cheme_hw2.cpp

// Includes: Libraries needed for different tasks
#include <iostream>            // For printing output to the console
#include <vector>              // For using arrays that can grow/shrink in size
#include <random>              // For random number generation
#include <chrono>              // For measuring time intervals
#include <cmath>               // For math functions like abs()
#include <iomanip>             // For formatting output (decimal places)
using namespace std;           // Makes C++ syntax a bit simpler for beginners

int main() {
    // The known value of pi (same as in your Python code)
    const double pi = 3.14159265359;

    // Vectors (dynamic arrays) to store results like your Python lists
    vector<double> pis;              // Estimates of pi
    vector<double> percent_errors;   // Percent errors
    vector<double> times;            // Times for each experiment

    // List of trial counts (sample sizes), matching your Python list
    // Note: In C++, underscores in numbers are not allowed
    vector<long long> counts = {100, 100, 100, 100, 100, 1000, 10000, 100000, 1000000, 10000000, 100000000};

    // Set up random number generation: This is equivalent to Python's random.random()
    random_device rd;                // Used for seeding: "real" randomness from device
    mt19937 gen(rd());               // Mersenne Twister engine (standard random engine)
    uniform_real_distribution<> dis(-1.0, 1.0);  // Generates real numbers between -1.0 & +1.0

    // Go through each trial count as in your Python for loop
    for (auto count : counts) {
        long long inside = 0;        // Counter for points inside the quarter-circle

        // Start timer (records current time before trials begin)
        auto start_time = chrono::high_resolution_clock::now();

        // Loop over all counts
        for (long long i = 0; i < count; ++i) {
            // Generate random x, y between -1 and 1 (uniformly distributed)
            double x = dis(gen);
            double y = dis(gen);

            // If point is inside the unit circle, increment "inside"
            if (x*x + y*y <= 1.0)
                ++inside;
        }

        // End timer (records current time after trials)
        auto end_time = chrono::high_resolution_clock::now();

        // Calculate the fraction inside and estimate for pi, as in your code
        double frac = static_cast<double>(inside) / static_cast<double>(count);  // Must convert to double!
        double val = frac * 4.0;     // Monte Carlo estimate of pi

        pis.push_back(val);          // Store result
        double pe = fabs(pi - val) / pi * 100.0;    // fabs() is "float absolute value"
        percent_errors.push_back(pe);

        // Calculate elapsed time in *seconds*
        chrono::duration<double> elapsed = end_time - start_time;
        times.push_back(elapsed.count());
    }

    // Print results to console in a readable way (similar to your Python prints)
    cout << "pi:\n";
    for (size_t i = 0; i < pis.size(); ++i)
        cout << fixed << setprecision(8) << pis[i] << " ";
    cout << endl;

    cout << "percent errors:\n";
    for (size_t i = 0; i < percent_errors.size(); ++i)
        cout << fixed << setprecision(6) << percent_errors[i] << " ";
    cout << endl;

    cout << "times (seconds):\n";
    for (size_t i = 0; i < times.size(); ++i)
        cout << fixed << setprecision(6) << times[i] << " ";
    cout << endl;

    // For plotting, output data to files or formatted text for later use in Python/Excel/Google Sheets/etc

    // Create pis_mod as in your code (average of first five, then the rest unchanged)
    vector<double> pis_mod;
    // Calculate the mean of the first five entries
    double mean_first_five = 0.0;
    for (int i = 0; i < 5; ++i) mean_first_five += pis[i];
    mean_first_five /= 5.0;
    pis_mod.push_back(mean_first_five);

    // Add the remaining values unchanged
    for (size_t i = 5; i < pis.size(); ++i)
        pis_mod.push_back(pis[i]);

    // Print a table for easy copy-pasting into Python for plotting
    cout << "\nFor plotting in Python, copy the following:\n";
    cout << "counts = [100, 1000, 10000, 100000, 1000000, 10000000, 100000000]\n";
    cout << "pis_mod = [";
    for (size_t i = 0; i < pis_mod.size(); ++i) {
        cout << pis_mod[i];
        if (i < pis_mod.size()-1) cout << ", ";
    }
    cout << "]\n";
    cout << "times = [";
    for (size_t i = 4; i < times.size(); ++i) { // times[4:] in python
        cout << times[i];
        if (i < times.size()-1) cout << ", ";
    }
    cout << "]\n";

    // If you want to output to files, you could use <fstream> library (ask me if you want this).

    return 0; // Main function ends
}