找出前N个自然数的置换，以使i％Pi的总和最大

给定数字N。任务是找到前N个自然数的置换P ，以使i％P _i的总和最大。任务是找到最大可能的和而不是排列。

例子：

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 
 

方法：最大可能总和为(N *(N – 1))/ 2 ，它由排列2、3、4、5 ….. N，1形成。

下面是上述方法的实现：

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

 
// 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 sum
function Max_Sum(n)
{
    return parseInt((n * (n - 1)) / 2);
}
 
// Driver code
let n = 8;
 
// Function call
document.write(Max_Sum(n));
 
// This code is contributed by rishavmahato348
 

输出：

28