# How to add all the diagonal elements of a matrix in C++

In this tutorial, we will learn how to add all diagonal elements of a matrix in C++ with Algorithm.

In order to add all diagonal elements of a matrix, it is important to make sure that the size/length of the row and column must be same. This is because if they are not the same, then we will not get the appropriate diagonal. which will lead to a false answer. appropriate diagonal means:

consider two matrices of size 3*378 5 642 1 23we can see that the above matrix of size 3*3 has appropriate diagonal as if we start from one corner, we will end up another corner.Therefore, this matrix has appropriate diagonal. --------------------------------------------------------------------------------- consider two matrices of size 3*412 4 7 217 5 7 415 we can see that the above matrix of size 3*4 has inappropriate diagonal as if we start form one corner, we are not ending up with another corner. Therefore, this matrix has inappropriate diagonal.

## Add all the diagonal elements of a matrix

let’s take an example to understand how the addition of all diagonal elements looks like.

Example:

consider a matrix of size 5*5 Input matrix:15 7 4624568 8 754 1 7410526 4 78The addition of all diagonal elements should be: 1 + 4 + 5 + 0 + 8 + 2 + 4 + 6 + 6 = 36

**Note: **The green bold elements in the matrix are the diagonal elements in the above examples.

## Algorithm

- Declare and initialize a matrix of size
**m*n**in the main function. (m = size of row, n = size column) - declare and initialize a variable with zero say “
**sum = 0**“ - check whether ‘
**n**‘ is equal to ‘**m**‘. Then proceed for next steps. - Declare two loops, one form i = 0 to ‘n’ and another inside the first loop which will go from j = 0 to ‘m’.
- Inside the second loop check whether
**i = j**or “**i + j****= n – 1″**. if yes, then for every true**arr[i][j]**, add**arr[i][j]**to**“sum”.** - print the value of
**sum**.

**Note: **we can use either ‘n’ or ‘m’ to check the condition for loop or inside the loop. because the value of ‘n’ and ‘m’ is equal, which is already checked in **step 3**.

## Program to add all diagonal elements of a matrix in C++

#include <cstdlib> #include <iostream> #define size 100 using namespace std; int main(int argc, char** argv) { int arr[size][size], n, m, sum = 0; cout<<"Enter the length of row: "; cin>>n; cout<<"Enter the length of column: "; cin>>m; //checking for equality of m and n if(n != m){ cout<<"Length of rows and columns must be equal."; exit(0); } //Taking input in matrix 'arr' cout<<"\nEnter the elements of matrix: \n"; for(int i = 0;i < n; i++){ for(int j = 0;j < m;j++){ cin>>arr[i][j]; } } //Finding sum of all diagonal elements cout<<"\nSum of All diagonal elements is: "; for(int i = 0; i < n; i++){ for(int j = 0; j < m; j++){ if(i == j || i + j == n - 1){ sum = sum + arr[i][j]; } } } //Printing the sum of all diagonal elements of entered matrix cout<<endl<<sum; return 0; }

**Output: **

Enter the length of row: 5 Enter the length of column: 5 Enter the elements of matrix: 1 5 7 4 6 2 4 5 6 8 8 7 5 4 1 7 4 1 0 5 2 6 4 7 8 Sum of All diagonal elements is: 36

**Time complexity:** O(n^2)

**Note:** In the program, the maximum size of the matrix is restricted to 100 only as the matrix size is initialized with “matrix [size] [size] ” and here the size = 100 from “#define size 100”

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