Rearrange an array to maximize i*arr[i]

Given an array of N integers, you have to select all of these integers in any order. For every integer you select, you get points equal to the value of: the selected integer * number of integers selected before the current integer. Your task is to maximize these points.
Note: You can select every integer exactly 1 time.

Examples:

Input: a = {1, 4, 2, 3, 9}
Output: 56
The optimal solution for this array would be select the numbers in the order 1, 2, 3, 4, 9 that gives points 0, 2, 6, 12, 36 respectively and giving a total maximum points of 56.



Input: a = {1, 2, 2, 4, 9}
Output: 54
The optimal solution for this array would be select the numbers in the order 1, 2, 2, 4, 9 that gives points 0, 2, 4, 12, 36 respectively and giving a total maximum points of 54.

The idea is to use Greedy Approach, i.e., maximize multiplier for the largest element.
We sort the given array and start picking elements in this sorted manner, starting with the first element.

Below is the implementation of the above approach:

C++

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// C++ program for the Optimal Solution
#include <bits/stdc++.h> 
#include <iostream>
using namespace std;
  
    // Function to calculate the maximum points
    // earned by making an optimal selection on
    // the given array
    static int findOptimalSolution(int a[], int N)
    {
        // Sorting the array
        sort(a, a+N); 
        // Variable to store the total points earned
        int points = 0;
  
        for (int i = 0; i < N; i++) {
            points += a[i] * i;
        }
        return points;
    }
  
    // Driver code
int main() {
    int a[] = { 1, 4, 2, 3, 9 };
    int N = sizeof(a)/sizeof(a[0]);
        cout<<(findOptimalSolution(a, N));
      
    return 0;
}

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Java

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// Java program for the Optimal Solution
import java.io.*;
import java.util.*;
  
class GFG {
  
    // Function to calculate the maximum points
    // earned by making an optimal selection on
    // the given array
    static int findOptimalSolution(int[] a, int N)
    {
        // Sorting the array
        Arrays.sort(a);
  
        // Variable to store the total points earned
        int points = 0;
  
        for (int i = 0; i < N; i++) {
            points += a[i] * i;
        }
        return points;
    }
  
    // Driver code
    public static void main(String args[])
    {
        int[] a = { 1, 4, 2, 3, 9 };
        int N = a.length;
        System.out.println(findOptimalSolution(a, N));
    }
}

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Python3

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# Python3 program for the Optimal Solution 
  
# Function to calculate the maximum points 
# earned by making an optimal selection on 
# the given array 
def findOptimalSolution(a, N) :
          
    # Sorting the array 
    a.sort()  
      
    # Variable to store the total points earned 
    points = 0 
    
    for i in range(0, N):
        points += a[i] *
       
    return points 
    
      
if __name__ == "__main__":
      
    a = [1, 4, 2, 3, 9
    N = len(a) 
    print(findOptimalSolution(a, N)) 

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C#

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//C# program for the Optimal Solution
using System;
  
public class GFG{
      
        // Function to calculate the maximum points 
    // earned by making an optimal selection on 
    // the given array 
    static int findOptimalSolution(int[]a, int N) 
    
        // Sorting the array 
        Array.Sort(a); 
  
        // Variable to store the total points earned 
        int points = 0; 
  
        for (int i = 0; i < N; i++) { 
            points += a[i] * i; 
        
        return points; 
    
  
    // Driver code 
    static public void Main (){
        int[] a = { 1, 4, 2, 3, 9 }; 
        int N = a.Length; 
        Console.WriteLine(findOptimalSolution(a, N)); 
    }
//This code is contributed by ajit    
}

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PHP

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<?php
// PHP program for the Optimal Solution
  
// Function to calculate the maximum 
// points earned by making an optimal
// selection on the given array
function findOptimalSolution($a, $N)
{
    // Sorting the array
    sort($a);
  
    // Variable to store the
    // total points earned
    $points = 0;
  
    for ($i = 0; $i < $N; $i++) 
    {
        $points += $a[$i] * $i;
    }
    return $points;
}
  
// Driver code
$a = array( 1, 4, 2, 3, 9 );
$N = sizeof($a);
  
echo (findOptimalSolution($a, $N));
  
// This code is contributed by ajit
?>

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Output:

56


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Improved By : jit_t, rituraj_jain