Round 1
Questions: You are given an array products of size n, where products[i] represents the number of items of product type i. These products need to be packed into batches for shipping.
The batch packing must adhere to the following conditions:
- No two items in the same batch can be of the same product type.
- The number of items packed in the current batch must be strictly greater than the number packed in the previous batch.
- Each item can be packed only once, and it is not required to pack every item.
Task: Write a function maximizeGroups that returns the maximum number of valid batches that can be prepared.
Function Signature:
public static int maximizeGroups(List<Integer> products);
Input Example:
List<Integer> products = Arrays.asList(2, 8, 1, 7, 6, 3); System.out.println(maximizeGroups(products));
Output Example:
4
Explanation:
- First batch: [2] (remaining: [2, 8, 1, 7, 6, 3])
- Second batch: [2, 3] (remaining: [2, 8, 1, 7, 6])
- Third batch: [1, 2, 3] (remaining: [2, 8, 7, 6])
- Fourth batch: [0, 1, 2, 3] (remaining: [0, 5])
Thus, the maximum number of batches is 4.
Candidate's Approach
To solve the Batch Packing Problem, the candidate can use a greedy approach. The idea is to keep track of the number of items packed in the previous batch and ensure that each subsequent batch has more items than the last. The candidate can sort the products in descending order and attempt to create batches starting from the largest available product counts, ensuring that the conditions are met.
- Sort the products in descending order.
- Initialize a variable to keep track of the last batch size.
- Iterate through the sorted products, attempting to form batches while adhering to the constraints.
- Count the number of valid batches formed.
Challenges may include ensuring that the batches are formed optimally without violating the constraints.
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