# 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.

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.`
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 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  `

Output:

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

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