Find the sum of elements of the Matrix generated by the given rules

28 May, 2022
Given three integers A, B, and R, the task is to find the sum of all the elements of the matrix generated by the given rules: 
The first row will contain a single element which is A and the rest of the elements will be 0.The next row will contain two elements all of which are (A + B) and the rest are 0s.Third row will contain (A + B + B) three times and the rest are 0s and so on.The matrix will contain only R rows.
The first row will contain a single element which is A and the rest of the elements will be 0.
The next row will contain two elements all of which are (A + B) and the rest are 0s.
Third row will contain (A + B + B) three times and the rest are 0s and so on.
The matrix will contain only R rows.
For example, if A = 5, B = 3 and R = 3 then the matrix will be: 5 0 0 8 8 0 11 11 11Examples:  
Input: A = 5, B = 3, R = 3 Output: 54 5 + 8 + 8 + 11 + 11 + 11 = 54Input: A = 7, B = 56, R = 1 Output: 7 
Approach: Initialize sum = 0 and for every 1 ≤ i ≤ R update sum = sum + (i * A). After every iteration update A = A + B. Print the final sum in the end.Below is the implementation of the above approach:  
C++
Java
Python3
C#
Javascript
// C++ implementation of the approach#include <iostream>using namespace std; // Function to return the required sumint sum(int A, int B, int R){     // To store the sum    int sum = 0;     // For every row    for (int i = 1; i <= R; i++) {         // Update the sum as A appears i number        // of times in the current row        sum = sum + (i * A);         // Update A for the next row        A = A + B;    }     // Return the sum    return sum;} // Driver codeint main(){     int A = 5, B = 3, R = 3;    cout << sum(A, B, R);     return 0;}
// JAVA implementation of the approachimport java.util.*;import java.lang.*;import java.io.*; class GFG{ // Function to return the required sumstatic int sum(int A, int B, int R){     // To store the sum    int sum = 0;     // For every row    for (int i = 1; i <= R; i++)    {         // Update the sum as A appears i number        // of times in the current row        sum = sum + (i * A);         // Update A for the next row        A = A + B;    }     // Return the sum    return sum;} // Driver codepublic static void main (String[] args)              throws java.lang.Exception{    int A = 5, B = 3, R = 3;         System.out.print(sum(A, B, R));}} // This code is contributed by nidhiva
# Python3 implementation of the approach # Function to return the required sumdef Sum(A, B, R):     # To store the sum    ssum = 0     # For every row    for i in range(1, R + 1):         # Update the sum as A appears i number        # of times in the current row        sum = sum + (i * A)         # Update A for the next row        A = A + B     # Return the sum    return sum # Driver codeA, B, R = 5, 3, 3print(Sum(A, B, R)) # This code is contributed by Mohit Kumar
// C# implementation of the approachusing System; class GFG{ // Function to return the required sumstatic int sum(int A, int B, int R){     // To store the sum    int sum = 0;     // For every row    for (int i = 1; i <= R; i++)    {         // Update the sum as A appears i number        // of times in the current row        sum = sum + (i * A);         // Update A for the next row        A = A + B;    }     // Return the sum    return sum;} // Driver codepublic static void Main (){    int A = 5, B = 3, R = 3;         Console.Write(sum(A, B, R));}} // This code is contributed by anuj_67..
<script>// JAVA SCRIPT  implementation of the approach// Function to return the required sumfunction sum( A,  B,  R){     // To store the sum    let sum = 0;     // For every row    for (let i = 1; i <= R; i++)    {         // Update the sum as A appears i number        // of times in the current row        sum = sum + (i * A);         // Update A for the next row        A = A + B;    }     // Return the sum    return sum;} // Driver code     let A = 5, B = 3, R = 3;         document.write(sum(A, B, R)); //contributed by bobby </script>
54
 
Time Complexity: O(R), since there runs a loop for once from 1 to R.
Auxiliary Space: O(1), since no extra space has been taken.
mohit kumar 29
nidhiva
vt_m
aditya7409
gottumukkalabobby
simmytarika5
subhammahato348
Mathematical
Matrix
Mathematical
Matrix
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