生日悖论

Question

我想在java中模拟生日悖论。出于某种原因，我的输出（概率）一直非常接近1，例如模拟（10）->09268。一开始，你可以看到我的模拟应该接近的概率。我已经在代码中查找错误很长一段时间了，所以我希望你们中的任何人都能帮助我。我已经查找了生日悖论的其他代码，但似乎没有一个能帮助我处理奇怪的输出。附言：你可以忽略//TODO，一旦我启动并运行代码，就会修复它。感谢是提前！

static final int DAYS_IN_YEAR = 365;
static final int NUMBER_OF_SIMULATIONS = 500; 
LCG random;
HashSet<Integer> birthdaySet = new HashSet<Integer>();
BirthdayProblem2(){
    birthdaySet.clear();
    random = new LCG(); //random numbers between 0 and 1
}
int generateBirthday(){ //generates random birthday
    return (int) Math.round(Math.random()*DAYS_IN_YEAR); //TODO use LGC
}
double iteration(int numberOfStudents){ //one iteration from the simulation
    int sameBirthdays = 0;
    for (int i = 0; i < numberOfStudents; i++){
        int bd = generateBirthday();
        if (birthdaySet.contains(bd)){
            sameBirthdays++;
        } else {
            birthdaySet.add(bd);
        }           
    }
    return (double) sameBirthdays/numberOfStudents; //probability of two students having the same birthday
}
void simulation(int numberOfStudents){
    double probabilitySum = 0;
    for (int i = 0; i < NUMBER_OF_SIMULATIONS; i++){
        probabilitySum += iteration(numberOfStudents);
    }
    System.out.printf("For n=%d -> P=%.4f n", numberOfStudents, probabilitySum/NUMBER_OF_SIMULATIONS);
}
private void start() {
    simulation(10); //should be about 0.1
    simulation(20); //should be about 0.4
    simulation(23); //should be about 0.5
    simulation(35); //should be about 0.8
}
public static void main(String[] argv) {
    new BirthdayProblem2().start();
}

}

Answer 1

您没有在迭代之间清除birthdaySet。将其从字段更改为局部变量可以防止类似的错误，因为为什么首先需要将其作为字段？

另一方面，generateBirthday应该使用Random.nextInt(DAYS_IN_YEAR)。Random的一个实例是作为字段的主要候选者。那条LCG random;线是什么？

更新

方法iteration()应该返回布尔值，用于判断是否有生日相同的学生。返回的真值数除以调用数等于概率。

由于一年中的天数相对较少，布尔数组将比Set更快，因此这里有更新的代码：

private static final int DAYS_IN_YEAR = 365;
private static final int NUMBER_OF_SIMULATIONS = 500;
private Random rnd = new Random();
private int generateBirthday() {
    return this.rnd.nextInt(DAYS_IN_YEAR);
}
private boolean iteration(int numberOfStudents) { //one iteration from the simulation
    boolean[] present = new boolean[DAYS_IN_YEAR];
    for (int i = 0; i < numberOfStudents; i++) {
        int birthday = generateBirthday();
        if (present[birthday])
            return true;
        present[birthday] = true;
    }
    return false;
}
void simulation(int numberOfStudents){
    int count = 0;
    for (int i = 0; i < NUMBER_OF_SIMULATIONS; i++)
        if (iteration(numberOfStudents))
            count++;
    System.out.printf("For n=%d -> P=%.4f%n", numberOfStudents, (double)count/NUMBER_OF_SIMULATIONS);
}

样本输出

For n=10 -> P=0.1340
For n=20 -> P=0.4120
For n=23 -> P=0.5080
For n=35 -> P=0.8160

For n=10 -> P=0.1200
For n=20 -> P=0.4120
For n=23 -> P=0.5260
For n=35 -> P=0.8140

For n=10 -> P=0.1260
For n=20 -> P=0.3920
For n=23 -> P=0.5080
For n=35 -> P=0.7920

将NUMBER_OF_SIMULATIONS增加到5_000_000:

For n=10 -> P=0.1167
For n=20 -> P=0.4113
For n=23 -> P=0.5075
For n=35 -> P=0.8145

For n=10 -> P=0.1168
For n=20 -> P=0.4113
For n=23 -> P=0.5072
For n=35 -> P=0.8142

Answer 2

由于andreas已经声明birthdaySet应在迭代之间清除，否则该集合将包含来自先前模拟的数据

然而，在你的设计中还有另一个致命的缺陷，看看维基百科页面：

在概率论中，生日问题或生日悖论涉及在一组n个随机选择的人中，他们中的某一对会有相同生日的概率

有可能至少有两个人的生日相同。这意味着只要2等于1，就应该返回1。

我在下面的代码中总结了一下

import java.util.HashSet;
import java.util.Random;
public class BirthdayProblem2 {
    static final int DAYS_IN_YEAR = 365;
    static final int NUMBER_OF_SIMULATIONS = 500;
    Random random;
    HashSet<Integer> birthdaySet = new HashSet<Integer>();
    BirthdayProblem2() { random = new Random(); }
    int generateBirthday() { return random.nextInt(DAYS_IN_YEAR); }
    double iteration(int numberOfStudents) { //one iteration from the simulation
        birthdaySet.clear();
        for (int i = 0; i < numberOfStudents; i++) {
            int bd = generateBirthday();
            if (birthdaySet.contains(bd)) {
                return 1.0;
            }
            birthdaySet.add(bd);
        }
        return 0.0;
    }
    void simulation(int numberOfStudents) {
        double probabilitySum = 0;
        for (int i = 0; i < NUMBER_OF_SIMULATIONS; i++) {
            probabilitySum += iteration(numberOfStudents);
        }
        System.out.printf("For n = %d -> P = %.4f n", numberOfStudents, probabilitySum / NUMBER_OF_SIMULATIONS);
    }
    private void start() {
        simulation(10); //should be about 0.1
        simulation(20); //should be about 0.4
        simulation(23); //should be about 0.5
        simulation(35); //should be about 0.8
    }
    public static void main(String... whatever) { new BirthdayProblem2().start(); }
}