Program to print the Diagonals of a Matrix in O(N) time

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

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

Appraoch:

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.
4. In this method, we use one loop i.e. a loop to find the diagonal elements as per below formula:
principal diagonal = matrix[i][i];
secondary diagonal = matrix[i][n - i - 1];

where 0 &leq i &leq n

Below is the implementation of the above approach:

C++

 // C++ Program to print the Diagonals of a Matrix    #include using namespace std;    const int MAX = 100;    // Function to print the Principal Diagonal void 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 Diagonal void 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 code int 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 prthe Diagonals of a Matrix  MAX = 100;    # Function to prthe Principal Diagonal def printPrincipalDiagonal(mat, n):     print("Principal Diagonal: ", end = "");        for i in range(n):            # Condition for principal diagonal         print(mat[i][i], end= ", ");            print();    # Function to prthe Secondary Diagonal def 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 code if __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

Output:

Principal Diagonal: 1, 6, 3, 8,
Secondary Diagonal: 4, 7, 2, 5,

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