CODEWITHSUNDEEP
c++booleanbirthday-paradox
AlecWhite
AlecWhite

Reputation: 11

C++ Birthday Paradox Using a Boolean Function

I have an assignment where I need to calculate the probability that two people share the same birthday for a given room size (in my case 50) over many trials (5000). I have to assign the birthdays randomly to the number of people in the room. The difference is I need to use a Boolean function to check the if the Birthdays are the same. I cannot figure why my outputs are off, but I believe it has something to do with two of my loops. 

> 

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

    bool SameBirthday(int birthdays[], int numpeople);
    const int MAX_PEOPLE = 50;
    const double NUM_TRIALS = 5000.0;
    const int DAYS_IN_YEAR = 365;

    int main(void)
    {
        int numMatches = 0;
        int people = 2;
        int trial = 0;
        int numpeople = 0;
        int i = 0;
        int birthdays[MAX_PEOPLE];
        bool Match;
        double Probability = 0;
        srand(time(0));
    for (people = 2; people <= MAX_PEOPLE; people++)
        {
            numMatches = 0;

            for (trial = 0; trial < NUM_TRIALS; trial++)
            {
                for (i = 0; i < people; i++)
                {
                    birthdays[i] = (rand() % 365 + 1);
                    numpeople = i;

                }
                if ((SameBirthday(birthdays, numpeople) == true))
                    {
                        numMatches++;
                    }
            }
            Probability = (numMatches / NUM_TRIALS);
            cout << "For " << people << ", the probability of two birthdays is about " << Probability << endl;
        }
    }
    bool SameBirthday(int birthdays[], int numpeople)
    {

        bool match = false;
        int numberofmatches = 0;
        //Use this function to attempt to search the giving array birthdays and   count up number of times
        //at least two people have matching birthdays for any given 1 trial
        for (int SpaceOne = 0; SpaceOne < numpeople; SpaceOne++)
        {
            for (int SpaceTwo = SpaceOne + 1; SpaceTwo < numpeople; SpaceTwo++)
            {
                if (birthdays[SpaceTwo] == birthdays[SpaceOne])
                {
                    return true;
                }
            }
        }
return false;
    }

    I know that the code has errors in certain spots that was because I started trying different things, but any help would be appreciated. 
EDIT- My only issue now is that for my output I have a zero for the probability of 2 people in the room have a birthday, which is not right. It seems like my outputs are like a person off, the probability of 2 people is shown as the probability for three people and so on. 
EDIT(8-31-2015): I also forgot to mention that my Professor stated that my SameBirthday function needed the parameters: birthday[], and numpeople so I cannot use MAX_PEOPLE as a parameter. My professor also suggested using a triple nested for loop within the main body of the function. I believe what is making my output off by one for each person relates to the triple nested for loop, but I am unsure what would cause the issue.

Upvotes: 1

Views: 880

Answers (4)

Ethan Bradford
Ethan Bradford

Reputation: 780

Your other problem is that numpeople will always be the number of people minus 1. You don't actually need that variable at all. Your "people" variable is the correct number of people.

Upvotes: 0

user3437460
user3437460

Reputation: 17454

To clarify issues from other parts of your coding. I think this is what your school wants.

int main(){
    //All your variables

    for(int x=0; x<NUM_TRIALS; x++){
        for(int y=0; y< MAX_PEOPLE; y++){
            birthdays[y] = (rand() % 365 + 1);
        }

        if(SameBirthday(birthdays, MAX_PEOPLE) == true)
            numMatches ++;              
    }
    Probability = ((double)numMatches / NUM_TRIALS);
    cout << "For " << people << ", the probability of two birthdays is about " 
    << Probability << endl;     
}

NUM_TRIALS to generate 5000 datasets. Hence, you generate birthday for 50 students 5000 times. For each trial within a class of 50, you check whether there are 2 person with same birthday. If there is, numMatches + 1.

After 5000 trials, you get the probability.

Upvotes: 0

user3437460
user3437460

Reputation: 17454

Just do it like this:

bool SameBirthday(int birthdays[], int numPeople)
{
    for(int x=0; x<numPeople; x++){         
        for(int y=0; y<numPeople; y++){
            if(birthdays[x] == birthdays[y])
                return true;
        }
    }
    return false;
}

Your logic in your nested loop is wrong..

for (SpaceOne = 0; SpaceOne < numpeople - 1; SpaceOne++)
    for (SpaceTwo = SpaceOne + 1; SpaceTwo < numpeople; SpaceTwo++)

Your inner loop is skipping n number of checks where n equals SpaceOne.

By the way, this is not C programming. You can declare variable within a for-loop.

Upvotes: 2

Ethan Bradford
Ethan Bradford

Reputation: 780

I see two problems with the actual functionality. First, SameBirthday needs to return a value (false) when there is no birthday match. You can do that at the end of the function, after all the loops are done.

Second, you need to increment numMatches when you find a match.

Upvotes: 0

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