考试中知道自己的成绩以及其他所有人的成绩，计算在特定情况下自己参加复试的概率。

      写在最前，我是菜鸟，到现在接触python不足两周，这期间看书以及视频学习基本知识，不过总感觉效果不理想。前几天我参加了一个事业单位招聘考试，两天后公布了所有考生的成绩，一共3196名。看完后我就有个想法，想计算我能参加复试的概率，就拿python来练手，边练边学，看效果怎样。

      要求是这样的：

            总参考人数3196名考生的考号和对应分数在excel表格中，已知我所报考单位只招聘一人，报考该单位考生一共71人，按1：3参加复试，也就是说这71人里边前三名可以参               加复试。已知我的成绩，想求我能参加复试的概率。（注：在这3196名考生中，不知道是哪70人和自己报考同一单位）

       因为是新手，接下来我会详细记录我的学习过程，如果在看文章的你也是刚刚接触python并想深入学习，希望我的学习历程能对你有所帮助，若有幸能被高手读到，还希望能不吝指教。

      我把目标拆分成几个步骤，如下：

            1，除去自己，在其余3195名中找出包含70个元素的所有组合，并统计组合的个数为Y；

　　　　 2，将自己的成绩添加到每个组合中；

　　　　 3，对这些组合从大到小排序；

　　　　 4，统计自己的成绩在前三名的组合的个数为X；

　　　　 5，计算X/Y，即得自己能参加复试的概率。

       下面各个解决

             1，首先解决如何找出包含70个元素的组合，代码如下

                 

import itertools
Combinatorial_Sequences = itertools.combinations(test_result,70) #test_result是存储成绩序列的变量

               刚开始问题就出现了，电脑一直卡死，我猜想问题应该是结果太多，计算量太大。于是我决定计算一下组合的个数，根据基本公式C(m,n)=m!/[(m-n)!*n!]，编写代码如下：

def combinatorial_num(m,n):  #定义求解组合个数函数
    t = 1
    i = m-1
    u = n-1
    while t < n:
        m = m*i
        i -= 1
        t += 1
    while u >0:
        n = n*u
        u -= 1
    return int(m/n)
>>> combinatorial_num(3195,70)
8014553219879436656594612402147999867010534534563546688481573383337953460075426682671389800532431942744732420482095853198125506158432530850643968

>>> combinatorial_num(5,3)   #刚才忘记了，我要验证一下这段代码正确与否，好让你相信上面那一长串数字是正确的结果。
10
>>> combinatorial_num(6,4)
15
>>> combinatorial_num(7,3)
35

         

     显然组合个数太TM多了，怪不得会卡死。所以，必须改变路线——缩小数字，在理想情况下计算结果。但是这样就没办法计算我能参加复试的概率了，不过这也无妨，因为结果已经公布了——我没有进入复试，管他呢，现在的目标是学习Python解决我提出的问题。

     问题更改为

             总参考人数15名考生的考号和对应分数在excel表格中，已知我所报考单位只招聘一人，报考该单位考生一共4人，按1：2参加复试，也就是说这4人里边前2名可以参                                  加复试。已知我的成绩排在第5名，想求我能参加复试的概率。（注：在这15名考生中，不知道是哪4人和自己报考同一单位）

第一步：除去自己，在其余15名中找出包含3个元素的所有组合；

          请原谅我真的把这364个组合一并贴出来了

import itertools
all_results = [81.25,80.05,78.95,78.7,76.65,76.5,76.15,75.7,75.15,74.25,73.9,73.75,73.7,73.65,73.4]    #15个考生的成绩列表
exclude_me = all_results[:4]+all_results[5:]     #假设自己是第5名，除去自己的成绩（注：python从0开始计数）
combinations_exclude_me = itertools.combinations(exclude_me,3）   #计算出包含三个元素的所有组合，存在变量combinations_exclude_me中
print(list(combinations_exclude_me))      #输出所有组合

[(81.25, 80.05, 78.95), (81.25, 80.05, 78.7), (81.25, 80.05, 76.5), (81.25, 80.05, 76.15), (81.25, 80.05, 75.7), (81.25, 80.05, 75.15), (81.25, 80.05, 74.25), (81.25, 80.05, 73.9), (81.25, 80.05, 73.75), (81.25, 80.05, 73.7), (81.25, 80.05, 73.65), (81.25, 80.05, 73.4), (81.25, 78.95, 78.7), (81.25, 78.95, 76.5), (81.25, 78.95, 76.15), (81.25, 78.95, 75.7), (81.25, 78.95, 75.15), (81.25, 78.95, 74.25), (81.25, 78.95, 73.9), (81.25, 78.95, 73.75), (81.25, 78.95, 73.7), (81.25, 78.95, 73.65), (81.25, 78.95, 73.4), (81.25, 78.7, 76.5), (81.25, 78.7, 76.15), (81.25, 78.7, 75.7), (81.25, 78.7, 75.15), (81.25, 78.7, 74.25), (81.25, 78.7, 73.9), (81.25, 78.7, 73.75), (81.25, 78.7, 73.7), (81.25, 78.7, 73.65), (81.25, 78.7, 73.4), (81.25, 76.5, 76.15), (81.25, 76.5, 75.7), (81.25, 76.5, 75.15), (81.25, 76.5, 74.25), (81.25, 76.5, 73.9), (81.25, 76.5, 73.75), (81.25, 76.5, 73.7), (81.25, 76.5, 73.65), (81.25, 76.5, 73.4), (81.25, 76.15, 75.7), (81.25, 76.15, 75.15), (81.25, 76.15, 74.25), (81.25, 76.15, 73.9), (81.25, 76.15, 73.75), (81.25, 76.15, 73.7), (81.25, 76.15, 73.65), (81.25, 76.15, 73.4), (81.25, 75.7, 75.15), (81.25, 75.7, 74.25), (81.25, 75.7, 73.9), (81.25, 75.7, 73.75), (81.25, 75.7, 73.7), (81.25, 75.7, 73.65), (81.25, 75.7, 73.4), (81.25, 75.15, 74.25), (81.25, 75.15, 73.9), (81.25, 75.15, 73.75), (81.25, 75.15, 73.7), (81.25, 75.15, 73.65), (81.25, 75.15, 73.4), (81.25, 74.25, 73.9), (81.25, 74.25, 73.75), (81.25, 74.25, 73.7), (81.25, 74.25, 73.65), (81.25, 74.25, 73.4), (81.25, 73.9, 73.75), (81.25, 73.9, 73.7), (81.25, 73.9, 73.65), (81.25, 73.9, 73.4), (81.25, 73.75, 73.7), (81.25, 73.75, 73.65), (81.25, 73.75, 73.4), (81.25, 73.7, 73.65), (81.25, 73.7, 73.4), (81.25, 73.65, 73.4), (80.05, 78.95, 78.7), (80.05, 78.95, 76.5), (80.05, 78.95, 76.15), (80.05, 78.95, 75.7), (80.05, 78.95, 75.15), (80.05, 78.95, 74.25), (80.05, 78.95, 73.9), (80.05, 78.95, 73.75), (80.05, 78.95, 73.7), (80.05, 78.95, 73.65), (80.05, 78.95, 73.4), (80.05, 78.7, 76.5), (80.05, 78.7, 76.15), (80.05, 78.7, 75.7), (80.05, 78.7, 75.15), (80.05, 78.7, 74.25), (80.05, 78.7, 73.9), (80.05, 78.7, 73.75), (80.05, 78.7, 73.7), (80.05, 78.7, 73.65), (80.05, 78.7, 73.4), (80.05, 76.5, 76.15), (80.05, 76.5, 75.7), (80.05, 76.5, 75.15), (80.05, 76.5, 74.25), (80.05, 76.5, 73.9), (80.05, 76.5, 73.75), (80.05, 76.5, 73.7), (80.05, 76.5, 73.65), (80.05, 76.5, 73.4), (80.05, 76.15, 75.7), (80.05, 76.15, 75.15), (80.05, 76.15, 74.25), (80.05, 76.15, 73.9), (80.05, 76.15, 73.75), (80.05, 76.15, 73.7), (80.05, 76.15, 73.65), (80.05, 76.15, 73.4), (80.05, 75.7, 75.15), (80.05, 75.7, 74.25), (80.05, 75.7, 73.9), (80.05, 75.7, 73.75), (80.05, 75.7, 73.7), (80.05, 75.7, 73.65), (80.05, 75.7, 73.4), (80.05, 75.15, 74.25), (80.05, 75.15, 73.9), (80.05, 75.15, 73.75), (80.05, 75.15, 73.7), (80.05, 75.15, 73.65), (80.05, 75.15, 73.4), (80.05, 74.25, 73.9), (80.05, 74.25, 73.75), (80.05, 74.25, 73.7), (80.05, 74.25, 73.65), (80.05, 74.25, 73.4), (80.05, 73.9, 73.75), (80.05, 73.9, 73.7), (80.05, 73.9, 73.65), (80.05, 73.9, 73.4), (80.05, 73.75, 73.7), (80.05, 73.75, 73.65), (80.05, 73.75, 73.4), (80.05, 73.7, 73.65), (80.05, 73.7, 73.4), (80.05, 73.65, 73.4), (78.95, 78.7, 76.5), (78.95, 78.7, 76.15), (78.95, 78.7, 75.7), (78.95, 78.7, 75.15), (78.95, 78.7, 74.25), (78.95, 78.7, 73.9), (78.95, 78.7, 73.75), (78.95, 78.7, 73.7), (78.95, 78.7, 73.65), (78.95, 78.7, 73.4), (78.95, 76.5, 76.15), (78.95, 76.5, 75.7), (78.95, 76.5, 75.15), (78.95, 76.5, 74.25), (78.95, 76.5, 73.9), (78.95, 76.5, 73.75), (78.95, 76.5, 73.7), (78.95, 76.5, 73.65), (78.95, 76.5, 73.4), (78.95, 76.15, 75.7), (78.95, 76.15, 75.15), (78.95, 76.15, 74.25), (78.95, 76.15, 73.9), (78.95, 76.15, 73.75), (78.95, 76.15, 73.7), (78.95, 76.15, 73.65), (78.95, 76.15, 73.4), (78.95, 75.7, 75.15), (78.95, 75.7, 74.25), (78.95, 75.7, 73.9), (78.95, 75.7, 73.75), (78.95, 75.7, 73.7), (78.95, 75.7, 73.65), (78.95, 75.7, 73.4), (78.95, 75.15, 74.25), (78.95, 75.15, 73.9), (78.95, 75.15, 73.75), (78.95, 75.15, 73.7), (78.95, 75.15, 73.65), (78.95, 75.15, 73.4), (78.95, 74.25, 73.9), (78.95, 74.25, 73.75), (78.95, 74.25, 73.7), (78.95, 74.25, 73.65), (78.95, 74.25, 73.4), (78.95, 73.9, 73.75), (78.95, 73.9, 73.7), (78.95, 73.9, 73.65), (78.95, 73.9, 73.4), (78.95, 73.75, 73.7), (78.95, 73.75, 73.65), (78.95, 73.75, 73.4), (78.95, 73.7, 73.65), (78.95, 73.7, 73.4), (78.95, 73.65, 73.4), (78.7, 76.5, 76.15), (78.7, 76.5, 75.7), (78.7, 76.5, 75.15), (78.7, 76.5, 74.25), (78.7, 76.5, 73.9), (78.7, 76.5, 73.75), (78.7, 76.5, 73.7), (78.7, 76.5, 73.65), (78.7, 76.5, 73.4), (78.7, 76.15, 75.7), (78.7, 76.15, 75.15), (78.7, 76.15, 74.25), (78.7, 76.15, 73.9), (78.7, 76.15, 73.75), (78.7, 76.15, 73.7), (78.7, 76.15, 73.65), (78.7, 76.15, 73.4), (78.7, 75.7, 75.15), (78.7, 75.7, 74.25), (78.7, 75.7, 73.9), (78.7, 75.7, 73.75), (78.7, 75.7, 73.7), (78.7, 75.7, 73.65), (78.7, 75.7, 73.4), (78.7, 75.15, 74.25), (78.7, 75.15, 73.9), (78.7, 75.15, 73.75), (78.7, 75.15, 73.7), (78.7, 75.15, 73.65), (78.7, 75.15, 73.4), (78.7, 74.25, 73.9), (78.7, 74.25, 73.75), (78.7, 74.25, 73.7), (78.7, 74.25, 73.65), (78.7, 74.25, 73.4), (78.7, 73.9, 73.75), (78.7, 73.9, 73.7), (78.7, 73.9, 73.65), (78.7, 73.9, 73.4), (78.7, 73.75, 73.7), (78.7, 73.75, 73.65), (78.7, 73.75, 73.4), (78.7, 73.7, 73.65), (78.7, 73.7, 73.4), (78.7, 73.65, 73.4), (76.5, 76.15, 75.7), (76.5, 76.15, 75.15), (76.5, 76.15, 74.25), (76.5, 76.15, 73.9), (76.5, 76.15, 73.75), (76.5, 76.15, 73.7), (76.5, 76.15, 73.65), (76.5, 76.15, 73.4), (76.5, 75.7, 75.15), (76.5, 75.7, 74.25), (76.5, 75.7, 73.9), (76.5, 75.7, 73.75), (76.5, 75.7, 73.7), (76.5, 75.7, 73.65), (76.5, 75.7, 73.4), (76.5, 75.15, 74.25), (76.5, 75.15, 73.9), (76.5, 75.15, 73.75), (76.5, 75.15, 73.7), (76.5, 75.15, 73.65), (76.5, 75.15, 73.4), (76.5, 74.25, 73.9), (76.5, 74.25, 73.75), (76.5, 74.25, 73.7), (76.5, 74.25, 73.65), (76.5, 74.25, 73.4), (76.5, 73.9, 73.75), (76.5, 73.9, 73.7), (76.5, 73.9, 73.65), (76.5, 73.9, 73.4), (76.5, 73.75, 73.7), (76.5, 73.75, 73.65), (76.5, 73.75, 73.4), (76.5, 73.7, 73.65), (76.5, 73.7, 73.4), (76.5, 73.65, 73.4), (76.15, 75.7, 75.15), (76.15, 75.7, 74.25), (76.15, 75.7, 73.9), (76.15, 75.7, 73.75), (76.15, 75.7, 73.7), (76.15, 75.7, 73.65), (76.15, 75.7, 73.4), (76.15, 75.15, 74.25), (76.15, 75.15, 73.9), (76.15, 75.15, 73.75), (76.15, 75.15, 73.7), (76.15, 75.15, 73.65), (76.15, 75.15, 73.4), (76.15, 74.25, 73.9), (76.15, 74.25, 73.75), (76.15, 74.25, 73.7), (76.15, 74.25, 73.65), (76.15, 74.25, 73.4), (76.15, 73.9, 73.75), (76.15, 73.9, 73.7), (76.15, 73.9, 73.65), (76.15, 73.9, 73.4), (76.15, 73.75, 73.7), (76.15, 73.75, 73.65), (76.15, 73.75, 73.4), (76.15, 73.7, 73.65), (76.15, 73.7, 73.4), (76.15, 73.65, 73.4), (75.7, 75.15, 74.25), (75.7, 75.15, 73.9), (75.7, 75.15, 73.75), (75.7, 75.15, 73.7), (75.7, 75.15, 73.65), (75.7, 75.15, 73.4), (75.7, 74.25, 73.9), (75.7, 74.25, 73.75), (75.7, 74.25, 73.7), (75.7, 74.25, 73.65), (75.7, 74.25, 73.4), (75.7, 73.9, 73.75), (75.7, 73.9, 73.7), (75.7, 73.9, 73.65), (75.7, 73.9, 73.4), (75.7, 73.75, 73.7), (75.7, 73.75, 73.65), (75.7, 73.75, 73.4), (75.7, 73.7, 73.65), (75.7, 73.7, 73.4), (75.7, 73.65, 73.4), (75.15, 74.25, 73.9), (75.15, 74.25, 73.75), (75.15, 74.25, 73.7), (75.15, 74.25, 73.65), (75.15, 74.25, 73.4), (75.15, 73.9, 73.75), (75.15, 73.9, 73.7), (75.15, 73.9, 73.65), (75.15, 73.9, 73.4), (75.15, 73.75, 73.7), (75.15, 73.75, 73.65), (75.15, 73.75, 73.4), (75.15, 73.7, 73.65), (75.15, 73.7, 73.4), (75.15, 73.65, 73.4), (74.25, 73.9, 73.75), (74.25, 73.9, 73.7), (74.25, 73.9, 73.65), (74.25, 73.9, 73.4), (74.25, 73.75, 73.7), (74.25, 73.75, 73.65), (74.25, 73.75, 73.4), (74.25, 73.7, 73.65), (74.25, 73.7, 73.4), (74.25, 73.65, 73.4), (73.9, 73.75, 73.7), (73.9, 73.75, 73.65), (73.9, 73.75, 73.4), (73.9, 73.7, 73.65), (73.9, 73.7, 73.4), (73.9, 73.65, 73.4), (73.75, 73.7, 73.65), (73.75, 73.7, 73.4), (73.75, 73.65, 73.4), (73.7, 73.65, 73.4)]
>>>

 

          昨天看了微软build大会，一直到夜里3点，白天没休息，太困了，明天继续。   

      接下来任务是将我的成绩添加到各个组合中。问题来了，在经过多次尝试之后发现无法将元素添加进去，后来知道元组在确定之后是不允许修改的。所以需要把上面列表中的364个元组转换为列表。代码如下(这里只用假设的例子完成转换过程）

     然后将自己的成绩添加到各个列表（此处假设将6添加到个列表），将这两步一并给出。

a = [(5,2,7),(8,4,1),(9,3,6)]    #假设一个包含三个元组的列表a
i = 0
new_a = []
while i < (len(a)):   
    t = list(a[i])   #将a的第i个元素转换为列表并赋给变量t
    t.append(6)   #将元素‘6’添加到个列表
    new_a = new_a + [t]   
    i +=1
print(new_a)


[[5, 2, 7, 6], [8, 4, 1, 6], [9, 3, 6, 6]]    
>>> 

    然后对各个列表从大到小排序

new_a = [[5, 2, 7, 6], [8, 4, 1, 6], [9, 3, 6, 6]]   
i = 0
sorted_a = []
while i < len(new_a):
    new_a[i].sort(reverse=True)   # 将各个列表从大到小排序
    sorted_a = sorted_a + [new_a[i]]   # 拼接列表
    i += 1
print(sorted_a)

[[7, 6, 5, 2], [8, 6, 4, 1], [9, 6, 6, 3]]
 >>> 

    下面统计6在各个列表中排前三名的个数，并计算排前三名的个数站总组合个数的比例

sorted_a = [[7, 6, 5, 2], [8, 6, 4, 1], [9, 6, 6, 3]]
i = 0   
n = 0
while i < len(sorted_a):
    t = sorted_a[i].index(6)    #查找6在各个列表中的排名位数，返回给t
    if t < 3:                   
        n +=1    #当t<3时，即排在前三名时，计数变量n加1
    else :
        n = n    #当不在前三名，计数不变
    i += 1
print('排在前三位的个数为',n)
print('总组合个数为',len(sorted_a))
final_p = n/(len(sorted_a))    #排前三个数除以总组合个数
print("参加复试的概率为","%.2f%%" % (final_p*100))   #以百分比形式打印出此概率


>>> 
 排在前三位的个数为 3
 总组合个数为 3
 参加复试的概率为 100.00%        #   -_-||  这算是自己讽刺自己么，明明没参加复试，还找一个概率是100%的例子。。。 

   好吧，最后就用原始数据，当然是截取过的原始数据，来用完整代码跑一下。

import itertools

all_results = [81.25,80.05,78.95,78.7,76.65,76.5,76.15,75.7,75.15,74.25,73.9,73.75,73.7,73.65,73.4]
results_exclude_me = all_results[:4]+all_results[5:]  #除去我的分数
all_combinations = list(itertools.combinations(results_exclude_me,3))  #得到除我以外的含有三个元素的所有组合
i = 0
success_num = 0  #初始化排前三位的个数
while i < (len(all_combinations)):
     t = list(all_combinations[i])    #将元组转换为列表
     t.append(all_results[4])    #将我的成绩添加到各组合
     t.sort(reverse=True)        #对组合进行排序
     n = t.index(all_results[4])
     if n < 3:
         success_num +=1
     else:
         success_num = success_num
     i += 1
combinations_num = len(all_combinations)
print('排在前三位的次数为：',success_num)
print('总组合个数为：',combinations_num)
print('参加复试的概率为',"%.2f%%" % ((success_num/combinations_num)*100))

结果如下

>>> 
当测试者排第4位时

排在前三位的次数为： 360 
总组合个数为： 364
参加复试的概率为 98.90%

     

当测试者排第8位时：     #此行非程序运行得到
排在前三位的次数为： 308
总组合个数为： 364
参加复试的概率为 84.62%
>>> 

 

至此完毕，暂时得到了最初想要的结果，不过我认为还有太多地方可以改进，暂时想到的改进点有：

　　　　1，原始数据可以通过读取文件的方式导入

　　　　2，如果能和使用者交互会更好，比如允许使用者输入自己的名次，然后得到结果。

写在最后

      程序虽然很小，可是完成下来真的学到了太多的知识，远远比啃书本效率高很多。事先本来想在最后把在这个过程学到的知识点罗列出来，不过玩了才发现，真是太多了，有些只是很小的方面，比如说冒号的使用，所以就不罗列了。

      望各路大神不吝指教！