Program to print the Diagonals of a Matrix

Given a 2D square matrix, print the Principal and Secondary diagonals.

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

For example, consider the following 4 X 4 input matrix.

A00 A01 A02 A03
A10 A11 A12 A13
A20 A21 A22 A23
A30 A31 A32 A33

The primary diagonal is formed by the elements A00, A11, A22, A33.
Condition for Principal Diagonal:

The row-column condition is row = column.

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.

Method 1:
In this method, we use two loops i.e. a loop for columns and a loop for rows and in the inner loop we check for the condition stated above.

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 Diagonal
void printPrincipalDiagonal(int mat[][MAX], int n)
{
    cout << "Principal Diagonal: ";

    for (int i = 0; i < n; i++) {
        for (int j = 0; j < n; j++) {

            // Condition for principal diagonal
            if (i == j)
                cout << mat[i][j] << ", ";
        }
    }
    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++) {
        for (int j = 0; j < n; j++) {

            // Condition for secondary diagonal
            if ((i + j) == (n - 1))
                cout << mat[i][j] << ", ";
        }
    }
    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 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++) {
            for (int j = 0; j < n; j++) {

                // Condition for principal diagonal
                if (i == j) {
                    System.out.print(mat[i][j] + ", ");
                }
            }
        }
        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++) {
            for (int j = 0; j < n; j++) {

                // Condition for secondary diagonal
                if ((i + j) == (n - 1)) {
                    System.out.print(mat[i][j] + ", ");
                }
            }
        }
        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 Rajput-Ji

Python3

# Python3 Program to print the Diagonals of a Matrix
MAX = 100

# Function to print the Principal Diagonal
def printPrincipalDiagonal(mat, n):
    print("Principal Diagonal: ", end = "")

    for i in range(n):
        for j in range(n):

            # Condition for principal diagonal
            if (i == j):
                print(mat[i][j], end = ", ")
    print()

# Function to print the Secondary Diagonal
def printSecondaryDiagonal(mat, n):
    print("Secondary Diagonal: ", end = "")

    for i in range(n):
        for j in range(n):

            # Condition for secondary diagonal
            if ((i + j) == (n - 1)):
                print(mat[i][j], end = ", ")
    print()

# Driver code
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 Mohit Kumar

// C# Program to print the Diagonals of a Matrix
using System;

class GFG {
    static int MAX = 100;

    // Function to print the Principal Diagonal
    static void printPrincipalDiagonal(int[, ] mat, int n)
    {
        Console.Write("Principal Diagonal: ");

        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++) {

                // Condition for principal diagonal
                if (i == j) {
                    Console.Write(mat[i, j] + ", ");
                }
            }
        }
        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++) {
            for (int j = 0; j < n; j++) {

                // Condition for secondary diagonal
                if ((i + j) == (n - 1)) {
                    Console.Write(mat[i, j] + ", ");
                }
            }
        }
        Console.WriteLine("");
    }

    // 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 29AjayKumar

JavaScript

<script>

    // Javascript Program to print the Diagonals of a Matrix
    
    let MAX = 100;
 
    // Function to print the Principal Diagonal
    function printPrincipalDiagonal(mat, n)
    {
        document.write("Principal Diagonal: ");
 
        for (let i = 0; i < n; i++) {
            for (let j = 0; j < n; j++) {
 
                // Condition for principal diagonal
                if (i == j) {
                    document.write(mat[i][j] + ", ");
                }
            }
        }
        document.write("</br>");
    }
 
    // Function to print the Secondary Diagonal
    function printSecondaryDiagonal(mat, n)
    {
        document.write("Secondary Diagonal: ");
 
        for (let i = 0; i < n; i++) {
            for (let j = 0; j < n; j++) {
 
                // Condition for secondary diagonal
                if ((i + j) == (n - 1)) {
                    document.write(mat[i][j] + ", ");
                }
            }
        }
        document.write("</br>");
    }
    
    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);
    
</script>

Output

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

Complexity Analysis:

Time Complexity: O(n²).
As there is a nested loop involved so the time complexity is squared.
Auxiliary Space: O(1).
As no extra space is occupied.

Method 2:
In this method, the same condition for printing the diagonal elements can be achieved using a single for loop.
Approach:

For Principal Diagonal elements: Run a for a loop until n, where n is the number of columns, and print array[i][i] where i is the index variable.
For Secondary Diagonal elements: Run a for a loop until n, where n is the number of columns and print array[i][k] where i is the index variable and k = array_length - 1. Decrease k until 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 Diagonal
void printPrincipalDiagonal(int mat[][MAX], int n)
{
    cout << "Principal Diagonal: ";

    for (int i = 0; i < n; i++) {
        // Printing principal diagonal
        cout << mat[i][i] << ", ";
    }
    cout << endl;
}

// Function to print the Secondary Diagonal
void printSecondaryDiagonal(int mat[][MAX], int n)
{
    cout << "Secondary Diagonal: ";
    int k = n - 1;
    for (int i = 0; i < n; i++) {
        // Printing secondary diagonal
        cout << mat[i][k--] << ", ";
    }
    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;
}

// This code is contributed by yashbeersingh42

Java

// Java Program to print the 
// Diagonals of a Matrix
class Main{
  
static int MAX = 100;
    
// Function to print the Principal Diagonal
public static void printPrincipalDiagonal(int mat[][], 
                                          int n)
{
  System.out.print("Principal Diagonal: ");

  for (int i = 0; i < n; i++) 
  {
    // Printing principal diagonal
    System.out.print(mat[i][i] + ", ");
  }
  System.out.println();
}

// Function to print the Secondary Diagonal
public static void printSecondaryDiagonal(int mat[][], 
                                          int n)
{
  System.out.print("Secondary Diagonal: ");
  int k = n - 1;
  
  for (int i = 0; i < n; i++) 
  {
    // Printing secondary diagonal
    System.out.print(mat[i][k--] + ", ");
  }
  System.out.println();
}

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 divyeshrabadiya07

Python3

# Python3 program to print the
# Diagonals of a Matrix
MAX = 100

# Function to print the Principal Diagonal
def printPrincipalDiagonal(mat, n):

    print("Principal Diagonal: ", end = "")

    for i in range(n):
        
        # Printing principal diagonal
        print(mat[i][i], end = ", ")

    print()

# Function to print the Secondary Diagonal
def printSecondaryDiagonal(mat, n):

    print("Secondary Diagonal: ", end = "")
    k = n - 1
    
    for i in range(n):
        
        # Printing secondary diagonal
        print(mat[i][k], end = ", ")
        k -= 1

    print()
    
# Driver Code
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 divyesh072019

// C# program for the 
// above approach
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++) 
  {
    // Printing principal diagonal
    Console.Write(mat[i, i] + ", ");
  }
  Console.Write("\n");
}
 
// Function to print the 
// Secondary Diagonal
static void printSecondaryDiagonal(int [,]mat, 
                                   int n)
{
  Console.Write("Secondary Diagonal: ");
  int k = n - 1;
  
  for (int i = 0; i < n; i++) 
  {
    // Printing secondary diagonal
    Console.Write(mat[i, k--] + ", ");
  }
  
  Console.Write("\n");
}
    
    
// Driver code
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 rutvik_56

JavaScript

<script>

    // Javascript Program to print the
    // Diagonals of a Matrix

    let MAX = 100;
     
    // Function to print the Principal Diagonal
    function printPrincipalDiagonal(mat, n)
    {
      document.write("Principal Diagonal: ");

      for (let i = 0; i < n; i++)
      {
        // Printing principal diagonal
        document.write(mat[i][i] + ", ");
      }
      document.write("</br>");
    }

    // Function to print the Secondary Diagonal
    function printSecondaryDiagonal(mat, n)
    {
      document.write("Secondary Diagonal: ");
      let k = n - 1;

      for (let i = 0; i < n; i++)
      {
        // Printing secondary diagonal
        document.write(mat[i][k--] + ", ");
      }
      document.write("</br>");
    }
    
    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);
    
</script>

Output

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

Complexity Analysis:

Time Complexity: O(n).
As there is only one loop involved so the time complexity is linear.
Auxiliary Space: O(1).
As no extra space is occupied.

Using list comprehensions:

Approach:

Define a function print_diagonals that takes a 2D list (matrix) as input.
Get the length of the matrix and store it in the variable n.
Use a list comprehension to create a list of the principal diagonal elements. To do this, iterate over the range from 0 to n and for each index i, append matrix[i][i] to the list principal.
Print the list of principal diagonal elements using the join() method to convert the list to a string separated by commas.
Use another list comprehension to create a list of the secondary diagonal elements. To do this, iterate over the range from 0 to n and for each index i, append matrix[i][n-1-i] to the list secondary.
Print the list of secondary diagonal elements using the join() method to convert the list to a string separated by commas.
Example usage: Create a 2D list matrix, call the print_diagonals function with matrix as input.

C++

#include <iostream>
#include <vector>

// Function to print the principal and secondary diagonals
// of a matrix
void printDiagonals(std::vector<std::vector<int> >& matrix)
{
    int n
        = matrix
              .size(); // Get the size of the square matrix

    // Get the principal diagonal
    std::vector<int> principal(n);
    for (int i = 0; i < n; i++) {
        principal[i] = matrix[i][i];
    }

    // Print the principal diagonal
    std::cout << "Principal Diagonal: ";
    for (int i = 0; i < n; i++) {
        std::cout << principal[i];
        if (i != n - 1) {
            std::cout << ", ";
        }
    }
    std::cout << std::endl;

    // Get the secondary diagonal
    std::vector<int> secondary(n);
    for (int i = 0; i < n; i++) {
        secondary[i] = matrix[i][n - 1 - i];
    }

    // Print the secondary diagonal
    std::cout << "Secondary Diagonal: ";
    for (int i = 0; i < n; i++) {
        std::cout << secondary[i];
        if (i != n - 1) {
            std::cout << ", ";
        }
    }
    std::cout << std::endl;
}

int main()
{
    std::vector<std::vector<int> > matrix
        = { { 1, 2, 3, 4 },
            { 4, 3, 2, 1 },
            { 7, 8, 9, 6 },
            { 6, 5, 4, 3 } };

    printDiagonals(matrix);

    return 0;
}

Java

import java.io.*;
public class GFG {
    public static void printDiagonals(int[][] matrix) {
        int n = matrix.length;
        // Get the principal diagonal
        int[] principal = new int[n];
        for (int i = 0; i < n; i++) {
            principal[i] = matrix[i][i];
        }
        System.out.print("Principal Diagonal: ");
        for (int i = 0; i < n; i++) {
            System.out.print(principal[i]);
            if (i != n - 1) {
                System.out.print(", ");
            }
        }
        System.out.println();
        // Get the secondary diagonal
        int[] secondary = new int[n];
        for (int i = 0; i < n; i++) {
            secondary[i] = matrix[i][n - 1 - i];
        }
        System.out.print("Secondary Diagonal: ");
        for (int i = 0; i < n; i++) {
            System.out.print(secondary[i]);
            if (i != n - 1) {
                System.out.print(", ");
            }
        }
        System.out.println();
    }
    public static void main(String[] args) {
        int[][] matrix = {
            {1, 2, 3, 4},
            {4, 3, 2, 1},
            {7, 8, 9, 6},
            {6, 5, 4, 3}
        };
        printDiagonals(matrix);
    }
}

Python3

def print_diagonals(matrix):
    n = len(matrix)
    # Get the principal diagonal
    principal = [matrix[i][i] for i in range(n)]
    print("Principal Diagonal:", ", ".join(map(str, principal)))
    # Get the secondary diagonal
    secondary = [matrix[i][n-1-i] for i in range(n)]
    print("Secondary Diagonal:", ", ".join(map(str, secondary)))

# Example usage
matrix = [[1, 2, 3, 4], [4, 3, 2, 1], [7, 8, 9, 6], [6, 5, 4, 3]]
print_diagonals(matrix)

using System;

public class GFG {
    public static void PrintDiagonals(int[,] matrix) {
        int n = matrix.GetLength(0);
        
        // Get the principal diagonal
        int[] principal = new int[n];
        for (int i = 0; i < n; i++) {
            principal[i] = matrix[i, i];
        }
        
        Console.Write("Principal Diagonal: ");
        for (int i = 0; i < n; i++) {
            Console.Write(principal[i]);
            if (i != n - 1) {
                Console.Write(", ");
            }
        }
        Console.WriteLine();
        
        // Get the secondary diagonal
        int[] secondary = new int[n];
        for (int i = 0; i < n; i++) {
            secondary[i] = matrix[i, n - 1 - i];
        }
        
        Console.Write("Secondary Diagonal: ");
        for (int i = 0; i < n; i++) {
            Console.Write(secondary[i]);
            if (i != n - 1) {
                Console.Write(", ");
            }
        }
        Console.WriteLine();
    }
    
    public static void Main(string[] args) {
        int[,] matrix = {
            {1, 2, 3, 4},
            {4, 3, 2, 1},
            {7, 8, 9, 6},
            {6, 5, 4, 3}
        };
        
        PrintDiagonals(matrix);
    }
}

JavaScript

function print_diagonals(matrix) {
    let n = matrix.length;
    // Get the principal diagonal
    let principal = [];
    for (let i = 0; i < n; i++) {
        principal.push(matrix[i][i]);
    }
    console.log("Principal Diagonal:", principal.join(", "));
    // Get the secondary diagonal
    let secondary = [];
    for (let i = 0; i < n; i++) {
        secondary.push(matrix[i][n - 1 - i]);
    }
    console.log("Secondary Diagonal:", secondary.join(", "));
}

// Example usage
let matrix = [
    [1, 2, 3, 4],
    [4, 3, 2, 1],
    [7, 8, 9, 6],
    [6, 5, 4, 3]
];
print_diagonals(matrix);

Output

Principal Diagonal: 1, 3, 9, 3
Secondary Diagonal: 4, 2, 8, 6

The time complexity of this approach is also O(n^2)

The auxiliary space is O(n).

Program to print the Diagonals of a Matrix

Using list comprehensions:

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