C++模拟n门问题_牛客博客

这个门数可以自己更改

#include <cstdlib>
#include <ctime>
#include <iomanip>
#include <iostream>
#include <vector>
using namespace std;

#define LEN 999999
#define How_Many_Doors 100

bool Test(bool IsChange)
{
   
    vector<bool> Doors(How_Many_Doors, false);
    int realCarLocation = rand() % How_Many_Doors;
    Doors.at(realCarLocation) = true;
    int ChallengerFirst = rand() % How_Many_Doors;
    bool ChangeYourMind = IsChange;
    if (ChallengerFirst != realCarLocation)
    {
   
        return ChangeYourMind ? true : false;
    }
    else
    {
   
        return ChangeYourMind ? false : true;
    }
}
int main()
{
   
    srand(time(0));
    int WinTimes1 = 0, WinTimes2 = 0;
    for (unsigned long i = 0; i < LEN; i++)
    {
   
        if (Test(true))
            WinTimes1++;
        if (Test(false))
            WinTimes2++;
    }

    cout << fixed << setprecision(4) << "Change: " << 100.00 * WinTimes1 / LEN << "%" << endl;
    cout << fixed << setprecision(4) << "Not Change: " << 100.00 * WinTimes2 / LEN << "%" << endl;
    return 0;
}

若门数为 $100$
若门数为 $3$

多试几组数字，可以发现若门数为n，那么换门赢的概率为 $\frac{n-1}{n}$ ，不换门赢的概率为 $\frac{1}{n}$