Brainstorming Quiz, Day - 6 Solution

Answer:13:01 (1:01) PM

#include <cmath>
#include <iostream>
#include <string>
using namespace std;

int findTime(double p) {
    return ceil(sqrt(2 * 365 * log(1 / (1 - p))));
}

string timeFrom12_30PM(double p) {
    int minutes = findTime(p);
    int totalMinutes = 30 + minutes - 1; // Adding minutes to 12:30 PM and -1 due to the presence of person at 12:30
    int hours = 12 + totalMinutes / 60; // Calculate hours
    int mins = totalMinutes % 60; // Calculate minutes
    return to_string(hours) + ":" + (mins < 10 ? "0" : "") + to_string(mins);
}

int main() {
    cout << "ARRIVAL TIME FROM 12:30 PM: " << timeFrom12_30PM(0.75) << endl;
    return 0;
}

Short Explanation: This program determines the time a student should arrive to achieve a given probability of winning based on the birthday paradox.

1. findTime(double p):
   • Calculates the number of participants needed for the probability pp using the formula: n≈2⋅365⋅ln⁡(11−p)n \approx \sqrt{2 \cdot 365 \cdot \ln\left(\frac{1}{1-p}\right)}
   • Rounds up to the nearest integer.
2. timeFrom12_30PM(double p):
   • Adds the required minutes to 12:30 PM based on the number of participants.
   • Adjusts the time to account for the first participant already present at 12:30 PM.
   • Converts the total minutes to hours and minutes in a readable format.
3. main():
   • Calls the timeFrom12_30PM function with p=0.75p = 0.75 and prints the calculated arrival time.