Create matrix whose sum of diagonals in each sub matrix is even Last Updated : 10 Feb, 2022 Summarize Comments Improve Suggest changes Share Like Article Like Report Given a number N, the task is to create a square matrix of size N*N with values in range [1, N*N], such that the sum of each diagonal of an even sub-square matrix is even. Examples: Input: N = 3Output: 1 2 3 4 5 6 7 8 9 Explanation:For each even sub-square matrix the sum of each diagonal is a even number.1 2 4 5 sum of each diagonal is 6 and 6 i.e even number. Input: N = 4Output: 1 2 3 4 6 5 8 7 9 10 11 12 14 13 16 15 Explanation: For each even sub-square matrix the sum of each diagonal is a even number.1 2 6 5 sum of each diagonal is 6 and 8 i.e even number. Approach: The idea is to arrange elements from 1 to N*N in the below-given ways: Initialize odd and even by 1 and 2 elements respectively.Iterate two nested loop in the range [0, N].If the sum of indices in the two nested loops is even the print the value of odd and increment odd by 2 and if the sum is odd then print the value of even, and increment even by 2. Below is the implementation of the above approach: C++ // C++ program for the above approach #include <iostream> using namespace std; // Function to print N*N order matrix // with all sub-matrix of even order // is sum of its diagonal also even void evenSubMatrix(int N) { // Even index int even = 1; // Odd index int odd = 2; // Iterate two nested loop for (int i = 0; i < N; i++) { for (int j = 0; j < N; j++) { // For even index the element // should be consecutive odd if ((i + j) % 2 == 0) { cout << even << " "; even += 2; } // for odd index the element // should be consecutive even else { cout << odd << " "; odd += 2; } } cout << "\n"; } } // Driver Code int main() { // Given order of matrix int N = 4; // Function call evenSubMatrix(N); return 0; } Java // Java program for the above approach import java.util.*; class GFG{ // Function to print N*N order matrix // with all sub-matrix of even order // is sum of its diagonal also even static void evenSubMatrix(int N) { // Even index int even = 1; // Odd index int odd = 2; // Iterate two nested loop for(int i = 0; i < N; i++) { for(int j = 0; j < N; j++) { // For even index the element // should be consecutive odd if ((i + j) % 2 == 0) { System.out.print(even + " "); even += 2; } // For odd index the element // should be consecutive even else { System.out.print(odd + " "); odd += 2; } } System.out.println(); } } // Driver code public static void main(String[] args) { // Given order of matrix int N = 4; // Function call evenSubMatrix(N); } } // This code is contributed by offbeat Python3 # Python3 program for the above approach # Function to print N*N order matrix # with all sub-matrix of even order # is sum of its diagonal also even def evenSubMatrix(N): # Even index even = 1 # Odd index odd = 2 # Iterate two nested loop for i in range(N): for j in range(N): # For even index the element # should be consecutive odd if ((i + j) % 2 == 0): print(even, end = " ") even += 2 # For odd index the element # should be consecutive even else: print(odd, end = " ") odd += 2 print() # Driver Code # Given order of matrix N = 4 # Function call evenSubMatrix(N) # This code is contributed by sanjoy_62 C# // C# program for the above approach using System; class GFG{ // Function to print N*N order matrix // with all sub-matrix of even order // is sum of its diagonal also even static void evenSubMatrix(int N) { // Even index int even = 1; // Odd index int odd = 2; // Iterate two nested loop for(int i = 0; i < N; i++) { for(int j = 0; j < N; j++) { // For even index the element // should be consecutive odd if ((i + j) % 2 == 0) { Console.Write(even + " "); even += 2; } // For odd index the element // should be consecutive even else { Console.Write(odd + " "); odd += 2; } } Console.WriteLine(); } } // Driver code public static void Main(String[] args) { // Given order of matrix int N = 4; // Function call evenSubMatrix(N); } } // This code is contributed by amal kumar choubey JavaScript <script> // Java script program for the above approach // Function to print N*N order matrix // with all sub-matrix of even order // is sum of its diagonal also even function evenSubMatrix( N) { // Even index let even = 1; // Odd index let odd = 2; // Iterate two nested loop for(let i = 0; i < N; i++) { for(let j = 0; j < N; j++) { // For even index the element // should be consecutive odd if ((i + j) % 2 == 0) { document.write(even + " "); even += 2; } // For odd index the element // should be consecutive even else { document.write(odd + " "); odd += 2; } } document.write("<br>"); } } // Driver code // Given order of matrix let N = 4; // Function call evenSubMatrix(N); // This code is contributed by manoj </script> Output: 1 2 3 4 6 5 8 7 9 10 11 12 14 13 16 15 Time Complexity: O(N*N)Auxiliary Space: O(1) Comment More infoAdvertise with us Next Article Create matrix whose sum of diagonals in each sub matrix is even T thakurabhaysingh445 Follow Improve Article Tags : Pattern Searching Mathematical Matrix Write From Home DSA school-programming submatrix +3 More Practice Tags : MathematicalMatrixPattern Searching Similar Reads DSA Tutorial - Learn Data Structures and Algorithms DSA (Data Structures and Algorithms) is the study of organizing data efficiently using data structures like arrays, stacks, and trees, paired with step-by-step procedures (or algorithms) to solve problems effectively. 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