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 = 10Input: 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 <bits/stdc++.h>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 sumint Max_Sum(int n){ return (n * (n - 1)) / 2;}// Driver codeint main(){ int n = 8; // Function call cout << Max_Sum(n); return 0;} |
Java
// Java implementation of the approachimport java.io.*;public 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 sumstatic int Max_Sum(int n){ return (n * (n - 1)) / 2;}// Driver codepublic 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 sumdef Max_Sum(n) : return (n * (n - 1)) // 2;# Driver codeif __name__ == "__main__" : n = 8; # Function call print(Max_Sum(n)); # This code is contributed by AnkitRai01 |
C#
// C# implementation of the approachusing 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 sumstatic int Max_Sum(int n){ return (n * (n - 1)) / 2;}// Driver codepublic static void Main (String[] args){ int n = 8; // Function call Console.WriteLine(Max_Sum(n));}}// This code is contributed by Princi Singh |
Javascript
<script>// Javascript 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 sumfunction Max_Sum(n){ return parseInt((n * (n - 1)) / 2);}// Driver codelet n = 8;// Function calldocument.write(Max_Sum(n));// This code is contributed by rishavmahato348</script> |
Output:
28
Time Complexity: O(1)
Auxiliary Space: O(1)
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