> For the complete documentation index, see [llms.txt](https://gl01.gitbook.io/gfg-editorials/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://gl01.gitbook.io/gfg-editorials/2023/11-2023-nov-6/07-sum-of-upper-and-lower-triangles.md).

# 07. Sum of Upper and Lower Triangles

The problem can be found at the following link: [Question Link](https://www.geeksforgeeks.org/problems/sum-of-upper-and-lower-triangles-1587115621/1)

![](https://badgen.net/badge/Level/Easy/green)

## My Approach

To calculate the sum of the upper and lower triangles of a given square matrix,

* I use two nested loops to iterate through each element of the matrix.
  * I maintain two variables `out[0]` and `out[1]` to store the sums of the upper and lower triangles, respectively.
  * If the current element is in or above the main diagonal (i.e., `i <= j`), I add it to `out[0]`.
  * If the current element is in or below the main diagonal (i.e., `i >= j`), I add it to `out[1]`.

## Time and Auxiliary Space Complexity

* **Time Complexity**: `O(n^2)`, where `n` is the size of the square matrix.
* **Auxiliary Space Complexity**: `O(1)` as we only use a constant amount of space for the `out` vector.

## Code (C++)

```cpp
class Solution {
public:
    vector<int> sumTriangles(const vector<vector<int> >& matrix, int n) {
        vector<int> out(2, 0);
        
        for (int i = 0; i < n; ++i) {
            for (int j = 0; j < n; ++j) {
                if (i <= j)
                    out[0] += matrix[i][j];
                if (i >= j)
                    out[1] += matrix[i][j];
            }
        }
        return out;
    }
};
```

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