#!/usr/bin/env python

# -*- encoding: utf-8 -*-

# 最大公约数，公倍数，素因子分解，闰年判断，找零钱，斐波那契数列

"""

基本的初等数学类

最大公约数，公倍数，素因子分解，闰年判断，找零钱，斐波那契数列

"""

__author__ = 'Xiong Neng'

# 闰年判断

def isLeapYear(year):

return (not year % 4 and year % 100) or (not year % 400)

# 找零钱

def mod(money):

cent = int(money * 100)

all_cent = {25: 0, 10: 0, 5: 0, 1: 0}

for k in all_cent:

all_cent[k], cent = divmod(cent, k)

return all_cent

# 最大公约数，辗转相除法

def maxCommonDivisor(m, n):

while True:

remainder = m % n

if not remainder:

return n

else:

m, n = n, remainder

# 最小公倍数

def minCommonMultiple(m, n):

return m * n / maxCommonDivisor(m, n)

# 素数的判断

def isprime(n):

result = True

for i in range(n / 2, 1, -1):

if n % i == 0:

result = False

break

return result

# 获取n的所有因子

def getfactors(n):

result = [n]

for i in range(n / 2, 0, -1):

if n % i == 0:

result.append(i)

return result

# 素因子分解

def decompose(n):

all_factors = getfactors(n)

all_factors.remove(1)

all_factors.remove(n)

prime_factors = [x for x in all_factors if isprime(x)]

prime_factors.sort(reverse=True)

result = []

remainder = n

for f in prime_factors:

while remainder >= f:

qut, rem = divmod(remainder, f)

if rem != 0:

break

else:

remainder = qut

result.append(f)

return result

# 获取前N个斐波那契数列

def fibonacci(n):

result = []

if n == 1:

result.append(1)

elif n >= 2:

result.append(1)

result.append(1)

for i in range(2, n):

result.append(result[-1] + result[-2])

return result

def main():

print(fibonacci(8))

mod(0.78)

print(maxCommonDivisor(24, 36))

print(minCommonMultiple(24, 36))

if __name__ == '__main__':

main()