双色球笔记3--输出所有中奖号码

1、功能

本文主要根据中奖类别输出所有中奖号码，双色球奖项分为6种，如下所示：
一等奖（6+1）中奖概率为：红球33选6乘以蓝球16选1=1/17721088=0.0000056%；
二等奖（6+0）中奖概率为：红球33选6乘以蓝球16选1=15/17721088=0.0000846%；
三等奖（5+1）中奖概率为：红球33选5乘以蓝球16选1=162/17721088=0.000914%；
四等奖（5+0、4+1）中奖概率为：红球33选5乘以蓝球16选0=7695/17721088=0.0434%；
五等奖（4+0、3+1）中奖概率为：红球33选4乘以蓝球16选0=137475/17721088=0.7758%；
六等奖（2+1、1+1、0+1）中奖概率为：红球33选2乘以蓝球16选1=1043640/17721088=5.889%；
共计中奖率：6.71%。

2、代码

根据双色球种类，笔者将其进行如下归类。左边红球表示1到6-右边蓝球表示7，*表示不同的个数，.表示相同的个数，以下计算都约定红球升序。

1）综合预览

该部分计算各项中奖数量、中奖率等问题：

# -*- coding:utf-8 -*-
def fn(x):ret = 1for i in range(1,x+1):ret = ret*ireturn retdef cn(x,y):ret = fn(x)/(fn(y)*fn(x-y))return retif __name__=='__main__':ret = 16*cn(33,6)print('All:',ret)ret1 = 1print('L1',ret1)ret2 = 15print('L2',ret2)ret3 = cn(6,5)*27print('L3',ret3)ret4 = cn(6,5)*27*15+cn(6,4)*cn(27,2)print('L4',ret4)ret5 = cn(6,4)*cn(27,2)*15+cn(6,3)*cn(27,3)print('L5',ret5)ret6 = cn(6,2)*cn(27,4)+cn(6,1)*cn(27,5)+cn(27,6)print('L6',ret6)retSum = ret1+ret2+ret3+ret4+ret5+ret6print('retSum:',retSum)print('Rate:',1.0*retSum/ret)

2）单项实现

根据约定，笔者将1-6等奖的抽象分布归纳如下：

Level1：包括 ......-.
L1只包括1种情况，sum=1

Level2：包括 ......-*
L2只包括1类，sum=15=1*15

Level3：包括 .....*-.
L3只包括1类，sum=162=C(6,5)*C(27,1)*1
说明：红球5个相同1个不同C(6,5)*C(27,1)，蓝球相同

Level4：包括 .....*-* 和 ....**-.
L4包括2类，sum=7695=L3*15+C(6,4)*C(27,2)*1
L4_1:.....*-*
说明：红球5个相同1个不同C(6,5)*C(27,1)，蓝球不同C(15,1)，即L3*15
L4_2:....**-.
说明：红球4个相同2个不同C(6,4)*C(27,2)，蓝球相同

Level5：包括 ....**-* 和 ...***-.
L5包括2类，sum=137475=L4_2*15+C(6,3)*C(27,3)*1
L5_1:....**-*
说明：红球4个相同2个不同C(6,2)*C(27,4)，蓝球不同C(15,1)，即L4_2*15
L5_2:...***-.
说明：红球3个相同3个不同C(6,3)*C(27,3)，蓝球相同

Level6：包括 ..****-. 和 .*****-. 以及 ******-.
L6包括3类，sum=1188988=C(6,2)*C(27,4)*1+C(6,1)*C(27,5)*1+C(27,6)*1
L6_1:..****-.
说明：红球2个相同4个不同C(6,2)*C(27,4)，篮球相同
L6_2:.*****-.
说明：红球1个相同5个不同C(6,1)*C(27,5)，篮球相同
L6_3:******-.
说明：红球0个相同6个不同C(27,6)，篮球相同

代码如下：

# -*- coding:utf-8 -*-
import csvdef SaveToCSV(dataList,fileName,rwtype='w'):with open(fileName, rwtype, newline='') as csvfile:writer  = csv.writer(csvfile)for row in dataList:writer.writerow(row)def Level1(lsList):print('\nL1',lsList)print('......-.')retList = [lsList]return retListdef Level2(lsList):print('\nL2',lsList)print('......-*')retList = []for i in range(1,17):tmp = lsList[0:]if(i != lsList[6]):tmp[6] = iretList.append(tmp)return retListdef Level3(lsList):print('\nL3',lsList)print('.....*-.')retList = []leftList = [] #save numbers that can be usedlsList6 = lsList[0:6]for i in range(1,34):if(i not in lsList6):leftList.append(i)lsList5 = [] #save lists which contain 5 numbers in lslistfor i in range(0,len(lsList)-1):lsListBak = lsList[0:]lsListBak.remove(lsList[i])lsList5.append(lsListBak)for i in lsList5:for j in leftList:tmp = i[0:5]tmp.append(j)tmp.sort()retList.append(tmp)retList.sort()for i in retList:i.append(lsList[6])return retListdef Level4_1(lsList):retList = []retListL3 = Level3(lsList)for i in range(1,17):if(i != lsList[6]):for j in retListL3:tmp = j[0:]tmp[6] = iretList.append(tmp)retList.sort()return retList
def Level4_2(lsList):retList = []lsListLeft = lsList[0:6]#get all C(6,4)lsList6_4 = []lsList6_2 = []for i in range(0,5):for j in range(i+1,6):tmpList = [lsListLeft[i],lsListLeft[j]]lsList6_2.append(tmpList)for i in lsList6_2:tmpList = lsListLeft[0:]tmpList.remove(i[0])tmpList.remove(i[1])lsList6_4.append(tmpList)#get all C(27,2)lsList27 = []for i in range(1,34):if(i not in lsListLeft):lsList27.append(i)lsList27_2 = []for i in range(0,26):for j in range(i+1,27):tmpList = [lsList27[i],lsList27[j]]lsList27_2.append(tmpList)#get all C(6,4) and C(27,2)for i in lsList6_4:for j in lsList27_2:tmpList = i[0:]tmpList.append(j[0])tmpList.append(j[1])tmpList.sort()tmpList.append(lsList[6])retList.append(tmpList)           retList.sort()return retList
def Level4(lsList):print('\nL4',lsList)retList = []print('.....*-*')retList4_1 = Level4_1(lsList)print('....**-.')retList4_2 = Level4_2(lsList)for i in retList4_1:retList.append(i)for i in retList4_2:retList.append(i)retList.sort()return retListdef Level5_1(lsList):retList = []retList4_2 = Level4_2(lsList)for i  in range(1,17):if(i != lsList[6]):for j in retList4_2:tmp = j[0:]tmp[6] = iretList.append(tmp)retList.sort()return retList
def Level5_2(lsList):retList = []lsListLeft = lsList[0:6]#get all C(6,3)lsList6_3 = []for i in range(0,4):for j in range(i+1,5):for k in range(j+1,6):tmpList = [lsListLeft[i],lsListLeft[j],lsListLeft[k]]lsList6_3.append(tmpList)#get all C(27,3)lsList27 = []for i in range(1,34):if(i not in lsListLeft):lsList27.append(i)lsList27_3 = []for i in range(0,25):for j in range(i+1,26):for k in range(j+1,27):tmpList = [lsList27[i],lsList27[j],lsList27[k]]lsList27_3.append(tmpList)#get all C(6,3) and C(27,3)for i in lsList6_3:for j in lsList27_3:tmpList = i[0:]tmpList.append(j[0])tmpList.append(j[1])tmpList.append(j[2])tmpList.sort()tmpList.append(lsList[6])retList.append(tmpList)          retList.sort()return retList
def Level5(lsList):print('\nL5',lsList)retList = []print('....**-*')retList5_1 = Level5_1(lsList)print('...***-.')retList5_2 = Level5_2(lsList)for i in retList5_1:retList.append(i)for i in retList5_2:retList.append(i)retList.sort()return retListdef Level6_1(lsList):retList = []#get all C(6,2)lsListLeft = lsList[0:6]lsList6_2 = []for i in range(0,5):for j in range(i+1,6):tmpList = [lsListLeft[i],lsListLeft[j]]lsList6_2.append(tmpList)#get all C(27,4)lsList27 = []for i in range(1,34):if(i not in lsListLeft):lsList27.append(i)lsList27_4 = []for i in range(0,24):for j in range(i+1,25):for k in range(j+1,26):for l in range(k+1,27):tmpList = [lsList27[i],lsList27[j],lsList27[k],lsList27[l]]lsList27_4.append(tmpList)#merge C(6,2) and C(27,4)for i in lsList6_2:for j in lsList27_4:tmpList = i[0:]tmpList.append(j[0])tmpList.append(j[1])tmpList.append(j[2])tmpList.append(j[3])tmpList.sort()tmpList.append(lsList[6])retList.append(tmpList)           retList.sort()return retList
def Level6_2(lsList):retList = []#get all C(6,1)lsListLeft = lsList[0:6]lsList6_1 = []for i in range(0,6):tmpList = [lsListLeft[i]]lsList6_1.append(tmpList)#get all C(27,5)lsList27 = []for i in range(1,34):if(i not in lsListLeft):lsList27.append(i)lsList27_5 = []for i in range(0,23):for j in range(i+1,24):for k in range(j+1,25):for l in range(k+1,26):for m in range(l+1,27):tmpList = [lsList27[i],lsList27[j],lsList27[k],lsList27[l],lsList27[m]]lsList27_5.append(tmpList)#merge C(6,1) and C(27,5)for i in lsList6_1:for j in lsList27_5:tmpList = i[0:]tmpList.append(j[0])tmpList.append(j[1])tmpList.append(j[2])tmpList.append(j[3])tmpList.append(j[4])tmpList.sort()tmpList.append(lsList[6])retList.append(tmpList)          retList.sort()return retList
def Level6_3(lsList):retList = []lsListLeft = lsList[0:6]#get all C(27,6)lsList27 = []for i in range(1,34):if(i not in lsListLeft):lsList27.append(i)lsList27_6 = []for i in range(0,22):for j in range(i+1,23):for k in range(j+1,24):for l in range(k+1,25):for m in range(l+1,26):for n in range(m+1,27):tmpList = [lsList27[i],lsList27[j],lsList27[k],lsList27[l],lsList27[m],lsList27[n]]lsList27_6.append(tmpList)#merge C(27,6)for j in lsList27_6:tmpList = []tmpList.append(j[0])tmpList.append(j[1])tmpList.append(j[2])tmpList.append(j[3])tmpList.append(j[4])tmpList.append(j[5])tmpList.sort()tmpList.append(lsList[6])retList.append(tmpList)            retList.sort()return retList
def Level6(lsList):print('\nL6',lsList)retList = []print('..****-.')retList6_1 = Level6_1(lsList)print('.*****-.')retList6_2 = Level6_2(lsList)print('******-.')retList6_3 = Level6_3(lsList)for i in retList6_1:retList.append(i)for i in retList6_2:retList.append(i)for i in retList6_3:retList.append(i)retList.sort()return retListif __name__=='__main__':lsList = [1,2,3,4,5,10,6]####################################retList1 = Level1(lsList)print('L1 count:',len(retList1))retList1.append(['count',len(retList1)])SaveToCSV(retList1,'Level1.csv','w')    ####################################retList2 = Level2(lsList)print('L2 count:',len(retList2))retList2.append(['count',len(retList2)])SaveToCSV(retList2,'Level2.csv','w')  ####################################retList3 = Level3(lsList)print('L3 count:',len(retList3))retList3.append(['count',len(retList3)])SaveToCSV(retList3,'Level3.csv','w')####################################retList4 = Level4(lsList)print('L4 count:',len(retList4))retList4.append(['count',len(retList4)])SaveToCSV(retList4,'Level4.csv','w')####################################retList5 = Level5(lsList)print('L5 count:',len(retList5))retList5.append(['count',len(retList5)])SaveToCSV(retList5,'Level5.csv','w')####################################retList6 = Level6(lsList)print('L6 count:',len(retList6))retList6.append(['count',len(retList6)])SaveToCSV(retList6,'Level6.csv','w')

3、说明

本代码当前测试环境为python3.5