Step by Step solution about How to resolve the algorithm Unbias a random generator step by step in the C++ programming language

The provided C++ code simulates two types of coin flips: biased and unbiased. A biased coin flip gives a result of 1 with a higher probability, while an unbiased coin flip gives a result of 0 or 1 with equal probability.

Here's a breakdown of the code:

• The code includes the <iostream> and <random> header files.

• A global std::default_random_engine named generator is initialized. This is used for generating random numbers.

• biased(int n) function:

  • It takes an integer n as an argument.
  • It uses a std::uniform_int_distribution to generate a random integer between 1 and n.
  • It returns true if the generated integer is 1, which represents a biased coin flip towards 1.

• unbiased(int n) function:

  • It takes an integer n as an argument.
  • It uses two biased coin flips to simulate an unbiased coin flip.
  • It first performs two biased coin flips and checks if the results are the same.
  • If the results are different, it returns the result of the first flip.
  • If the results are the same, it performs another biased coin flip and repeats the process until it gets different results.
  • This method effectively simulates an unbiased coin flip because the probability of getting 0 or 1 is equal.

• In the main function:

  • A loop iterates from n = 3 to n = 6.
  • For each n, it simulates 100,000 biased and unbiased coin flips.
  • It counts the number of times 0 or 1 appears in both biased and unbiased flips.
  • Finally, it prints out the results for each n, showing the percentages of 0 and 1 appearing in both biased and unbiased flips.

The output of the program shows that the biased coin flip favors 1, as expected, while the unbiased coin flip has close to 50% probability for both 0 and 1.

#include <iostream>
#include <random>

std::default_random_engine generator;
bool biased(int n) {
    std::uniform_int_distribution<int> distribution(1, n);
    return distribution(generator) == 1;
}

bool unbiased(int n) {
    bool flip1, flip2;

    /* Flip twice, and check if the values are the same.
     * If so, flip again. Otherwise, return the value of the first flip. */

    do {
        flip1 = biased(n);
        flip2 = biased(n);
    } while (flip1 == flip2);

    return flip1;
}

int main() {
    for (size_t n = 3; n <= 6; n++) {
        int biasedZero = 0;
        int biasedOne = 0;
        int unbiasedZero = 0;
        int unbiasedOne = 0;

        for (size_t i = 0; i < 100000; i++) {
            if (biased(n)) {
                biasedOne++;
            } else {
                biasedZero++;
            }
            if (unbiased(n)) {
                unbiasedOne++;
            } else {
                unbiasedZero++;
            }
        }

        std::cout << "(N = " << n << ")\n";
        std::cout << "Biased:\n";
        std::cout << "   0 = " << biasedZero << "; " << biasedZero / 1000.0 << "%\n";
        std::cout << "   1 = " << biasedOne << "; " << biasedOne / 1000.0 << "%\n";
        std::cout << "Unbiased:\n";
        std::cout << "   0 = " << unbiasedZero << "; " << unbiasedZero / 1000.0 << "%\n";
        std::cout << "   1 = " << unbiasedOne << "; " << unbiasedOne / 1000.0 << "%\n";
        std::cout << '\n';
    }
    return 0;
}