Python 秘密圣诞老人计划 - 如何获得更高的成功率

Question

我决定制作一个Python 程序，该程序根据硬编码限制生成秘密圣诞老人配对（例如，某人找不到他的妻子）。我的家人日程很忙，所以很难组织每个人随机抽帽子。

我的程序很少崩溃，因为不幸的随机配对使剩余的配对不合法（但是，我在测试脚本部分中发现了它们）。将其视为亲自重新绘制。

但是，当我的程序成功时，我无需亲自查看配对就知道配对是正确的，因为我的程序会测试有效性。明天，我将不得不找到一种方法，使用这些配对从我的电子邮件帐户向每个人发送一封电子邮件，告诉他们他们拥有谁，而我却不知道谁拥有谁，甚至谁拥有我。

以下是我的完整程序代码（所有代码都是我自己的；我没有在网上查找任何解决方案，因为我希望自己能完成最初的挑战）：

# Imports

import random
import copy
from random import shuffle

# Define Person Class

class Person:
    def __init__(self, name, email):
        self.name = name
        self.email = email
        self.isAllowedToHaveSecretSanta = True
        self.isSecretSanta = False
        self.secretSanta = None

# ----- CONFIGURATION SCRIPT -----

# Initialize people objects

brother1 = Person("Brother1", "brother1@gmail.com")
me = Person("Me", "me@gmail.com")
brother2 = Person("Brother2", "brother2@gmail.com")
brother2Girlfriend = Person("Brother2Girlfriend", "brother2Girlfriend@gmail.com")
brother3 = Person("Brother3", "brother3@gmail.com")
brother3Girlfriend = Person("Brother3Girlfriend", "brother3Girlfriend@gmail.com")
brother4 = Person("Brother4", "brother4@gmail.com")
brother4Girlfriend = Person("Brother4Girlfriend", "brother4Girlfriend@gmail.com")
brother5 = Person("Brother5", "brother5@yahoo.com")
brother5Girlfriend = Person("Brother5Girlfriend", "brother5Girlfriend@gmail.com")
myDad = Person("MyDad", "myDad@gmail.com")
myDad.isAllowedToHaveSecretSanta = False
myMom = Person("MyMom", "myMom@gmail.com")
myMom.isAllowedToHaveSecretSanta = False
dadOfBrother4Girlfriend = Person("DadOfBrother4Girlfriend", "dadOfBrother4Girlfriend@gmail.com")
momOfBrother4Girlfriend = Person("MomOfBrother4Girlfriend", "momOfBrother4Girlfriend@gmail.com")

# Initialize list of people

personList = [brother1,
              me,
              brother2,
              brother2Girlfriend,
              brother3,
              brother3Girlfriend,
              brother4,
              brother4Girlfriend,
              brother5,
              brother5Girlfriend,
              myDad,
              myMom,
              dadOfBrother4Girlfriend,
              momOfBrother4Girlfriend]

# Initialize pairing restrictions mapping
# This is a simple dictionary where the key
# is a person and the value is a list of people who
# can't be that person's secret santa (they might
# be mom, girlfriend, boyfriend, or any reason)

restrictionsMapping = {brother1.name: [],
                       me.name: [], #anybody can be my secret santa
                       brother2.name: [brother2Girlfriend.name],
                       brother2Girlfriend.name: [brother2.name],
                       brother3.name: [brother3Girlfriend.name],
                       brother3Girlfriend.name: [brother3.name],
                       brother4.name: [brother4Girlfriend.name, dadOfBrother4Girlfriend.name, momOfBrother4Girlfriend.name],
                       brother4Girlfriend.name: [brother4.name, dadOfBrother4Girlfriend.name, momOfBrother4Girlfriend.name],
                       brother5.name: [brother5Girlfriend.name],
                       brother5Girlfriend.name: [brother5.name],
                       dadOfBrother4Girlfriend.name: [momOfBrother4Girlfriend.name, brother4Girlfriend.name, brother4.name],
                       momOfBrother4Girlfriend.name: [dadOfBrother4Girlfriend.name, brother4Girlfriend.name, brother4.name]}

# Define Secret Santa Class (Necessary for testing script)

class SecretSantaPairingProcess:

    # INITIALIZER

    def __init__(self, personList, restrictionsMapping):
        self.personList = copy.deepcopy(personList)
        self.restrictionsMapping = restrictionsMapping
        self.isValid = True

    # INSTANCE METHODS

    # Define a method that generates the list of eligible secret santas for a person
    def eligibleSecretSantasForPerson(self, thisPerson):
        # instantiate a list to return
        secretSantaOptions = []
        for thatPerson in self.personList:
            isEligible = True
            if thatPerson is thisPerson:
                isEligible = False
                # print("{0} CAN'T receive from {1} (can't receive from self)".format(thisPerson.name, thatPerson.name))
            if thatPerson.name in self.restrictionsMapping[thisPerson.name]:
                isEligible = False
                # print("{0} CAN'T receive from {1} (they're a couple)".format(thisPerson.name, thatPerson.name))
            if thatPerson.isSecretSanta is True:
                isEligible = False
                # print("{0} CAN'T receive from {1} ({1} is alrady a secret santa)".format(thisPerson.name, thatPerson.name))
            if isEligible is True:
                # print("{0} CAN receive from {1}".format(thisPerson.name, thatPerson.name))
                secretSantaOptions.append(thatPerson)
        # shuffle the options list we have so far
        shuffle(secretSantaOptions)
        # return this list as output
        return secretSantaOptions

    # Generate pairings
    def generatePairings(self):
        for thisPerson in self.personList:
            if thisPerson.isAllowedToHaveSecretSanta is True:
                # generate a temporary list of people who are eligible to be this person's secret santa
                eligibleSecretSantas = self.eligibleSecretSantasForPerson(thisPerson)
                # get a random person from this list
                thatPerson = random.choice(eligibleSecretSantas)
                # make that person this person's secret santa
                thisPerson.secretSanta = thatPerson
                thatPerson.isSecretSanta = True
                # print for debugging / testing
                # print("{0}'s secret santa is {1}.".format(thisPerson.name, thatPerson.name))

    # Validate pairings
    def validatePairings(self):
        for person in self.personList:
            if person.isAllowedToHaveSecretSanta is True:
                if person.isSecretSanta is False:
                        # print("ERROR - {0} is not a secret santa!".format(person.name))
                        self.isValid = False
                if person.secretSanta is None:
                    # print("ERROR - {0} does not have a secret santa!".format(person.name))
                    self.isValid = False
                if person.secretSanta is person:
                    self.isValid = False
                if person.secretSanta.name in self.restrictionsMapping[person.name]:
                    self.isValid = False
                for otherPerson in personList:
                    if (person is not otherPerson) and (person.secretSanta is otherPerson.secretSanta):
                        # print("ERROR - {0}'s secret santa is the same as {1}'s secret santa!".format(person.name, otherPerson.name))
                        self.isValid = False


# ----- EXECUTION SCRIPT -----

### Generate pairings
##
##secretSanta = SecretSantaPairingProcess(personList, restrictionsMapping)
##secretSanta.generatePairings()
##
### Validate results
##
##secretSanta.validatePairings()
##if secretSanta.isValid is True:
##    print("This is valid")
##else:
##    print("This is not valid")

# ----- TESTING SCRIPT -----

successes = 0
failures = 0
crashes = 0
successfulPersonLists = []

for i in range(1000):
    try:
        secretSanta = SecretSantaPairingProcess(personList, restrictionsMapping)
        secretSanta.generatePairings()
        secretSanta.validatePairings()
        if secretSanta.isValid is True:
            # print("This is valid")
            successes += 1
            successfulPersonLists.append(secretSanta.personList)
        else:
            # print("This is not valid")
            failures += 1
    except:
        crashes += 1
    print("Finished test {0}".format(i))

print("{0} successes".format(successes))
print("{0} failures".format(failures))
print("{0} crashes".format(crashes))

for successList in successfulPersonLists:
    print("----- SUCCESS LIST -----")
    for successPerson in successList:
        if successPerson.isAllowedToHaveSecretSanta is True:
            print("{0}'s secret santa is {1}".format(successPerson.name, successPerson.secretSanta.name))
        else:
            print("{0} has no secret santa".format(successPerson.name))

请原谅我有一些多余的代码，但我已经离开 Python 有一段时间了，没有太多时间重新学习和重新研究概念。

起初，我的程序测试如下：大部分成功测试，0 次失败（非法配对），很少崩溃（原因我上面提到的）。然而，那是在我的家人决定为今年的秘密圣诞老人添加新规则之前。我妈妈可能是某人的秘密圣诞老人，爸爸也可能是，但没有人可以成为他们的秘密圣诞老人（因为每个人每年都会收到礼物）。我哥嫂的父母也要包括在内，我哥、他老婆和他嫂嫂之间不能有任何配对。

当我加入这些新的限制规则时，我的测试大多失败，很少成功（因为随机性通常导致 2 或 1 人在执行结束时没有秘密圣诞老人）。见下文：

Secret Santa 流程中设置的限制越多，要解决的问题就越复杂。我渴望提高这个项目的成功率。有办法吗？在考虑秘密圣诞老人的限制时，我需要考虑哪些规则（置换规则或数学上的通用规则）？

Answer 1

这是bipartite matching problem。您有两组节点：一组用于提供者，一组用于接收者。每个集合都有一个用于您家庭中每个人的节点。如果该对有效，则从给予者到接收者有一条边。否则没有优势。然后应用二分匹配算法。