将N ^ 2个数分成相等总和的N组

给定一个偶数N。任务是考虑从1到N ^2的数字，将它们分成相等数目的N个组。

例子：

Input: N = 2
Output: {1, 4}, {2, 3}
Two groups of equal sum are 1, 4 and 2,3

Input: N = 4
Output: 
{ 1, 16} { 2, 15} 
{ 3, 14} { 4, 13} 
{ 5, 12} { 6, 11} 
{ 7, 10} { 8, 9}

方法：前N ^2个数字之和的公式： Sum =(N ² *(N ² +1))/ 2 。

因此，每个组的总和将是=(N ² + 1)* N ^2/2

让我们考虑以下类型的对(1，N ² )，(2，N ² -1)，依此类推。

由于N ²是偶数，所以可以使用正好N / 2个这样的对来构成每个组。

下面是上述方法的实现：

C++

// C++ implementation of the above approach
#include 
using namespace std;
  
// Function to print N groups of equal sum
void printGroups(int n)
{
    int x = 1;
    int y = n * n;
  
    // No. of Groups
    for (int i = 1; i <= n; i++) {
  
        // n/2 pairs
        for (int j = 1; j <= n / 2; j++) {
            cout << "{ " << x << ", " << y << "} ";
            x++;
            y--;
        }
  
        cout << endl;
    }
}
  
// Driver code
int main()
{
    int n = 4;
    printGroups(n);
  
    return 0;
}

Java

// Java implementation of the above approach
  
import java.io.*;
  
class GFG {
      
  
  
// Function to print N groups of equal sum
static void printGroups(int n)
{
    int x = 1;
    int y = n * n;
  
    // No. of Groups
    for (int i = 1; i <= n; i++) {
  
        // n/2 pairs
        for (int j = 1; j <= n / 2; j++) {
            System.out.print("{ " + x + ", " + y + "} ");
            x++;
            y--;
        }
  
        System.out.println();
    }
}
  
// Driver code
  
    public static void main (String[] args) {
            int n = 4;
    printGroups(n);
    }
}
// This code is contributed by shs

Python3

# Python implementation of the above approach
  
# Function to print N groups of equal sum
def printGroups(n) :
      
    x = 1
    y = n * n
      
    # No. of Groups
    for i in range(1, n + 1) :
          
        # n/2 pairs
        for j in range(1, n // 2 + 1) :
              
            print("{",x,",",y,"}",end = " ")
              
            x += 1
            y -= 1
          
        print()
          
         
# Driver code
if __name__ == "__main__" :
      
    n = 4
      
    # Function call
    printGroups(n)
  
# This code is contributed by Ryuga

C#

// Java implementation of the 
// above approach
using System;
  
class GFG 
{
      
// Function to print N groups 
// of equal sum
static void printGroups(int n)
{
    int x = 1;
    int y = n * n;
  
    // No. of Groups
    for (int i = 1; i <= n; i++) 
    {
  
        // n/2 pairs
        for (int j = 1; j <= n / 2; j++)
        {
            Console.Write("{ " + x + ", " + y + "} ");
            x++;
            y--;
        }
  
        Console.WriteLine();
    }
}
  
// Driver code
public static void Main ()
{
    int n = 4;
    printGroups(n);
}
}
  
// This code is contributed by shs

输出：

{ 1, 16} { 2, 15} 
{ 3, 14} { 4, 13} 
{ 5, 12} { 6, 11} 
{ 7, 10} { 8, 9}