(x)) == self._count and x[-1] != 0]    
  
‍    ‍def _generate_numbers_from_digit_list(self, digit_list, revert=False):
       """
       由一个数字列表返回对应的数，例如：
       [1, 2, 3, 4, 5], False -> 12345
       [1, 2, 3, 4, 5], True  -> 54321
       """
       return sum([digit * 10**index for index, digit in enumerate(digit_list if not revert else digit_list[::-1])])

class NumberAttr(object):
   """
   NumberAttr:数属性
   """
    
    def __init__(self, number):
       super(NumberAttr, self).__init__()
       self._number = number    

    def get_digit_by_pos(self, pos):
       """
       获取数某个位置上的数字
       1234, 1 -> 4
       4321, 1 -> 1
       """
       number = self._number        
        while pos:
           (div, mod) = divmod(number, 10)
           number = div
           pos -= 1
       return mod
        
    def get_number_bits(self):
       """
       获取数共有多少位
       123 -> 3
       4321 -> 4
       """
       number = self._number
       count = 0
       while number:
           (div, mod) = divmod(number, 10)
           number = div
           count += 1
       return count

# encoding=utf8

from data_generator import DataGenerator
from data_generator import NumberAttr

def abcde_multiple_f_edcba():
   # 红花映绿叶 * 春 = 叶绿映花红
   generator = DataGenerator(5)
   datas = generator.generate_numbers()
   digitals = generator.get_digitals()    
    for numbers in datas:
       (x, abcde, edcba) = numbers        
        if edcba > abcde and not edcba % abcde:  # 可以整除
           f = edcba // abcde
            if f not in x and f in digitals:
               print("{} X {} = {}".format(abcde, f, edcba))
            
def abcedf_multiple_f_gggggg():
   # 我们热爱科学 * 学 = 好好好好好好
   count = 6
   generator = DataGenerator(count)
   datas = generator.generate_numbers()    
    for numbers in datas:
       (x, abcdef, _) = numbers
       f = x[0]
       gggggg = abcdef * f
       (div, mod) = divmod(gggggg, 111111)
       attr = NumberAttr(gggggg)        
        if attr.get_number_bits() == count and not mod and div <= 9:
           print("{} X {} = {}".format(abcdef, f, gggggg))
        
def abcdef_add_abcdef_gehiba():
   # 少年早立志向 + 少年早立志向 = 有志何惧少年
   count = 6
   generator = DataGenerator(count)
   datas = generator.generate_numbers()    
    for numbers in datas:
       (x, abcdef, _) = numbers
       gehiba = abcdef + abcdef
       attr = NumberAttr(gehiba)
       a = attr.get_digit_by_pos(1)
       b = attr.get_digit_by_pos(2)
       i = attr.get_digit_by_pos(3)
       h = attr.get_digit_by_pos(4)
       e = attr.get_digit_by_pos(5)
       g = attr.get_digit_by_pos(6)        
        if a == x[5] and b == x[4] and e == x[1] and \
          g not in x and h not in x and i not in x and \
          g != h and g != i and h != i and \
          attr.get_number_bits() == count:
           print("{} + {} = {}".format(abcdef, abcdef, gehiba))
        
def abcd_add_bcd_add_cd_2004():
   # 学生 + 好学生 + 三好学生 = 2004
   generator = DataGenerator(4)
   datas = generator.generate_numbers()    
    for numbers in datas:
       (x, abcd, _) = numbers
       cd = x[0] + 10 * x[1]
       bcd = cd + 100 * x[2]        
        if abcd + bcd + cd == 2004:
           print("{} + {} + {} = 2004".format(abcd, bcd, cd))
        
if __name__ == "__main__":
   abcde_multiple_f_edcba()
   abcedf_multiple_f_gggggg()
   abcdef_add_abcdef_gehiba()
   abcd_add_bcd_add_cd_2004()
    pass

21978 X 4 = 87912
142857 X 7 = 999999
468532 + 468532 = 937064
1468 + 468 + 68 = 2004
[Finished in 3.2s]