OpenAI Backend Engineer Coding Questions

In order to improve rate limiting for OpenAI's API, we want to implement a system that optimally combines multiple requests into the fewest batch requests. Given an array of integers representing the request sizes and a maximum batch size, find the minimum number of batches needed to accommodate all requests.
Example 1:
Input: sizes = [2, 3, 4, 5], max_size = 6
Output: 3
Explanation: The optimal batches would be [2, 3], [4], [5]. Hence 3 batches are needed.
Example 2:
Input: sizes = [1, 2, 3, 4, 5], max_size = 5
Output: 3
Explanation: The total could be combined as [1, 2], [3, 4], [5] resulting in 3 batches.
Constraints:
- 1 <= sizes.length <= 1000
- 1 <= sizes[i] <= 1000
- 1 <= max_size <= 1000.

OpenAI aims to enhance user experience by suggesting models based on past usage. Your goal is to develop a function that selects model recommendations based on user interaction history represented as a directed graph.
Given a Graph object representing user interactions with models, implement a function that returns a list of recommended model IDs the user may like, based on depth-first search (DFS).
Example 1:
Input: Graph: {1: [2, 3], 2: [4], 3: [4], 4: []}, user_id: 1
Output: [4, 3, 2]
Explanation: The user has interacted with model 1, thus traversing through interactions leads to recommendations 4, 3, and 2.
Example 2:
Input: Graph: {5: [6], 6: [7], 7: [], 8: [7]}, user_id: 5
Output: [7, 6]
Explanation: The interactions lead to the models 7 and 6 based on the user’s initial interaction with model 5.
Constraints:
- The number of models n will be in the range 1 <= n <= 10^4.
- The number of interactions will be in the range 0 <= interactions <= 10^4.