07. Sum of Upper and Lower Triangles

The problem can be found at the following link: Question Link

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++)

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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