# Find the permutation of first N natural numbers such that sum of i % Pi is maximum possible

• Last Updated : 13 Mar, 2022

Given a number N. The task is to find the permutation P of first N natural numbers such that sum of i % Pi is maximum possible. The task is to find the maximum possible sum not it’s permutation.

Examples:

Input: N = 5
Output: 10
Possible permutation is 2 3 4 5 1.
Modulus values will be {1, 2, 3, 4, 0}.
1 + 2 + 3 + 4 + 0 = 10

Input: N = 8
Output: 28

Approach: Maximum possible sum is (N * (N – 1)) / 2 and it is formed by the permutation 2, 3, 4, 5, ….. N, 1

Below is the implementation of the above approach:

## C++

 `// C++ implementation of the approach``#include ``using` `namespace` `std;` `// Function to find the permutation of``// the first N natural numbers such that``// the sum of (i % Pi) is maximum possible``// and return the maximum sum``int` `Max_Sum(``int` `n)``{``    ``return` `(n * (n - 1)) / 2;``}` `// Driver code``int` `main()``{``    ``int` `n = 8;` `    ``// Function call``    ``cout << Max_Sum(n);` `    ``return` `0;``}`

## Java

 `// Java implementation of the approach``class` `GFG``{` `// Function to find the permutation of``// the first N natural numbers such that``// the sum of (i % Pi) is maximum possible``// and return the maximum sum``static` `int` `Max_Sum(``int` `n)``{``    ``return` `(n * (n - ``1``)) / ``2``;``}` `// Driver code``public` `static` `void` `main (String[] args)``{``    ``int` `n = ``8``;` `    ``// Function call``    ``System.out.println(Max_Sum(n));``}``}` `// This code is contributed by Rajput-Ji`

## Python3

 `# Python3 implementation of the approach` `# Function to find the permutation of``# the first N natural numbers such that``# the sum of (i % Pi) is maximum possible``# and return the maximum sum``def` `Max_Sum(n) :``    ` `    ``return` `(n ``*` `(n ``-` `1``)) ``/``/` `2``;` `# Driver code``if` `__name__ ``=``=` `"__main__"` `:``    ` `    ``n ``=` `8``;` `    ``# Function call``    ``print``(Max_Sum(n));``    ` `# This code is contributed by AnkitRai01`

## C#

 `// C# implementation of the approach``using` `System;` `class` `GFG``{` `// Function to find the permutation of``// the first N natural numbers such that``// the sum of (i % Pi) is maximum possible``// and return the maximum sum``static` `int` `Max_Sum(``int` `n)``{``    ``return` `(n * (n - 1)) / 2;``}` `// Driver code``public` `static` `void` `Main (String[] args)``{``    ``int` `n = 8;` `    ``// Function call``    ``Console.WriteLine(Max_Sum(n));``}``}` `// This code is contributed by Princi Singh`

## Javascript

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Output:

`28`

Time Complexity: O(1)

Auxiliary Space: O(1)

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