# Find the product of sum of two diagonals of a square Matrix

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
```

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

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:

 `// C++ program to find the product ` `// of the sum of diagonals. ` ` `  `#include ` `using` `namespace` `std; ` ` `  `// Function to find the product  ` `// of the sum of diagonals. ` `long` `long` `product(vector> &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 code ` `int` `main() ` `{ ` `    ``vector> 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 code ` `public` `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 code ` `if` `__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 code ` `public` `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 `

Output:
```30
```

Time complexity: O(N)

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