Find the product of sum of two diagonals of a square Matrix - GeeksforGeeks

20 Apr, 2021
Given a square matrix mat consisting of integers of size NxN, the task is to calculate the product between the sums of its diagonal.Examples:  
Input: mat[][] = {{5, 8, 1}, 
                   {5, 10, 3}, 
                   {-6, 17, -9}}
Output: 30
Sum of primary diagonal = 5 + 10 + (-9) = 6.
Sum of secondary diagonal = 1 + 10 + (-6) = 5.
Product = 6 * 5 = 30.

Input: mat[][] = {{22, -8, 11}, 
                   {55, 87, -1}, 
                   {-61, 69, 19}}
Output: 4736
 
Naive approach: Traverse the entire matrix and find the diagonal elements. Calculate the sums across the two diagonals of a square matrix. Then, just take the product of the two sums obtained. Time complexity: O(N2)Naive approach: Traverse just the diagonal elements instead of the entire matrix by observing the pattern in the indices of the diagonal elements. Below is the implementation of this approach:  
CPP
Java
Python3
C#
Javascript
// C++ program to find the product// of the sum of diagonals. #include <bits/stdc++.h>using namespace std; // Function to find the product// of the sum of diagonals.long long product(vector<vector<int>> &mat, int n){    // Initialize sums of diagonals    long long d1 = 0, d2 = 0;     for (int i = 0; i < n; i++)    {        d1 += mat[i][i];        d2 += mat[i][n - i - 1];    }         // Return the answer    return 1LL * d1 * d2;} // Driven codeint main(){    vector<vector<int>> mat = {{ 5, 8, 1},                               { 5, 10, 3},                               { -6, 17, -9}};                                    int n = mat.size();         // Function call    cout << product(mat, n);         return 0;}
// Java program to find the product// of the sum of diagonals.  class GFG{  // Function to find the product// of the sum of diagonals.static long product(int [][]mat, int n){    // Initialize sums of diagonals    long d1 = 0, d2 = 0;      for (int i = 0; i < n; i++)    {        d1 += mat[i][i];        d2 += mat[i][n - i - 1];    }          // Return the answer    return 1L * d1 * d2;}  // Driven codepublic static void main(String[] args){    int [][]mat = {{ 5, 8, 1},                               { 5, 10, 3},                               { -6, 17, -9}};                                     int n = mat.length;          // Function call    System.out.print(product(mat, n));      }} // This code is contributed by 29AjayKumar
# Python3 program to find the product# of the sum of diagonals. # Function to find the product# of the sum of diagonals.def product(mat,n):     # Initialize sums of diagonals    d1 = 0    d2 = 0     for i in range(n):         d1 += mat[i][i]        d2 += mat[i][n - i - 1]     # Return the answer    return d1 * d2  # Driven codeif __name__ == '__main__':    mat = [[5, 8, 1],        [5, 10, 3],        [-6, 17, -9]]     n = len(mat)     # Function call    print(product(mat, n))     # This code is contributed by mohit kumar 29   
// C# program to find the product// of the sum of diagonals.using System; class GFG{ // Function to find the product// of the sum of diagonals.static long product(int [,]mat, int n){    // Initialize sums of diagonals    long d1 = 0, d2 = 0;     for (int i = 0; i < n; i++)    {        d1 += mat[i, i];        d2 += mat[i, n - i - 1];    }         // Return the answer    return 1L * d1 * d2;} // Driven codepublic static void Main(String[] args){    int [,]mat = {{ 5, 8, 1},                    { 5, 10, 3},                    { -6, 17, -9}};                                     int n = mat.GetLength(0);         // Function call    Console.Write(product(mat, n));}} // This code is contributed by Princi Singh
<script>// Javascript program to find the product// of the sum of diagonals. // Function to find the product// of the sum of diagonals.function product(mat, n){    // Initialize sums of diagonals    let d1 = 0, d2 = 0;     for (let i = 0; i < n; i++)    {        d1 += mat[i][i];        d2 += mat[i][n - i - 1];    }         // Return the answer    return d1 * d2;} // Driven code    let mat = [[ 5, 8, 1],                               [ 5, 10, 3],                               [ -6, 17, -9]];                                    let n = mat.length;         // Function call    document.write(product(mat, n)); // This code is contributed by rishavmahato348.</script>
30
 
Time complexity: O(N) 
mohit kumar 29
29AjayKumar
princi singh
rishavmahato348
Mathematical
Matrix
School Programming
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