重新排列数组以最大化 i*arr[i]

给定一个包含 N 个整数的数组，您必须按任意顺序选择所有这些整数。对于您选择的每个整数，您将获得等于以下值的分数：所选整数 * 在当前整数之前选择的整数数。你的任务是最大化这些点。
注意：您可以精确地选择每个整数 1 次。
例子：

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. 
 

这个想法是使用贪婪方法，即最大化最大元素的乘数。
我们对给定的数组进行排序并以这种排序方式开始挑选元素，从第一个元素开始。
下面是上述方法的实现：

C++

// C++ program for the Optimal Solution
#include 
#include 
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;
}

Java

// 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));
    }
}

Python3

# 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] * i
      
    return points
   
     
if __name__ == "__main__":
     
    a = [1, 4, 2, 3, 9]
    N = len(a)
    print(findOptimalSolution(a, N))

C#

//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   
}

Javascript

    // Javascript 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
        a.sort(function(a, b){return a - b});
   
        // Variable to store the total points earned
        let points = 0;
   
        for (let i = 0; i < N; i++) {
            points += a[i] * i;
        }
        return points;
    }
     
    let a = [ 1, 4, 2, 3, 9 ];
    let N = a.length;
    document.write(findOptimalSolution(a, N));
 

输出：

56

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