Open In App

C++ Program to Efficiently Compute Sums of Diagonals of a Matrix

Last Updated : 17 Jan, 2023
Improve
Improve
Like Article
Like
Save
Share
Report

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. 
 

  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 (Brute Force) :

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 <bits/stdc++.h>
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;
}


Output:  

Principal Diagonal:18
Secondary Diagonal:18

Time Complexity: O(N*N), as we are using nested loops to traverse N*N times.

Auxiliary Space: O(1), as we are not using any extra space.
 

Method 2 (Efficient Approach) :

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 <bits/stdc++.h>
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;
}


Output :

Principal Diagonal:18
Secondary Diagonal:18

Time Complexity: O(N), as we are using a loop to traverse N times.

Auxiliary Space: O(1), as we are not using any extra space.
Please refer complete article on Efficiently compute sums of diagonals of a matrix for more details!



Similar Reads

Java Program to Efficiently compute sums of diagonals of a matrix
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. Condition for Principal Diagonal: The row-column condition is row = column
3 min read
Python Program to Efficiently compute sums of diagonals of a matrix
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. Condition for Principal Diagonal: The row-column condition is row = column
3 min read
Php Program to Efficiently compute sums of diagonals of a matrix
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. Condition for Principal Diagonal: The row-column condition is row = column
3 min read
Javascript Program to Efficiently compute sums of diagonals of a matrix
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. Condition for Principal Diagonal: The row-column condition is row = column
3 min read
Efficiently compute sums of diagonals of a matrix
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. Condition for Principal Diagonal: The row-column condition is row = column
10 min read
Center element of matrix equals sums of half diagonals
Given a matrix of odd order i.e(5*5). Task is to check if the center element of the matrix is equal to the individual sum of all the half diagonals. Examples: Input : mat[][] = { 2 9 1 4 -2 6 7 2 11 4 4 2 9 2 4 1 9 2 4 4 0 2 4 2 5 } Output : Yes Explanation : Sum of Half Diagonal 1 = 2 + 7 = 9 Sum of Half Diagonal 2 = 9 + 0 = 9 Sum of Half Diagonal
7 min read
C++ Program to Find difference between sums of two diagonals
Given a matrix of n X n. The task is to calculate the absolute difference between the sums of its diagonal.Examples: Input : mat[][] = 11 2 4 4 5 6 10 8 -12 Output : 15 Sum of primary diagonal = 11 + 5 + (-12) = 4. Sum of primary diagonal = 4 + 5 + 10 = 19. Difference = |19 - 4| = 15. Input : mat[][] = 10 2 4 5 Output : 7 Recommended: Please solve
3 min read
Java Program to Find difference between sums of two diagonals
Given a matrix of n X n. The task is to calculate the absolute difference between the sums of its diagonal.Examples: Input : mat[][] = 11 2 4 4 5 6 10 8 -12 Output : 15 Sum of primary diagonal = 11 + 5 + (-12) = 4. Sum of primary diagonal = 4 + 5 + 10 = 19. Difference = |19 - 4| = 15. Input : mat[][] = 10 2 4 5 Output : 7 Recommended: Please solve
3 min read
Php Program to Find difference between sums of two diagonals
Given a matrix of n X n. The task is to calculate the absolute difference between the sums of its diagonal.Examples: Input : mat[][] = 11 2 4 4 5 6 10 8 -12 Output : 15 Sum of primary diagonal = 11 + 5 + (-12) = 4. Sum of primary diagonal = 4 + 5 + 10 = 19. Difference = |19 - 4| = 15. Input : mat[][] = 10 2 4 5 Output : 7 Recommended: Please solve
3 min read
Javascript Program to Find difference between sums of two diagonals
Given a matrix of n X n. The task is to calculate the absolute difference between the sums of its diagonal.Examples: Input : mat[][] = 11 2 4 4 5 6 10 8 -12 Output : 15 Sum of primary diagonal = 11 + 5 + (-12) = 4. Sum of primary diagonal = 4 + 5 + 10 = 19. Difference = |19 - 4| = 15. Input : mat[][] = 10 2 4 5 Output : 7 Recommended: Please solve
3 min read
Article Tags :
Practice Tags :