#!/usr/bin/python
# -*- coding: utf-8 -*-
def gcd(x,y):
#最大公因子
if x>y:x%=y
while x:
x,y=y%x,x
return y
def lcm(x,y):
#最小公倍数
return x*y/gcd(x,y)
def jhua(x):
t=gcd(x[0],x[1])
return [x[0]/t,x[1]/t]
def z42():
x,y=(120,36)
print x,y,"的最小公倍数是",lcm(x,y)
print x,y,"的最大公因子是",gcd(x,y)
def z43():
#比较两个分数的大小
def bijiao(x,y):
x,y=jhua(x),jhua(y)
m,n=x[0]*y[1],x[1]*y[0]
if m>n:
return '>'
elif m<n:
return '<'
else:
return '='
x,y=[1235,2356],[1357,2468]
print x,bijiao(x,y),y
def z44():
#找出方程1/x+1/y+1/z+1/a=1的解
def addf(x,y):
x,y=jhua(x),jhua(y)
return jhua([x[0]*y[1]+x[1]*y[0],y[1]*x[1]])
ai=range(2,13)
aii=range(2,43)
num=1
for i in ai:
for j in ai:
for m in ai:
for k in aii:
if i<=j<=m<=k:
r=[i,j,m,k]
t=reduce(addf, map(lambda x:[1,x],r))
if t==[1,1]:
print num,r
num+=1
def z45():
def fena(x,y):
#分子为1的分数叫做埃及分数把一个分数a/b分解成n个埃及分数的和
sh,yu=divmod(x,y)
re=[]
if yu:
t=sh+1
re+=[t]
y,x=y*t-x,x*t
re+=fena(x,y)
else:
re+=[x/y]
return re
print fena(99,19)
def z46():
#找出分子小于40，分母等于40的最简真分数,就是说分子和分母没有公因子的分数
num=1
for i in range(1,40):
y=40
if gcd(i,y)==1:
print num,[i,y]
num+=1
def z47():
def divf(x,y):
yu=[]
sh=[]
sh1,yu1=divmod(x,y)
sh+=[str(sh1),'.']
if yu1==0:return ''.join(sh[:-1])
while yu1 :
sh1,yu1=divmod(yu1*10,y)
sh+=[str(sh1)]
if yu1 not in yu:
yu+=[yu1]
else:
t=yu.index(yu1)
sh.insert(t+3,'(')
sh.append(')')
break
return ''.join(sh)
print divf(3737,27000)
print divf(12,100)
print divf(120,12)
if __name__ == '__main__':
s=""
for i in range(42,48):
s+='z'+str(i)+'()\n'
exec(s)
