# Efficiently compute sums of diagonals of a matrix

Given a 2D square matrix, find sum of elements in Principal and Secondary diagonals. 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.

1. Condition for Principal Diagonal: The row-column condition is row = column.
The secondary diagonal is formed by the elements A03, A12, A21, A30.
2. Condition for Secondary Diagonal: The row-column condition is row = numberOfRows – column -1.

Examples :

```Input :
4
1 2 3 4
4 3 2 1
7 8 9 6
6 5 4 3
Output :
Principal Diagonal: 16
Secondary Diagonal: 20

Input :
3
1 1 1
1 1 1
1 1 1
Output :
Principal Diagonal: 3
Secondary Diagonal: 3
```

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

Method 1 (O(n ^ 2) :

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++

 `// A simple C++ program to find sum of diagonals ` `#include ` `using` `namespace` `std; ` ` `  `const` `int` `MAX = 100; ` ` `  `void` `printDiagonalSums(``int` `mat[][MAX], ``int` `n) ` `{ ` `    ``int` `principal = 0, secondary = 0; ` `    ``for` `(``int` `i = 0; i < n; i++) { ` `        ``for` `(``int` `j = 0; j < n; j++) { ` ` `  `            ``// Condition for principal diagonal ` `            ``if` `(i == j) ` `                ``principal += mat[i][j]; ` ` `  `            ``// Condition for secondary diagonal ` `            ``if` `((i + j) == (n - 1)) ` `                ``secondary += mat[i][j]; ` `        ``} ` `    ``} ` ` `  `    ``cout << ``"Principal Diagonal:"` `<< principal << endl; ` `    ``cout << ``"Secondary Diagonal:"` `<< secondary << endl; ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``int` `a[][MAX] = { { 1, 2, 3, 4 }, { 5, 6, 7, 8 },  ` `                    ``{ 1, 2, 3, 4 }, { 5, 6, 7, 8 } }; ` `    ``printDiagonalSums(a, 4); ` `    ``return` `0; ` `} `

## Java

 `// A simple java program to find ` `// sum of diagonals ` `import` `java.io.*; ` ` `  `public` `class` `GFG { ` ` `  `    ``static` `void` `printDiagonalSums(``int` `[][]mat, ` `                                         ``int` `n) ` `    ``{ ` `        ``int` `principal = ``0``, secondary = ``0``; ` `        ``for` `(``int` `i = ``0``; i < n; i++) { ` `            ``for` `(``int` `j = ``0``; j < n; j++) { ` `     `  `                ``// Condition for principal ` `                ``// diagonal ` `                ``if` `(i == j) ` `                    ``principal += mat[i][j]; ` `     `  `                ``// Condition for secondary ` `                ``// diagonal ` `                ``if` `((i + j) == (n - ``1``)) ` `                    ``secondary += mat[i][j]; ` `            ``} ` `        ``} ` `     `  `        ``System.out.println(``"Principal Diagonal:"` `                                    ``+ principal); ` `                                     `  `        ``System.out.println(``"Secondary Diagonal:"` `                                    ``+ secondary); ` `    ``} ` ` `  `    ``// Driver code ` `    ``static` `public` `void` `main (String[] args) ` `    ``{ ` `         `  `        ``int` `[][]a = { { ``1``, ``2``, ``3``, ``4` `}, ` `                      ``{ ``5``, ``6``, ``7``, ``8` `},  ` `                      ``{ ``1``, ``2``, ``3``, ``4` `}, ` `                      ``{ ``5``, ``6``, ``7``, ``8` `} }; ` `                     `  `        ``printDiagonalSums(a, ``4``); ` `    ``} ` `} ` ` `  `// This code is contributed by vt_m. `

## Python3

 `# A simple Python program to  ` `# find sum of diagonals ` `MAX` `=` `100` ` `  `def` `printDiagonalSums(mat, n): ` ` `  `    ``principal ``=` `0` `    ``secondary ``=` `0``; ` `    ``for` `i ``in` `range``(``0``, n):  ` `        ``for` `j ``in` `range``(``0``, n):  ` ` `  `            ``# Condition for principal diagonal ` `            ``if` `(i ``=``=` `j): ` `                ``principal ``+``=` `mat[i][j] ` ` `  `            ``# Condition for secondary diagonal ` `            ``if` `((i ``+` `j) ``=``=` `(n ``-` `1``)): ` `                ``secondary ``+``=` `mat[i][j] ` `         `  `    ``print``(``"Principal Diagonal:"``, principal) ` `    ``print``(``"Secondary Diagonal:"``, secondary) ` ` `  `# Driver code ` `a ``=` `[[ ``1``, ``2``, ``3``, ``4` `], ` `     ``[ ``5``, ``6``, ``7``, ``8` `],  ` `     ``[ ``1``, ``2``, ``3``, ``4` `], ` `      ``[ ``5``, ``6``, ``7``, ``8` `]] ` `printDiagonalSums(a, ``4``) ` ` `  `# This code is contributed  ` `# by ihritik `

## C#

 `// A simple C# program to find sum ` `// of diagonals ` `using` `System; ` ` `  `public` `class` `GFG { ` ` `  `    ``static` `void` `printDiagonalSums(``int` `[,]mat, ` `                                        ``int` `n) ` `    ``{ ` `        ``int` `principal = 0, secondary = 0; ` `        ``for` `(``int` `i = 0; i < n; i++) { ` `            ``for` `(``int` `j = 0; j < n; j++) { ` `     `  `                ``// Condition for principal ` `                ``// diagonal ` `                ``if` `(i == j) ` `                    ``principal += mat[i,j]; ` `     `  `                ``// Condition for secondary ` `                ``// diagonal ` `                ``if` `((i + j) == (n - 1)) ` `                    ``secondary += mat[i,j]; ` `            ``} ` `        ``} ` `     `  `        ``Console.WriteLine(``"Principal Diagonal:"` `                                  ``+ principal); ` `                                   `  `        ``Console.WriteLine(``"Secondary Diagonal:"` `                                  ``+ secondary); ` `    ``} ` ` `  `    ``// Driver code ` `    ``static` `public` `void` `Main () ` `    ``{ ` `        ``int` `[,]a = { { 1, 2, 3, 4 }, ` `                     ``{ 5, 6, 7, 8 },  ` `                     ``{ 1, 2, 3, 4 }, ` `                     ``{ 5, 6, 7, 8 } }; ` `                      `  `        ``printDiagonalSums(a, 4); ` `    ``} ` `} ` ` `  `// This code is contributed by vt_m. `

## PHP

 ` `

Output:

```Principal Diagonal:18
Secondary Diagonal:18
```

This code takes O(n^2) time and O(1) auxiliary space

Method 2 (O(n) :

In this method we use one loop i.e. a loop for calculating sum of both the principal and secondary diagonals:

## C++

 `// An efficient C++ program to find sum of diagonals ` `#include ` `using` `namespace` `std; ` ` `  `const` `int` `MAX = 100; ` ` `  `void` `printDiagonalSums(``int` `mat[][MAX], ``int` `n) ` `{ ` `    ``int` `principal = 0, secondary = 0;  ` `    ``for` `(``int` `i = 0; i < n; i++) { ` `        ``principal += mat[i][i]; ` `        ``secondary += mat[i][n - i - 1];         ` `    ``} ` ` `  `    ``cout << ``"Principal Diagonal:"` `<< principal << endl; ` `    ``cout << ``"Secondary Diagonal:"` `<< secondary << endl; ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``int` `a[][MAX] = { { 1, 2, 3, 4 }, { 5, 6, 7, 8 },  ` `                     ``{ 1, 2, 3, 4 }, { 5, 6, 7, 8 } }; ` `    ``printDiagonalSums(a, 4); ` `    ``return` `0; ` `} `

## Java

 `// An efficient java program to find ` `// sum of diagonals ` `import` `java.io.*; ` ` `  `public` `class` `GFG { ` ` `  `    ``static` `void` `printDiagonalSums(``int` `[][]mat, ` `                                        ``int` `n) ` `    ``{ ` `        ``int` `principal = ``0``, secondary = ``0``;  ` `        ``for` `(``int` `i = ``0``; i < n; i++) { ` `            ``principal += mat[i][i]; ` `            ``secondary += mat[i][n - i - ``1``];  ` `        ``} ` `     `  `        ``System.out.println(``"Principal Diagonal:"` `                                   ``+ principal); ` `                                    `  `        ``System.out.println(``"Secondary Diagonal:"` `                                   ``+ secondary); ` `    ``} ` `     `  `    ``// Driver code ` `    ``static` `public` `void` `main (String[] args) ` `    ``{ ` `        ``int` `[][]a = { { ``1``, ``2``, ``3``, ``4` `}, ` `                      ``{ ``5``, ``6``, ``7``, ``8` `},  ` `                      ``{ ``1``, ``2``, ``3``, ``4` `}, ` `                      ``{ ``5``, ``6``, ``7``, ``8` `} }; ` `     `  `        ``printDiagonalSums(a, ``4``); ` `    ``} ` `} ` ` `  `// This code is contributed by vt_m. `

## Python3

 `# A simple Python3 program to find ` `# sum of diagonals ` `MAX` `=` `100` ` `  `def` `printDiagonalSums(mat, n): ` ` `  `    ``principal ``=` `0` `    ``secondary ``=` `0` `    ``for` `i ``in` `range``(``0``, n):  ` `        ``principal ``+``=` `mat[i][i] ` `        ``secondary ``+``=` `mat[i][n ``-` `i ``-` `1``] ` `         `  `    ``print``(``"Principal Diagonal:"``, principal) ` `    ``print``(``"Secondary Diagonal:"``, secondary) ` ` `  `# Driver code ` `a ``=` `[[ ``1``, ``2``, ``3``, ``4` `], ` `     ``[ ``5``, ``6``, ``7``, ``8` `],  ` `     ``[ ``1``, ``2``, ``3``, ``4` `], ` `     ``[ ``5``, ``6``, ``7``, ``8` `]] ` `printDiagonalSums(a, ``4``) ` ` `  `# This code is contributed ` `# by ihritik `

## C#

 `// An efficient C#program to find ` `// sum of diagonals ` `using` `System; ` ` `  `public` `class` `GFG { ` ` `  `    ``static` `void` `printDiagonalSums(``int` `[,]mat, ` `                                       ``int` `n) ` `    ``{ ` `        ``int` `principal = 0, secondary = 0;  ` `        ``for` `(``int` `i = 0; i < n; i++) { ` `            ``principal += mat[i,i]; ` `            ``secondary += mat[i,n - i - 1];  ` `        ``} ` `     `  `        ``Console.WriteLine(``"Principal Diagonal:"` `                                  ``+ principal); ` `                                   `  `        ``Console.WriteLine(``"Secondary Diagonal:"` `                                  ``+ secondary); ` `    ``} ` `     `  `    ``// Driver code ` `    ``static` `public` `void` `Main () ` `    ``{ ` `        ``int` `[,]a = { { 1, 2, 3, 4 }, ` `                     ``{ 5, 6, 7, 8 },  ` `                     ``{ 1, 2, 3, 4 }, ` `                     ``{ 5, 6, 7, 8 } }; ` `                      `  `        ``printDiagonalSums(a, 4); ` `    ``} ` `} ` ` `  `// This code is contributed by vt_m. `

## PHP

 ` `

Output :

```Principal Diagonal:18
Secondary Diagonal:18
```

This code takes O(n) time and O(1) auxiliary space

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Improved By : vt_m, jit_t, ihritik

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