Understand what the interviewer is asking for by using test cases and questions about the problem.

• Q
  • What is the desired outcome?
    • To count the number of non-empty subarrays where the sum of the elements is divisible by k.
  • What input is provided?
    • A list of integers collection_sizes and an integer k.

Plan the solution with appropriate visualizations and pseudocode.

General Idea: Use a prefix sum and a hashmap to count how many times each remainder modulo k has appeared, then use this to determine how many subarrays are divisible by k.

1) Initialize `prefix_sum` to 0 and `count` to 0. 2) Use a dictionary `prefix_count` to store the frequency of each prefix sum modulo `k`. 3) Iterate through `collection_sizes`: - Update `prefix_sum` with the current element. - Calculate the modulo `k` of the `prefix_sum`. - If the modulo has been seen before, add the frequency to `count`. - Update `prefix_count` with the current modulo. 4) Return `count`.

• Not correctly handling negative prefix sums.

def count_divisible_collections(collection_sizes, k): prefix_sum = 0 count = 0 prefix_count = {0: 1} # Initialize with 0: 1 to handle cases where the prefix sum itself is divisible by k for size in collection_sizes: prefix_sum += size mod = prefix_sum % k if mod in prefix_count: count += prefix_count[mod] prefix_count[mod] += 1 else: prefix_count[mod] = 1 return count