Given a 2D square matrix, the task is to print the Principal and Secondary diagonals of this matrix in O(N) time complexity. For O(N2) time, please refer this article.
Examples:
Input: 4 1 2 3 4 4 3 2 1 7 8 9 6 6 5 4 3 Output: Principal Diagonal: 1, 3, 9, 3 Secondary Diagonal: 4, 2, 8, 6 Input: 3 1 1 1 1 1 1 1 1 1 Output: Principal Diagonal: 1, 1, 1 Secondary Diagonal: 1, 1, 1
Approach:
1.Consider the following 4 X 4 input matrix.
A00 A01 A02 A03 A10 A11 A12 A13 A20 A21 A22 A23 A30 A31 A32 A33
2.The primary diagonal is formed by the elements A00, A11, A22, A33.
Condition for Principal Diagonal:
The row-column condition is row = column.
3.The secondary diagonal is formed by the elements A03, A12, A21, A30.
Condition for Secondary Diagonal:
The row-column condition is row = numberOfRows - column - 1.
In this method, we use one loop i.e. a loop to find the diagonal elements as per the below formula:
principal diagonal = matrix[i][i]; secondary diagonal = matrix[i][n - i - 1]; where 0 <= i <= n
Below is the implementation of the above approach:
C++
// C++ Program to print the Diagonals of a Matrix#include <bits/stdc++.h>using namespace std;const int MAX = 100;// Function to print the Principal Diagonalvoid printPrincipalDiagonal(int mat[][MAX], int n){ cout << "Principal Diagonal: "; for (int i = 0; i < n; i++) { // Condition for principal diagonal cout << mat[i][i] << ", "; } cout << endl;}// Function to print the Secondary Diagonalvoid printSecondaryDiagonal(int mat[][MAX], int n){ cout << "Secondary Diagonal: "; for (int i = 0; i < n; i++) { // Condition for secondary diagonal cout << mat[i][n - i - 1] << ", "; } cout << endl;}// Driver codeint main(){ int n = 4; int a[][MAX] = { { 1, 2, 3, 4 }, { 5, 6, 7, 8 }, { 1, 2, 3, 4 }, { 5, 6, 7, 8 } }; printPrincipalDiagonal(a, n); printSecondaryDiagonal(a, n); return 0;} |
Java
// Java Program to print the Diagonals of a Matrix class GFG { static final int MAX = 100; // Function to print the Principal Diagonal static void printPrincipalDiagonal(int mat[][], int n) { System.out.print("Principal Diagonal: "); for (int i = 0; i < n; i++) { // Condition for principal diagonal System.out.print(mat[i][i] + ", "); } System.out.println(); } // Function to print the Secondary Diagonal static void printSecondaryDiagonal(int mat[][], int n) { System.out.print("Secondary Diagonal: "); for (int i = 0; i < n; i++) { // Condition for secondary diagonal System.out.print(mat[i][n - i - 1] + ", "); } System.out.println(); } // Driver code public static void main (String[] args) { int n = 4; int a[][] = { { 1, 2, 3, 4 }, { 5, 6, 7, 8 }, { 1, 2, 3, 4 }, { 5, 6, 7, 8 } }; printPrincipalDiagonal(a, n); printSecondaryDiagonal(a, n); } }// This code is contributed by AnkitRai01 |
Python3
# Python Program to print the Diagonals of a Matrix MAX = 100;# Function to print the Principal Diagonaldef printPrincipalDiagonal(mat, n): print("Principal Diagonal: ", end = ""); for i in range(n): # Condition for principal diagonal print(mat[i][i], end= ", "); print();# Function to print the Secondary Diagonaldef printSecondaryDiagonal(mat, n): print("Secondary Diagonal: ", end = ""); for i in range(n): # Condition for secondary diagonal print(mat[i][n - i - 1], end = ", "); print();# Driver codeif __name__ == '__main__': n = 4; a = [[ 1, 2, 3, 4 ], [ 5, 6, 7, 8 ], [ 1, 2, 3, 4 ], [ 5, 6, 7, 8 ]]; printPrincipalDiagonal(a, n); printSecondaryDiagonal(a, n);# This code is contributed by PrinciRaj1992 |
C#
// C# Program to print the Diagonals of a Matrix using System;class GFG { // Function to print the Principal Diagonal static void printPrincipalDiagonal(int [,]mat, int n) { Console.Write("Principal Diagonal: "); for (int i = 0; i < n; i++) { // Condition for principal diagonal Console.Write(mat[i, i] + ", "); } Console.WriteLine(); } // Function to print the Secondary Diagonal static void printSecondaryDiagonal(int [,]mat, int n) { Console.Write("Secondary Diagonal: "); for (int i = 0; i < n; i++) { // Condition for secondary diagonal Console.Write(mat[i, n - i - 1] + ", "); } Console.WriteLine(); } // Driver code public static void Main() { int n = 4; int [,]a = { { 1, 2, 3, 4 }, { 5, 6, 7, 8 }, { 1, 2, 3, 4 }, { 5, 6, 7, 8 } }; printPrincipalDiagonal(a, n); printSecondaryDiagonal(a, n); } } // This code is contributed by AnkitRai01 |
Javascript
<script>// Java script Program to print the Diagonals of a Matrixlet MAX = 100; // Function to print the Principal Diagonal function printPrincipalDiagonal(mat,n) { document.write("Principal Diagonal: "); for (let i = 0; i < n; i++) { // Condition for principal diagonal document.write(mat[i][i] + ", "); } document.write("<br>"); } // Function to print the Secondary Diagonal function printSecondaryDiagonal(mat,n) { document.write("Secondary Diagonal: "); for (let i = 0; i < n; i++) { // Condition for secondary diagonal document.write(mat[i][n - i - 1] + ", "); } document.write("<br>"); } // Driver code let n = 4; let a = [[1, 2, 3, 4 ], [ 5, 6, 7, 8 ], [ 1, 2, 3, 4 ], [ 5, 6, 7, 8 ]]; printPrincipalDiagonal(a, n); printSecondaryDiagonal(a, n);// This code is contributed by sravan kumar Gottumukklala</script> |
Output:
Principal Diagonal: 1, 6, 3, 8, Secondary Diagonal: 4, 7, 2, 5,
Time complexity: O(n) for given n
Auxiliary space: O(1) as it is using constant space
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