生日悖论

Question

我想模拟java中的生日悖论。出于某种原因，我的输出（概率）一直非常接近 1，例如模拟（10）->0,9268。一开始你可以看到我的模拟应该接近的概率。很长一段时间以来，我一直在寻找我的代码中的错误，所以我希望你们中的任何人都能帮助我。我查找了生日悖论的其他代码，但其中 none 似乎能够帮助我处理奇怪的输出。 p.s。你可以忽略//TODO，一旦我得到代码和运行，我就会修复它。谢谢提前！

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

您没有清除迭代之间的 birthdaySet。将它从字段更改为局部变量将防止出现此类错误，因为为什么首先需要它作为字段？

换句话说，generateBirthday 应该使用 Random.nextInt(DAYS_IN_YEAR)。 Random 的实例是作为字段的主要候选者。那 LCG random; 行到底是什么？

更新

方法iteration() 应该return 布尔值，用于判断是否有相同生日的学生。真值数 returned 除以调用数等于概率。

由于一年中的天数相对较少，布尔数组会比 Set 更快，所以这里更新代码：

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);
}

示例输出

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

增加 NUMBER_OF_SIMULATIONS 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

正如 andreas 已经指出的那样 birthdaySet 应该在迭代之间被清除，否则该集合将包含来自先前模拟的数据

但是你的设计还有一个致命的缺陷，看看维基百科页面就知道了：

在概率论中，生日问题或生日悖论关注的是在一组 n 个随机选择的人中，其中一些人的生日相同的概率。

是至少有2个人生日相同的概率。这意味着只要 2 等于 1 就应该返回。

我在下面的代码中总结了它

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(); }
}

生日悖论

Birthday paradox

java

paradox

birthday-paradox