Construct a matrix with sum equal to the sum of diagonal elements

Last Updated : 23 Aug, 2021

Given an integer N, the task is to construct a matrix of size N² using positive and negative integers and excluding 0, such that the sum of the matrix is equal to the sum of the diagonal of the matrix.

Examples:

Input: N = 2
Output:
1 -2
2 4
Explanation:
Diagonal sum = (1 + 4) = 5
Matrix sum = (1 - 2 + 2 + 4) = 5

Input: N = 5
Output:
1 2 3 5 10
3 1 4 -9 1
-19 6 1 5 -8
4 -7 2 1 12
-17 1 1 1 1
Explanation:
Diagonal sum = (1 + 1 + 1 + 1 + 1) = 5
Matrix sum = 5

Approach:
The approach to solving the problem is to traverse all indices of the matrix and print a positive element(say y) at the N diagonal positions and equally distribute a single-valued positive and negative integer(say x and -x) in the remaining N² - N positions.

Below is the implementation of the above approach:

C++

// C++ program to implement // the above approach #include <bits/stdc++.h>  using namespace std;  // Function to construct matrix with // diagonal sum equal to matrix sum void constructmatrix(int N) {     bool check = true;      for (int i = 0; i < N; i++) {          for (int j = 0; j < N; j++) {              // If diagonal position             if (i == j) {                 cout << 1 << " ";             }              else if (check) {                  // Positive element                 cout << 2 << " ";                 check = false;             }             else {                  // Negative element                 cout << -2 << " ";                 check = true;             }         }          cout << endl;     } }  // Driver Code int main() {     int N = 5;      constructmatrix(5);      return 0; }

Java

// Java program to implement // the above approach public class Main {      // Function to construct matrix with     // diagonal sum equal to matrix sum     public static void constructmatrix(int N)     {         boolean check = true;          for (int i = 0; i < N; i++) {              for (int j = 0; j < N; j++) {                  // If diagonal position                 if (i == j) {                     System.out.print("1 ");                 }                 else if (check) {                      // Positive element                     System.out.print("2 ");                     check = false;                 }                 else {                     // Negative element                     System.out.print("-2 ");                     check = true;                 }             }              System.out.println();         }     }      // Driver Code     public static void main(String[] args)     {         int N = 5;          constructmatrix(5);     } }

Python3

# Python3 program to implement  # the above approach   # Function to construct matrix with  # diagonal sum equal to matrix sum  def constructmatrix(N):           check = bool(True)       for i in range(N):         for j in range(N):              # If diagonal position              if (i == j):                  print(1, end = " ")              elif (check):                   # Positive element                  print(2, end = " ")                 check = bool(False)                               else:                  # Negative element                  print(-2, end = " ")                 check = bool(True)           print()  # Driver code N = 5 constructmatrix(5)  # This code is contributed by divyeshrabadiya07

// C# program to implement // the above approach using System;  class GFG{      // Function to construct matrix with // diagonal sum equal to matrix sum public static void constructmatrix(int N) {     bool check = true;      for(int i = 0; i < N; i++)     {         for(int j = 0; j < N; j++)         {                          // If diagonal position             if (i == j)             {                 Console.Write("1 ");             }             else if (check)             {                                  // Positive element                 Console.Write("2 ");                 check = false;             }             else             {                                  // Negative element                 Console.Write("-2 ");                 check = true;             }         }         Console.WriteLine();     } }  // Driver Code static public void Main () {     int N = 5;      constructmatrix(N); } }  // This code is contributed by piyush3010

JavaScript

<script>  // Javascript program to implement // the above approach       // Function to construct matrix with     // diagonal sum equal to matrix sum     function constructmatrix(N)     {         let check = true;            for (let i = 0; i < N; i++) {                for (let j = 0; j < N; j++) {                    // If diagonal position                 if (i == j) {                     document.write("1 ");                 }                 else if (check) {                        // Positive element                     document.write("2 ");                     check = false;                 }                 else {                     // Negative element                     document.write("-2 ");                     check = true;                 }             }                document.write("<br/>");         }     }      // Driver Code              let N = 5;        constructmatrix(5);  </script>

Output:

1 2 -2 2 -2  2 1 -2 2 -2  2 -2 1 2 -2  2 -2 2 1 -2  2 -2 2 -2 1

Time Complexity: O(N²)
Auxiliary Space: O(1)

Print all the sub diagonal elements of the given square matrix

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Construct a matrix with sum equal to the sum of diagonal elements

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