python 练习 6

#!/usr/bin/python
# -*- coding: utf-8 -*-
from collections import deque
from math import log10
def permute(seq, index):
seqc = seq[:]
seqn = [seqc.pop()]
divider = 2
while seqc:
index, new_index = divmod(index,divider)
seqn.insert(new_index, seqc.pop())
divider += 1
return seqn
def z62():
#0~7八个数放到正方体的八个顶点上,每个面的四个数之和都相等
a=[0, 1, 2, 3, 4, 5, 6, 7]
n=sum(a)
if n%2==1:
return
else:
n/=2
for i in range(0,40320):
v1=permute(a,i)
if (v1[0] + v1[1] + v1[2] + v1[3] == n and
v1[0] + v1[1] + v1[4] + v1[5]== n and
v1[0] + v1[2] + v1[4] + v1[6] == n and
v1[0] + v1[4] + v1[4]+ v1[7] == n and
v1[0] + v1[1] > n / 2 and v1[5] > v1[7]):
print v1
return
def z58():
#构造拉丁方：拉丁方是指n*n方阵其中每行每列1到n这些数字,只出现一次
ss=6
d = deque(range(1,ss+1))
for i in range(ss):
d.rotate(1)
print list(d)
return
def z59():
'''答案如
1 2 3
4 5 6
其中每一列右大于左
每一行  下大于上
填入1~6    6个数字 '''
t=range(2,6)
for i in t:
for j in t:
for m in t:
n=14-i-j-m
if i!=j!=m!=i and j>i and n>m and n>i:
print [1,i,j]
print [m,n,6]
return
def iss(n):
s=''.join(map(str,n))
t=set(s)
m=len(s)
return len(t)==m and '0' not in t
def z60():
'''如192，384，576
384数第二数是192的二倍
576数第二数是192的三倍
同时各位数是1~9'''
for i in range(111,333):
t=[i,2*i,3*i]
if iss(t):print t
def z61():
#如361，529，784,他们三数是完全平方,如361=19*19同时各位数是1~9
ge=[x*x for x in range(11,31)]
for i in ge:
for j in ge:
for m in ge:
t=[i,j,m]
if i<j<m and iss(t):print t
def zz68(n):
if n==2 :return filter(lambda x: x%2==0,range(11,99))
t=[]
p=zz68(n-1)
for j in p:
for i in range(10):
nn=j*10+i
if iss([nn]) and nn%n==0:
t.append(nn)
return t
def z66():
'''除式还原
~          x7x
~  xx /--------
~    /   xxxxx
~        x77
~      ------
~         x7x
~         x7x
~         ----
~          xx
~          xx
~          ---
~           0
'''
for i in range(1,10):
for j in range(11,100):
m2 = i * j
m3 = 7 * j
if ((m2 % 100 == 77 and m2 >100) and (m3 / 10 % 10 == 7 and m3 > 100)):
for k in range(1,10):
if k*j<100:
print [i*100+70+k,j]
return
def z67():
'''除式还原2
~            x7xxx
~  xxx /-----------
~     /   xxxxxxxx
~         xxxx
~        ------
~          xxx
~          xxx
~        -------
~           xxxx
~            xxx
~         ---------
~             xxxx
~             xxxx
~          ---------
~                0
'''
g=lambda x,y:map(lambda a,b=x:int(log10(a*b))+1,y)==[4,3,3,4]
t=[8,9]
for i in range(100,142):
for j in t:
for m in t:
for n in t:
n1=j * 10000+7000+m * 100+n
e=[j,7,m,n]
if g(i,e) and (m * 100+n)*i/10000==10:
print n1,i,n1*i
return
def z68():
#个数由123456789组成,其中前两位如12 可以被2 整除,123可以被3 整除,
#前n位可以被n 整除,问他是多少
print zz68(9)
def z63():
'''减式还原
~        PEAR
-         ARA
-----------------
~         PEA
其中不同的字母代表不同的数字'''
t=range(0,10)
for i in t:
for j in t:
for k in t:
a,b,c= 100+k * 10+i,1000+k * 100+i * 10+j,i * 100+j * 10+i
if a==b-c:
print [a,b,c]
def z64():
'''乘式还原
其中 a代表0~9前五个数字
z代表0~9后五个数字
~      AZA
*     AAZ
-----------------
~     AAAA
~    AAZZ
~    ZAA
-----------------
~    ZAZAA'''
g=lambda y:''.join(map(lambda x:x> '4' and '0' or '1' ,str(y)))
t=range(1,5)
m=range(5,10)
t1=filter(lambda y:g(y)=='101',range(100,500))
for i in t1:
for j in filter(lambda y,x=i:g(y*x)=='011',t):
for k in filter(lambda y,x=i:g(y*x)=="1100",t):
for mm in filter(lambda y,x=i:g(y*x)=="1111",m):
jj =j *100+k *10+mm
if g(jj*i)=='01011':
print i,jj

return
def z65():
''' 乘式还原2
~      PPP
*      PP
-----------
~     PPPP
~    PPPP
-------------
~    PPPPP
其中18个p的位置上全是素数2，3，5，7'''
def g(n):
t=str(n)
return len(filter(lambda x: int(x) in (2,3,5,7),t))==len(t)
for i in range(222,778):
for j in range(11,78):
if g(i) and g(j) and g(i*j)  and g(j%10*i)and g(int(j/10)*i):
print i,j,i*j
if __name__ == '__main__':
s=""
for i in range(58,69):
s+='z'+str(i)+'()\n'
exec(s)