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Program to print the Diagonals of a Matrix in O(N) time
• Last Updated : 27 Apr, 2021

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 ``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 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):` `        ``# Condition for principal diagonal``        ``print``(mat[i][i], end``=` `", "``);``    ` `    ``print``();` `# Function to print the 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`

## Javascript

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

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