Given a positive integer N, the task is to construct a matrix of size N * N such that all the matrix elements are distinct from the range [1, N2] and the sum of elements in both the diagonals of every 2 * 2 submatrices is even.
Examples:
Input: N = 3
Output:
1 2 3
4 5 6
7 8 9
Explanation:
Diagonal elements of every 2 * 2 matrices in the output matrix are { {1, 5}, {2, 4}, {2, 6}, {3, 5}, {4, 8}, {5, 7}, {5, 9}, {6, 8} }. It can be observed that the sum of every diagonal is even.Input: N = 4
Output:
1 2 3 4
6 5 8 7
9 10 11 12
14 13 16 15
Approach: Follow the steps below to solve the problem:
- Initialize a matrix, say mat[][], to store the matrix elements such that all the matrix elements are distinct from the range [1, N2] and the sum of matrix elements in both the diagonals of every 2 * 2 submatrices is even.
- Initialize a variable, say odd = 1, to store odd numbers.
- Initialize a variable, say even = 2, to store even numbers.
- Fill all the matrix elements, mat[i][j], by checking the following conditions:
- If (i + j) % 2 = 0, then set mat[i][j] = odd and update odd += 2.
- Otherwise, set mat[i][j] = even and update even += 2.
- Finally, print the matrix mat[][].
Below is the implementation of the above approach:
C++
// C++ program for the above approach#include <bits/stdc++.h>using namespace std;// Function to construct a matrix such that// the sum elements in both diagonals of// every 2 * 2 matrices is evenvoid generateMatrix(int N){ // Stores odd numbers int odd = 1; // Stores even numbers int even = 2; // Store matrix elements such that // sum of elements in both diagonals // of every 2 * 2 submatrices is even int mat[N + 1][N + 1]; // Fill all the values of // matrix elements for (int i = 1; i <= N; i++) { for (int j = 1; j <= N; j++) { if ((i + j) % 2 == 0) { mat[i][j] = odd; // Update odd odd += 2; } else { mat[i][j] = even; // Update even even += 2; } } } // Print the matrix for (int i = 1; i <= N; i++) { for (int j = 1; j <= N; j++) { cout << mat[i][j] << " "; } cout << endl; }}// Driver Codeint main(){ int N = 4; generateMatrix(N); return 0;} |
Java
// Java program for the above approachimport java.io.*;class GFG{// Function to construct a matrix such that// the sum elements in both diagonals of// every 2 * 2 matrices is evenstatic void generateMatrix(int N){ // Stores odd numbers int odd = 1; // Stores even numbers int even = 2; // Store matrix elements such that // sum of elements in both diagonals // of every 2 * 2 submatrices is even int[][] mat = new int[N + 1][N + 1]; // Fill all the values of // matrix elements for(int i = 1; i <= N; i++) { for(int j = 1; j <= N; j++) { if ((i + j) % 2 == 0) { mat[i][j] = odd; // Update odd odd += 2; } else { mat[i][j] = even; // Update even even += 2; } } } // Print the matrix for(int i = 1; i <= N; i++) { for(int j = 1; j <= N; j++) { System.out.print(mat[i][j] + " "); } System.out.println(); }}// Driver Codepublic static void main(String[] args){ int N = 4; generateMatrix(N);}}// This code is contributed by Dharanendra L V |
Python3
# Python program for the above approach# Function to construct a matrix such that# the sum elements in both diagonals of# every 2 * 2 matrices is evendef generateMatrix(N): # Stores odd numbers odd = 1; # Stores even numbers even = 2; # Store matrix elements such that # sum of elements in both diagonals # of every 2 * 2 submatrices is even mat = [[0 for i in range(N + 1)] for j in range(N + 1)] ; # Fill all the values of # matrix elements for i in range(1, N + 1): for j in range(1, N + 1): if ((i + j) % 2 == 0): mat[i][j] = odd; # Update odd odd += 2; else: mat[i][j] = even; # Update even even += 2; # Print the matrix for i in range(1, N + 1): for j in range(1, N + 1): print(mat[i][j], end = " "); print();# Driver Codeif __name__ == '__main__': N = 4; generateMatrix(N);# This code is contributed by 29AjayKumar |
C#
// C# program for the above approachusing System;class GFG{// Function to construct a matrix such that// the sum elements in both diagonals of// every 2 * 2 matrices is evenstatic void generateMatrix(int N){ // Stores odd numbers int odd = 1; // Stores even numbers int even = 2; // Store matrix elements such that // sum of elements in both diagonals // of every 2 * 2 submatrices is even int[,] mat = new int[N + 1, N + 1]; // Fill all the values of // matrix elements for(int i = 1; i <= N; i++) { for(int j = 1; j <= N; j++) { if ((i + j) % 2 == 0) { mat[i, j] = odd; // Update odd odd += 2; } else { mat[i, j] = even; // Update even even += 2; } } } // Print the matrix for(int i = 1; i <= N; i++) { for(int j = 1; j <= N; j++) { Console.Write(mat[i, j] + " "); } Console.WriteLine(); }}// Driver Codestatic public void Main(){ int N = 4; generateMatrix(N);}}// This code is contributed by Dharanendra L V |
Javascript
<script>// Javascript program of the above approach// Function to construct a matrix such that// the sum elements in both diagonals of// every 2 * 2 matrices is evenfunction generateMatrix(N){ // Stores odd numbers let odd = 1; // Stores even numbers let even = 2; // Store matrix elements such that // sum of elements in both diagonals // of every 2 * 2 submatrices is even let mat = new Array(N + 1); // Loop to create 2D array using 1D array for (var i = 0; i < mat.length; i++) { mat[i] = new Array(2); } // Fill all the values of // matrix elements for(let i = 1; i <= N; i++) { for(let j = 1; j <= N; j++) { if ((i + j) % 2 == 0) { mat[i][j] = odd; // Update odd odd += 2; } else { mat[i][j] = even; // Update even even += 2; } } } // Print the matrix for(let i = 1; i <= N; i++) { for(let j = 1; j <= N; j++) { document.write(mat[i][j] + " "); } document.write("<br/>"); }} // Driver Code let N = 4; generateMatrix(N); </script> |
Output:
1 2 3 4 6 5 8 7 9 10 11 12 14 13 16 15
Time Complexity: O(N2)
Auxiliary Space: O(N2)
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