// clang++ -std=c++23 -Wall -Wextra -pedantic -D_CRT_SECURE_NO_WARNINGS elimination_analysis.cpp -g -o elimination_analysis.exe
// .\elimination_analysis.exe 7

#include <iostream>
#include <vector>

std::vector<long> analyzeRps(int n) {
    std::vector<long> remainOccur(n + 1);

    // All n players stay (0 get eliminated)
    // in 3 ^ n minus the number of other combinations.
    remainOccur[n] = 1;
    for (int i = 0; i < n; ++i) remainOccur[n] *= 3;

    // i players stay if they choose a winning option (eg. rock)
    // while all other n - i players choose the losing option (eg. scissors).
    long nextNChooseK = n;
    for (int i = 1; i < n; ++i) {
        remainOccur[i] = 3 * nextNChooseK;

        remainOccur[n] -= remainOccur[i];

        nextNChooseK = nextNChooseK * (n - i) / (i + 1);
    }

    return remainOccur;
}

std::vector<long> analyzeZzz(int n) {
    std::vector<long> remainOccur(n + 1);

    // i players stay if their option is in the majority.
    // This means that either all or fewer than n / 2 players can stay.
    long nextNChooseK = n;
    for (int i = 1; i < (n + 1) / 2; ++i) {
        remainOccur[i] = 2 * nextNChooseK;

        nextNChooseK = nextNChooseK * (n - i) / (i + 1);
    }

    // All n players stay (0 get eliminated)
    // if all choose the same option
    // or if it's a tie between the two options.
    remainOccur[n] = 2;
    // If n is even, nextNChooseK now equals n choose n / 2.
    if (n % 2 == 0) remainOccur[n] += nextNChooseK;

    return remainOccur;
}

void printAnalysis(const std::vector<long> &remainOccur) {
    for (size_t i = 0; i < remainOccur.size(); ++i) {
        std::cout << i << ": " << remainOccur[i] << std::endl;
    }

    long total = 0, weighted = 0;
    for (size_t i = 0; i < remainOccur.size(); ++i) {
        total += remainOccur[i];
        weighted += i * remainOccur[i];
    }
    std::cout << "Avg: " << weighted << "/" << total << "=" <<
        (double)weighted / total << std::endl;
}

int main(int argc, char *argv[]) {
    if (argc != 2) return 1;

    int n;
    if (std::sscanf(argv[1], "%d", &n) != 1) return 1;
    if (n < 3 || n > 15) return 1;

    std::cout << "ROCK PAPER SCISSORS" << std::endl;
    std::cout << "===================" << std::endl;
    printAnalysis(analyzeRps(n));
    std::cout << std::endl;

    std::cout << "ZIMI ZAMI ZUM" << std::endl;
    std::cout << "=============" << std::endl;
    printAnalysis(analyzeZzz(n));

    return 0;
}