Sum of the first M elements of Array formed by infinitely concatenating given array

Given an array arr[] consisting of N integers and a positive integer M, the task is to find the sum of the first M elements of the array formed by the infinite concatenation of the given array arr[].

Examples:

Input: arr[] = {1, 2, 3}, M = 5
Output: 9
Explanation:
The array formed by the infinite concatenation of the given array arr[] is of the form {1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, ... }.
The sum of the first M(= 5) elements of the array is 1 + 2 + 3 + 1 + 2 = 9.

Input: arr[] = {1}, M = 7
Output: 7

Approach: The given problem can be solved by using the Modulo Operator (%) and consider the given array as the circular array and find the sum of the first M elements accordingly. Follow the steps below to solve this problem:

• Initialize a variable, say sum as 0 to store the resultant sum of the first M elements of the new array.
• Iterate over the range [0, M - 1] using the variable i and increment the value of sum by arr[i%N].
• After completing the above steps, print the value of the sum as the result.

Below is the implementation of the above approach:

9

Time Complexity: O(M)
Auxiliary Space: O(1)