Split N^2 numbers into N groups of equal sum

Given an even number N. The task is to consider numbers from 1 to N2, split them into N groups of the equal sum.

Examples:

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}

Approach: Formula for sum of first N2 numbers: Sum = (N2 * (N2 + 1))/ 2.

Therefore, the sum of each group would be = (N2 + 1)* N2 / 2

Let us consider pairs of the following type (1, N2), (2, N2-1) and so on.

Since N2 is an even number, each group can be made using exactly N/2 such pairs.

Below is the implementation of the above approach:

C++

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// C++ implementation of the above approach
#include <bits/stdc++.h>
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;
}

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Java

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// 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

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Python3

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# 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

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C#

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// 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

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PHP

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<?php
// PHP implementation of the 
// above approach
  
// Function to print N groups 
// of equal sum
function printGroups($n)
{
    $x = 1;
    $y = $n * $n;
  
    // No. of Groups
    for ($i = 1; $i <= $n; $i++)
    {
  
        // n/2 pairs
        for ($j = 1; $j <= $n / 2; $j++) 
        {
            echo "{ " , $x , ", " , $y , " } ";
            $x++;
            $y--;
        }
  
        echo "\n";
    }
}
  
// Driver code
$n = 4;
printGroups($n);
      
// This code is contributed by shs
?>

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Output:

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


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