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}

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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++

 // 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

PHP



Output:

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

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