Minimum value possible of a given function from the given set

Given a set Sn that represents a finite set {1, 2, 3, ….., n}. Zn denotes the set of all subsets of Sn which contains exactly 2 elements. The task is to find the value of F(n).

Examples:

Input: N = 3 
Output: 4
For n=3 we get value 1, 2 times and 2, 1 times 
thus the answer would be 1 * 2 + 2 * 1 = 4.

Input: N = 10
Output: 165

For each value as we go from left to right in the set we get each value, n-value number of times that value. 
i.e. For each i, value to be added is (i + 1) * (n – i – 1)

Below is the implementation of the above approach: 

C++

// C++ implementation of above approach

#include <bits/stdc++.h>
using namespace std;
#define ll long long

// Function to find the value of F(n)
ll findF_N(ll n)
{

    ll ans = 0;
    for (ll i = 0; i < n; ++i)
        ans += (i + 1) * (n - i - 1);

    return ans;
}

// Driver code
int main()
{

    ll n = 3;
    cout << findF_N(n);

    return 0;
}

Java

// Java implementation of above approach

import java.io.*;

class GFG {

    // Function to find the value of F(n)
    static long findF_N(long n)
    {

        long ans = 0;
        for (long i = 0; i < n; ++i)
            ans += (i + 1) * (n - i - 1);

        return ans;
    }

    // Driver code

    public static void main(String[] args)
    {
        long n = 3;
        System.out.println(findF_N(n));
    }
}
// This code is contributed by anuj_67..

Python3

# Python3 implementation of
# above approach

# Function to find the value of F(n)


def findF_N(n):

    ans = 0
    for i in range(n):
        ans = ans + (i + 1) * (n - i - 1)

    return ans


# Driver code
n = 3
print(findF_N(n))

# This code is contributed by
# Sanjit_Prasad

C#

// C# implementation of above approach
using System;

class GFG {
    // Function to find the
    // value of F(n)
    static long findF_N(long n)
    {

        long ans = 0;
        for (long i = 0; i < n; ++i)
            ans += (i + 1) * (n - i - 1);

        return ans;
    }

    // Driver code
    public static void Main()
    {
        long n = 3;
        Console.WriteLine(findF_N(n));
    }
}

// This code is contributed by anuj_67

PHP

<?php
// PHP implementation of above approach

// Function to find the value of F(n)
function findF_N($n)
{

    $ans = 0;
    for ($i = 0; $i < $n; ++$i)
        $ans += ($i + 1) * ($n - $i - 1);

    return $ans;
}

// Driver code
$n = 3;
echo findF_N($n);

// This code is contributed
// by Akanksha Rai(Abby_akku)

Javascript

<script>

// JavaScript implementation of above approach

// Function to find the value of F(n)
function findF_N(n)
{

    var ans = 0;
    for (var i = 0; i < n; ++i)
        ans += (i + 1) * (n - i - 1);

    return ans;
}

// Driver code
var n = 3;
document.write( findF_N(n));

</script>

Output:

4

Time Complexity: O(n) // n is the length of the array

Space Complexity: O(1)