POTD Solutions | 07 Nov’ 23 | Sum of upper and lower triangles

View all POTD Solutions

Welcome to the daily solutions of our PROBLEM OF THE DAY (POTD). We will discuss the entire problem step-by-step and work towards developing an optimized solution. This will not only help you brush up on your concepts of Matrix but will also help you build up problem-solving skills.

POTD Solutions 07 November 2023

POTD 07 November: Sum of upper and lower triangles

Given a square matrix of size N*N, print the sum of upper and lower triangular elements. Upper Triangle consists of elements on the diagonal and above it. The lower triangle consists of elements on the diagonal and below it. 

Examples:

Input: {{6, 5, 4}, {1, 2, 5}, {7, 9, 7}}
Output: 29 32
Explanation: Sum of upper triangle = 6 + 5 + 4 + 2 + 5 + 7 = 29 and Sum of lower triangle = 6 + 1 + 2 + 7 + 9 + 7 = 32

Input: {{1, 1, 1}, {2, 2, 2}, {3, 3, 3}}
Output: 10 14
Explanation: Sum of upper triangle = 1 + 1 + 1 + 2 + 2 + 3 = 10 and Sum of lower triangle = 1 + 2 + 2 + 3 + 3 + 3 = 14

Find Sum of upper and lower triangles using Nested Loops:

Traverse the matrix and calculate the sum for upper and lower triangles accordingly. For upper triangle, sum all the cells which have row <= column and for lower triangle, sum all the cells which have row >= column.

Below is the implementation of the above approach:

C++

class Solution {
public:
    // Function to return sum of upper and lower triangles
    // of a matrix.
    vector<int>
    sumTriangles(const vector<vector<int> >& matrix, int n)
    {
        int i, j;
        int upper_sum = 0;
        int lower_sum = 0;

        // To calculate sum of upper triangle
        for (i = 0; i < n; i++) {
            for (j = 0; j < n; j++) {
                if (i <= j) {
                    upper_sum += matrix[i][j];
                }
            }
        }

        // To calculate sum of lower
        for (i = 0; i < n; i++) {
            for (j = 0; j < n; j++) {
                if (j <= i) {
                    lower_sum += matrix[i][j];
                }
            }
        }

        return vector<int>{ upper_sum, lower_sum };
    }
};

C

// Function to return sum of upper and lower triangles of a
// matrix.
int* sumTriangles(int n, int matrix[][n])
{
    int* ans = (int*)malloc(2 * sizeof(int));
    int i, j;
    int upper_sum = 0;
    int lower_sum = 0;

    // To calculate sum of upper triangle
    for (i = 0; i < n; i++) {
        for (j = 0; j < n; j++) {
            if (i <= j) {
                upper_sum += matrix[i][j];
            }
        }
    }

    // To calculate sum of lower
    for (i = 0; i < n; i++) {
        for (j = 0; j < n; j++) {
            if (j <= i) {
                lower_sum += matrix[i][j];
            }
        }
    }
    ans[0] = upper_sum;
    ans[1] = lower_sum;
    return ans;
}

Java

class Solution {
    // Function to return sum of upper and lower triangles
    // of a matrix.
    static ArrayList<Integer> sumTriangles(int matrix[][],
                                           int n)
    {
        // code here
        ArrayList<Integer> ans = new ArrayList<Integer>();
        int i, j;
        int upper_sum = 0;
        int lower_sum = 0;

        /*Calculate sum of upper triangle*/
        for (i = 0; i < n; i++) {
            for (j = 0; j < n; j++) {
                if (i <= j) {
                    upper_sum += matrix[i][j];
                }
            }
        }

        /*Calculate sum of lower*/
        for (i = 0; i < n; i++) {
            for (j = 0; j < n; j++) {
                if (j <= i) {
                    lower_sum += matrix[i][j];
                }
            }
        }

        ans.add(upper_sum);
        ans.add(lower_sum);
        return ans;
    }
}

Python3

# User function Template for python3


class Solution:

    # Function to return sum of upper and lower triangles of a matrix.
    def sumTriangles(self, matrix, n):
        # code here
        i, j = 0, 0
        upper_sum = 0
        lower_sum = 0
        ans = [0, 0]

        # To calculate sum of upper triangle
        for i in range(n):
            for j in range(n):
                if (i <= j):
                    upper_sum += matrix[i][j]

        # To calculate sum of lower
        for i in range(n):
            for j in range(n):
                if (j <= i):
                    lower_sum += matrix[i][j]

        ans[0] = upper_sum
        ans[1] = lower_sum
        return ans

Javascript

class Solution
{
    //Function to return sum of upper and lower triangles of a matrix.
    sumTriangles(mat, N)
    {
        // code here
        let i, j;
        let upper_sum = 0;
        let lower_sum = 0;
        let ans = [0, 0];

        /*to calculate sum of upper triangle*/
        for (i = 0; i < N; i++) {
            for (j = 0; j < N; j++) {
                if (i <= j) {
                    upper_sum += mat[i][j];
                }
            }
        }

        /*to calculate sum of lower*/
        for (i = 0; i < N; i++) {
            for (j = 0; j < N; j++) {
                if (j <= i) {
                    lower_sum += mat[i][j];
                }
            }
        }

        ans[0] = upper_sum;
        ans[1] = lower_sum;
        return ans;
    }
}

Time Complexity: O(N*N), where N is the number of rows or columns in the matrix
Auxiliary Space: O(1)