29. Total Count

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

Problem Description

You are given an array arr[] of positive integers and a threshold value k. For each element in the array, divide it into the minimum number of small integers such that each divided integer is less than or equal to k. Compute the total number of these integers across all elements of the array.

Example 1:

Input:

k = 3, arr[] = [5, 8, 10, 13]

Output:

14

Explanation: Each number can be expressed as a sum of smaller numbers less than or equal to k:

• 5 → (3 + 2),

• 8 → (3 + 3 + 2),

• 10 → (3 + 3 + 3 + 1),

• 13 → (3 + 3 + 3 + 3 + 1).

The total count is 2 + 3 + 4 + 5 = 14.

My Approach

1. Iterate Over Each Element:

   • For each element in arr, divide it into groups of size k or smaller.

   • Add the count of groups for each element to the total count.

2. Mathematical Breakdown:

   • For any number num in arr, the total number of groups required is given by:

     (num + k - 1) // k

     This expression divides num into chunks of size k, accounting for any remainder.

3. Final Answer:

   • Sum up the counts for all elements in the array to get the total count.

Time and Auxiliary Space Complexity

• Expected Time Complexity: O(n), where n is the size of the input array arr[], since we iterate over each element of the array once.

• Expected Auxiliary Space Complexity: O(1), as we use only a constant amount of extra space regardless of the input size.

Code (C++)

class Solution {
public:
    int totalCount(int k, vector<int>& arr) {
        int count = 0;
        for (int num : arr) {
            count += (num + k - 1) / k;
        }
        return count;
    }
};

Code (Java)

class Solution {
    int totalCount(int k, int[] arr) {
        int count = 0;
        for (int num : arr) {
            count += (num + k - 1) / k;
        }
        return count;
    }
}

Code (Python)

class Solution:
    def totalCount(self, k, arr):
        count = 0
        for num in arr:
            count += (num + k - 1) // k
        return count

Contribution and Support

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