# Efficiently compute sums of diagonals of a matrix

• Difficulty Level : Basic
• Last Updated : 19 May, 2021

Given a 2D square matrix, find the 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.

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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```

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

 ``

## Javascript

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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

 ``

## Javascript

 ``

Output :

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

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