数组中不同三元组对之间绝对差的最大总和

给定一个由N 个整数组成的数组arr[] ，任务是找到数组中所有三元组的不同对之间绝对差的最大和。

例子：

Input: arr[] = {1, 2, 3, 4}
Output: 6
Explanation:
The valid triplet is (1, 3, 4) as sum = |1 – 4| + |1 – 3| + |3 – 4| = 6, which is the maximum among all the triplets.

Input: arr[] = {2, 2, 2}
Output: 0

方法：解决给定问题的思路是将数组按升序排序，求数组首尾两个元素对的绝对差之和。请按照以下步骤解决问题：

• 初始化一个变量，比如sum ，以存储最大可能的总和。
• 按升序对给定的数组arr[]进行排序。
• 求数组的第一个和最后两个元素的对之间的差之和，即sum = (arr[N – 2] – arr[0]) + (arr[N – 1] – arr[0]) + (arr[N – 2] – arr[N – 1]) 。
• 完成上述步骤后，打印sum的值作为结果。

下面是上述方法的实现：

C++

// C++ program for the above approach
#include 
using namespace std;
 
// Function to find the maximum sum of
// absolute differences between
// distinct pairs of triplet in array
void maximumSum(int arr[], int N)
{
    // Stores the maximum sum
    int sum;
 
    // Sort the array in
    // ascending order
    sort(arr, arr + N);
 
    // Sum of differences between
    // pairs of the triplet
    sum = (arr[N - 1] - arr[0])
          + (arr[N - 2] - arr[0])
          + (arr[N - 1] - arr[N - 2]);
 
    // Print the sum
    cout << sum;
}
 
// Driver Code
int main()
{
    int arr[] = { 1, 3, 4, 2 };
    int N = sizeof(arr) / sizeof(arr[0]);
    maximumSum(arr, N);
 
    return 0;
}

Java

// Java program for the above approach
import java.util.*;
class GFG
{
 
  // Function to find the maximum sum of
  // absolute differences between
  // distinct pairs of triplet in array
  static void maximumSum(int[] arr, int N)
  {
 
    // Stores the maximum sum
    int sum;
 
    // Sort the array in
    // ascending order
    Arrays.sort(arr);
 
    // Sum of differences between
    // pairs of the triplet
    sum = (arr[N - 1] - arr[0]) + (arr[N - 2] - arr[0])
      + (arr[N - 1] - arr[N - 2]);
 
    // Print the sum
    System.out.println(sum);
  }
 
  // Driver Code
  public static void main(String[] args)
  {
    int[] arr = { 1, 3, 4, 2 };
    int N = arr.length;
    maximumSum(arr, N);
  }
}
 
// This code is contributed by susmitakundugoaldanga.

Python3

# Python program for the above approach
 
# Function to find the maximum sum of
# absolute differences between
# distinct pairs of triplet in array
def maximumSum(arr, N):
   
    # Stores the maximum sum
    sum = 0
     
    # Sort the array in
    # ascending order
    arr.sort()
     
    # Sum of differences between
    # pairs of the triplet
    sum = (arr[N - 1] - arr[0]) + (arr[N - 2] - arr[0]) + (arr[N - 1] - arr[N - 2]);
 
    # Print the sum
    print(sum)
 
# Driver Code
arr = [ 1, 3, 4, 2 ]
N = len(arr)
maximumSum(arr, N)
 
# This code is contributed by rohitsingh07052.

C#

// C# program for the above approach
using System;
using System.Collections.Generic;
 
class GFG
{
 
    // Function to find the maximum sum of
    // absolute differences between
    // distinct pairs of triplet in array
    static void maximumSum(int[] arr, int N)
    {
       
        // Stores the maximum sum
        int sum;
 
        // Sort the array in
        // ascending order
        Array.Sort(arr);
 
        // Sum of differences between
        // pairs of the triplet
        sum = (arr[N - 1] - arr[0]) + (arr[N - 2] - arr[0])
              + (arr[N - 1] - arr[N - 2]);
 
        // Print the sum
        Console.Write(sum);
    }
 
    // Driver Code
    public static void Main()
    {
        int[] arr = { 1, 3, 4, 2 };
        int N = arr.Length;
        maximumSum(arr, N);
    }
}
 
// This code is contributed by chitranayal.

Javascript

 
// Javascript program for the above approach
 
// Function to find the maximum sum of
// absolute differences between
// distinct pairs of triplet in array
function maximumSum(arr, N)
{
    // Stores the maximum sum
    let sum;
 
    // Sort the array in
    // ascending order
    arr.sort();
 
    // Sum of differences between
    // pairs of the triplet
    sum = (arr[N - 1] - arr[0])
        + (arr[N - 2] - arr[0])
        + (arr[N - 1] - arr[N - 2]);
 
    // Print the sum
    document.write(sum);
}
 
// Driver Code
 
    let arr = [ 1, 3, 4, 2 ];
    let N = arr.length;
    maximumSum(arr, N);
 
// This code is contributed by Mayank Tyagi
 

输出：

6

时间复杂度： O(N*log N)
辅助空间： O(1)

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