#include <bits/stdc++.h>

using namespace std;

//***********************************************************
// HackerRank Prepare > Mathematics > Fundamentals: Handshake
//***********************************************************

// Example: There are 3 attendees, p1, p2, and p3. p1 shakes hands
// with p2 and p3. p2 shakes hands with p3. Now they have all shaken
// hands after 3 handshakes.

// 3 choose 2 => 3! / 2! (3 - 2)! = 3;

int handshake(int n) {
    auto fact = [](int n)
    {
        auto fact_impl = [](int n, auto& fact_ref)
        {
            if(n == 1 || n == 0)
                 return 1;

            int fact = 1;
            while (n > 0)
            {
                fact *= n--;
            }            
            return fact;            
    
            // return n * fact_ref(n-1, fact_ref);
            
        };
        
        return fact_impl(n, fact_impl);
    };
    
    int r = 2;
    
    // using a rescursive or O(n) factorial function causes a runtime
    // error in hackerrank. Reduce the n choose r equation n!/r!(n-r)!
    // by substituting r = 2 to n * (n-1)/2

    // n! / 2! (n-2)! = n * (n-1) * (n-2) ... / 2! (n-2) * (n-3) ...
    //                = n * (n-1) / 2
    
    return n == 1 ? 0 : fact(n)/(r*fact(n-r));
}

int main()
{
    vector<tuple<vector<int>,vector<int>>> testCases = {
        // input  expected
        { {1,2}, {0,1} }
    };

    for (auto test: testCases)
    {
        vector<int>& inputV = get<0>(test);
        vector<int>& expectedV = get<1>(test);
        for (size_t i = 0; i < inputV.size(); i++)
        {
            int n = inputV.at(i);
            int result = handshake(n);
            int expected = expectedV.at(i);
            cout << n << endl;
            cout << result << endl;
            cout << expected << endl;
            cout << "----------\n";
        }
    }
}