# Sum of alternate elements of a N x N matrix

Given an NxN matrix. The task is to find the sum of the alternate elements of the given matrix.

For example, in a 2 x 2 matrix the alternate elements are { A[0][0], A[1, 1] } and { A[1][0], A[0][1] }.

Examples:

```Input: mat[][] = { { 1, 2},
{ 3, 4} }
Output : Sum of alternate elements : 5, 5
Explanation: The alternate elements are {1, 4}
and {2, 3} so their sum are 5, 5.

Input : mat[][] = { { 1, 2, 3 },
{ 4, 5, 6 },
{ 7, 8, 9 } }
Output : Sum of alternate elements :25, 20
```

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

The idea is to traverse the matrix and also keep a counter. We will add the elements whose counter value is even in one variable and with odd counter value in other and finally print the two sums on complete traversal of the matrix.

Below is the implementation of the above approach:

## C++

 `// C++ program to print sum of alternate ` `// elements of a N x N matrix ` `#include ` `using` `namespace` `std; ` ` `  `// Function to find the sum of alternate ` `// elements of a matrix ` `void` `sumAlternate(``int``* arr, ``int` `n) ` `{ ` `    ``int` `sum1 = 0, sum2 = 0; ` ` `  `    ``// check the alternate elements ` `    ``for` `(``int` `i = 0; i < n * n; i++) { ` ` `  `        ``// count the elements at even places ` `        ``if` `(i % 2 == 0) ` `            ``sum1 += *(arr + i); ` ` `  `        ``else` `// count the elements at odd places ` `            ``sum2 += *(arr + i); ` `    ``} ` ` `  `    ``cout << ``"Sum of alternate elements : "` `<< sum1 ` `         ``<< ``", "` `<< sum2 << endl; ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``int` `mat[3][3] = { { 1, 2, 3 }, ` `                      ``{ 4, 5, 6 }, ` `                      ``{ 7, 8, 9 } }; ` `    ``int` `n = 3; ` ` `  `    ``// find the sum of alternate elements ` `    ``sumAlternate(&mat[0][0], n); ` ` `  `    ``return` `0; ` `} `

## Java

 `// Java program to print sum of alternate ` `// elements of a N x N matrix ` ` `  `class` `GFG ` `{ ` `        ``// Function to find the sum of alternate ` `        ``// elements of a matrix ` `        ``static` `void` `sumAlternate(``int` `[][] mat, ``int` `n) ` `        ``{ ` `            ``int` `sum1 = ``0``, sum2 = ``0``; ` `            ``int` `cnt=``0``; ` `            ``// check the alternate elements ` `            ``for` `(``int` `i = ``0``; i < n; i++) { ` `         `  `                ``for``(``int` `j=``0``;j

## Python 3

 `# Python 3 program to print sum of  ` `# alternate elements of a N x N matrix ` ` `  `# Function to find the sum of  ` `# alternate elements of a matrix ` `def` `sumAlternate(arr, n): ` ` `  `    ``sum1 ``=` `0` `    ``sum2 ``=` `0` ` `  `    ``# check the alternate elements ` `    ``i ``=` `0` `    ``while` `i < n ``*` `n : ` ` `  `        ``# count the elements at  ` `        ``# even places ` `        ``if` `(i ``%` `2` `=``=` `0``): ` `            ``sum1 ``+``=` `(arr ``+` `i) ` ` `  `        ``else``: ``# count the elements  ` `              ``# at odd places ` `            ``sum2 ``+``=` `(arr ``+` `i) ` `             `  `        ``i ``+``=` `1` ` `  `    ``print``(``"Sum of alternate elements : "` `+`  `             ``str``(sum1) ``+` `", "` `+` `str``(sum2)) ` ` `  `# Driver code ` `if` `__name__ ``=``=` `"__main__"``: ` `    ``mat ``=` `[[ ``1``, ``2``, ``3` `], ` `        ``[``4``, ``5``, ``6` `], ` `        ``[``7``, ``8``, ``9` `]] ` `    ``n ``=` `3` ` `  `    ``# find the sum of alternate elements ` `    ``sumAlternate(mat[``0``][``0``], n) ` ` `  `# This code is contributed ` `# by ChitraNayal `

## C#

 `// C# program to print sum of alternate ` `// elements of a N x N matrix ` `using` `System; ` `class` `GFG ` `{ ` `// Function to find the sum of  ` `// alternate elements of a matrix ` `static` `void` `sumAlternate(``int``[,] mat,  ` `                         ``int` `n) ` `{ ` `    ``int` `sum1 = 0, sum2 = 0; ` `    ``int` `cnt = 0; ` `     `  `    ``// check the alternate elements ` `    ``for` `(``int` `i = 0; i < n; i++) ` `    ``{ ` ` `  `        ``for``(``int` `j = 0; j < n; j++) ` `        ``{ ` `            ``if` `(cnt % 2 == 0) ` `                ``sum1 += mat[i, j]; ` `     `  `            ``else` `// count the elements ` `                 ``// at odd places ` `                ``sum2 += mat[i, j]; ` `         `  `        ``cnt++; ` `        ``}  ` `    ``} ` ` `  `    ``Console.WriteLine(``"Sum of alternate elements : "` `+  ` `                                  ``sum1 + ``", "` `+ sum2); ` `} ` ` `  `// Driver code ` `public` `static` `void` `Main() ` `{ ` `    ``int``[,] mat = { { 1, 2, 3 }, ` `                    ``{ 4, 5, 6 }, ` `                    ``{ 7, 8, 9 } }; ` `    ``int` `n = 3; ` ` `  `    ``// find the sum of alternate elements ` `    ``sumAlternate(mat, n); ` `} ` `} ` ` `  `// This code is contributed ` `// by Akanksha Rai(Abby_akku) `

Output:

```Sum of alternate elements : 25, 20
```

Time Complexity: O(N2)

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Second year Department of Information Technology Jadavpur University

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