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

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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 above approach:

C++

 // C++ implementation of above approach #include 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



Output:

4

My Personal Notes arrow_drop_up Check out this Author's contributed articles.

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.