大小为2的组之间的最小差异

给定一个偶数个元素的数组，请使用这些数组元素形成2个组，以使总和最高的组与总和最低的组之间的差异最小。

注意：元素只能是一个组的一部分，并且必须至少是一个组的一部分。

例子：

Input : arr[] = {2, 6, 4, 3}
Output : 1
Groups formed will be (2, 6) and (4, 3), 
the difference between highest sum group
(2, 6) i.e 8 and lowest sum group (3, 4)
i.e 7 is 1.

Input : arr[] = {11, 4, 3, 5, 7, 1}
Output : 3
Groups formed will be (1, 11), (4, 5) and
(3, 7), the difference between highest 
sum group (1, 11) i.e 12 and lowest sum 
group (4, 5) i.e 9 is 3.

简单方法：一种简单的方法是尝试对数组元素的所有组合进行检查，并检查总和最高的组与总和最低的组之间的每组组合差异。总共将形成n *(n-1)/ 2个这样的基团(nC2)。
时间复杂度：O(n ^ 3)要生成组，需要进行n ^ 2次迭代，并检查每个组，需要n次迭代，因此在最坏的情况下需要n ^ 3次迭代。

高效方法：高效方法是使用贪婪方法。通过从数组的开头选择一个元素，然后从结尾选择一个元素，对整个数组进行排序并生成组。

C++

// CPP program to find minimum difference
// between groups of highest and lowest
// sums.
#include 
#define ll long long int
using namespace std;
  
ll calculate(ll a[], ll n)
{
    // Sorting the whole array.
    sort(a, a + n); 
  
    // Generating sum groups.
    vector s;
    for (int i = 0, j = n - 1; i < j; i++, j--) 
       s.push_back(a[i] + a[j]);
  
    ll mini = *min_element(s.begin(), s.end()); 
    ll maxi = *max_element(s.begin(), s.end()); 
  
    return abs(maxi - mini);
}
  
int main()
{
    ll a[] = { 2, 6, 4, 3 };
    int n = sizeof(a) / (sizeof(a[0]));
    cout << calculate(a, n) << endl;
    return 0;
}

Java

// Java program to find minimum
// difference between groups of 
// highest and lowest sums.
import java.util.Arrays;
import java.util.Collections;
import java.util.Vector;
  
  
class GFG {
  
static long calculate(long a[], int n)
{
    // Sorting the whole array.
    Arrays.sort(a); 
    int i,j;
      
    // Generating sum groups.
    Vector s = new Vector<>();
    for (i = 0, j = n - 1; i < j; i++, j--) 
        s.add((a[i] + a[j]));
          
    long mini = Collections.min(s);
    long maxi = Collections.max(s); 
    return Math.abs(maxi - mini);
}
  
// Driver code
public static void main(String[] args) 
{
    long a[] = { 2, 6, 4, 3 };
    int n = a.length;
    System.out.println(calculate(a, n));
    }
} 
// This code is contributed by 29AjayKumar

Python3

# Python3 program to find minimum 
# difference between groups of 
# highest and lowest sums.
def calculate(a, n):
      
    # Sorting the whole array.
    a.sort(); 
  
    # Generating sum groups.
    s = [];
    i = 0;
    j = n - 1;
    while(i < j):
        s.append((a[i] + a[j]));
        i += 1;
        j -= 1;
  
    mini = min(s); 
    maxi = max(s); 
  
    return abs(maxi - mini);
  
# Driver Code
a = [ 2, 6, 4, 3 ];
n = len(a);
print(calculate(a, n));
  
# This is contributed by mits

C#

// C# program to find minimum
// difference between groups of 
// highest and lowest sums.
using System;
using System.Linq;
using System.Collections.Generic;
  
class GFG 
{
  
    static long calculate(long []a, int n)
    {
        // Sorting the whole array.
        Array.Sort(a); 
        int i, j;
  
        // Generating sum groups.
        List s = new List();
        for (i = 0, j = n - 1; i < j; i++, j--) 
            s.Add((a[i] + a[j]));
  
        long mini = s.Min();
        long maxi = s.Max(); 
        return Math.Abs(maxi - mini);
    }
  
    // Driver code
    public static void Main() 
    {
        long []a = { 2, 6, 4, 3 };
        int n = a.Length;
        Console.WriteLine(calculate(a, n));
    }
}
  
//This code is contributed by Rajput-Ji

输出：

1

时间复杂度： O(n * log n)

询问： Inmobi

参考：https://www.hackerearth.com/problem/algorithm/project-team/