#!/usr/local/bin/python
# -*- coding: utf-8 -*-

from __future__ import division
from operator import mul

def P(m,n):
    '''
    基本概率计算: P(E)
    '''
    return m/n

def per(n):
    '''
    计算阶乘
    '''
    return reduce(mul,range(n,0,-1))

def combination(n,r):
    '''
    计算组合
    '''
    return per(n)/( per(r)*per(n-r) )

import unittest
class TestPermutations(unittest.TestCase):
    def setUp(self):
        pass
    def testPer(self):
        self.assertEqual(per(5),5*4*3*2*1)
    def testComb(self):
        self.assertEqual(combination(n=4,r=2),6)
        self.assertEqual(int(round(combination(n=49,r=6))),13983816)
    def testBasicpe(self):
        '''
        P(掷一公平骰子得出6)=1/6
        '''
        self.assertEqual(P(1,6),1.0/6.0)
    def testAdd(self):
        '''
        加法定理验证

        如果掷两粒公平骰子，擲出2和4的概率分别是多少？
        '''
        self.assertEqual( P(1,36),1/36 )
        self.assertEqual( P(1,36)+P(1,36)+P(1,36),3/36 )
    def testMultiplication(self):
        '''
        乘法定理验证

        假设掷三粒公平骰子所得出数字之积为k。P(k是奇数)是多少？
        P(k是奇数)=P(第一个数是奇数)*P(第二个数是奇数)*P(第三个数是奇数)=3/6*3/6*3/6=1/8
        '''
        self.assertEqual( P(3,6)*P(3,6)*P(3,6),1/8 )


if __name__ == '__main__':
    unittest.main()