OpenAI Interview Questions

Background: OpenAI continuously strives to improve the performance of its machine learning models based on provided data inputs. Efficient optimization algorithms are crucial for predicting outcomes accurately and ensuring models are trained effectively.
Problem statement: Given a list of integers representing the performance scores of an AI system on different datasets, you need to determine the maximum sum of non-adjacent scores possible. This means you cannot select scores that are consecutive.
Function/class signature:

• def max_non_adjacent_score(scores: List[int]) -> int:

Example 1:

• Input: [3, 2, 5, 10, 7]


• Output: 15


• Explanation: Choose scores 3, 10, and 2 to get 3 + 10 + 2 = 15, skipping the adjacent 2 and 5.

Example 2:

• Input: [1, 2, 3, 1]


• Output: 4


• Explanation: Choose scores 1 and 3 to get 1 + 3 = 4, avoiding the adjacent scores.

Constraints:

• 0 <= scores.length <= 1000


• 0 <= scores[i] <= 1000

Background: OpenAI often deals with large data flows and needs efficient algorithms to compute aggregates over its underlying data. Applications in AI systems and optimization problems can utilize these algorithms effectively.
Problem statement: Given a m x n grid filled with non-negative integers, find a path from the top-left corner to the bottom-right corner, which minimizes the sum of the values along the path. You can only move down or right at any point in time.
Function/class signature:

• def min_path_sum(grid: List[List[int]]) -> int:

Example 1:

• Input: [[1,3,1],[1,5,1],[4,2,1]]


• Output: 7


• Explanation: The path 1 → 3 → 1 → 2 → 1 minimizes the sum to 7.

Example 2:

• Input: [[1,2,3],[4,5,6]]


• Output: 12


• Explanation: The path 1 → 2 → 3 → 6 minimizes the sum to 12.

Constraints:

• 1 <= m, n <= 100


• 0 <= grid[i][j] <= 100

Background: OpenAI often deals with optimization problems that can benefit from strategies like the subset-sum problem. It's essential for resource allocation in AI training workflows where budget constraints are significant.
Problem statement: Given a set of n integers and a target integer target, determine if there's a subset of the given integers that adds up to exactly the target value. You should implement a function that efficiently solves this problem using dynamic programming.
Function/class signature:

• def subset_sum(nums: List[int], target: int) -> bool:

Example 1:

• Input: nums = [3, 34, 4, 12, 5, 2], target = 9


• Output: True


• Explanation: The subset {4, 5} adds up to 9.

Example 2:

• Input: nums = [1, 2, 3, 7], target = 6


• Output: True


• Explanation: The subset {1, 2, 3} adds up to 6.

Constraints:

• 0 < n <= 20


• -1000 <= nums[i] <= 1000


• 0 <= target <= 1000

Background: In designing efficient AI systems, OpenAI needs to optimize routes for data points that originate from multiple sources. This is crucial for minimizing response times in API services that rely on complex data paths.
Problem statement: You are given an undirected graph represented as a list of edges, and multiple source nodes. Your task is to find the shortest distance from any of the source nodes to all other nodes in the graph. The distance between two connected nodes is uniformly 1.
Function/class signature:

• def multi_source_shortest_path(edges: List[Tuple[int, int]], sources: List[int]) -> Dict[int, int]:

Example 1:
Input: edges = [(0, 1), (1, 2), (0, 2), (2, 3)], sources = [0]
Output: {0: 0, 1: 1, 2: 1, 3: 2}
Explanation: The shortest paths from node 0 are as follows: to itself is 0, to 1 is 1, to 2 is 1, and to 3 is 2.Example 2:
Input: edges = [(0, 1), (1, 2), (2, 3), (3, 4), (4, 1)], sources = [1, 3]
Output: {0: 2, 1: 0, 2: 1, 3: 0, 4: 1}
Explanation: The shortest distances are calculated from both sources 1 and 3.Constraints:

• The number of edges (|E|) is between 1 and 10^5.


• The number of nodes (|V|) is between 1 and 10^5.


• Each edge connects two different nodes.


• Nodes are labeled with integers from 0 to V-1.

Background: OpenAI often relies on human labelers to accurately annotate data for machine learning models. It is critical to ensure that labeling tasks are efficiently distributed among available labelers to maintain productivity and prevent overload.Problem statement: Given a set of labelers, a list of tasks with required time to complete, and models that need this data, create a function that returns a balanced assignment of tasks to each labeler. Every label should have an equitable workload within a specified limit.Function/class signature:

• def assign_tasks(labelers: List[str], tasks: List[int], max_load: int) -> Dict[str, List[int]]:

Example 1:

• Input: labelers = ['Alice', 'Bob', 'Charlie'], tasks = [3, 1, 4, 2, 5], max_load = 5


• Output: {'Alice': [3, 2], 'Bob': [1, 4], 'Charlie': [5]}


• Explanation: Each labeler has a total load that does not exceed the max_load of 5.

Example 2:

• Input: labelers = ['Dave', 'Eve'], tasks = [1, 2, 3], max_load = 3


• Output: {'Dave': [1, 2], 'Eve': [3]}

Constraints:

• 1 <= len(labelers) <= 10


• 1 <= len(tasks) <= 100


• 0 <= tasks[i] <= 10


• max_load > 0

Background: In many machine learning applications at OpenAI, including reinforcement learning and optimization problems, finding efficient pathways is crucial. This problem relates to ensuring optimal resource allocation in grid environments, possibly related to robotics or game simulations.
Problem statement: Given a 2D grid costs where each integer represents the cost to step on that cell, write a function to find the minimum cost to reach the bottom right corner of the grid from the top left corner. You can only move down or right at any point in time.
Function/class signature:

• def min_cost_path(costs: List[List[int]]) -> int:

Example 1:

• Input: [[1, 3, 1], [1, 5, 1], [4, 2, 1]]


• Output: 7


• Explanation: The path is 1 -> 3 -> 1 -> 1 -> 1, total cost = 7.

Example 2:

• Input: [[10, 2], [1, 1]]


• Output: 3


• Explanation: The path is 10 -> 1 -> 1, total cost = 3.

Constraints:

• 1 ≤ costs.length, costs[i].length ≤ 100


• 0 ≤ costs[i][j] ≤ 100

Background: OpenAI frequently works with time series data and machine learning models that involve sequential predictions. Identifying patterns, such as trends in data, is crucial for optimizing model performance.
Problem statement: Given an integer array nums, return the length of the longest increasing subsequence. A subsequence is formed by removing elements from the array without changing the order of the remaining elements. This problem is essential for analyzing sequences in large datasets relevant to OpenAI's products.
Function/class signature:

• def length_of_LIS(nums: List[int]) -> int:

Example 1:
Input: nums = [10,9,2,5,3,7,101,18]
Output: 4
Explanation: The longest increasing subsequence is [2,3,7,101], therefore the length is 4.
Example 2:
Input: nums = [0,1,0,3,2,3]
Output: 4
Explanation: The longest increasing subsequence is [0,1,2,3], therefore the length is 4.
Constraints:

• 1 <= nums.length <= 2500


• -10^4 <= nums[i] <= 10^4

OpenAI's inference API must handle continuous input streams efficiently, ensuring optimal latency and throughput.
Given an array of integers, find the maximum sum of a subarray of size k.

Function Signature

• def max_sum_subarray_of_k(arr: List[int], k: int) -> int: Returns the maximum sum of the subarray of size k.

Example 1:

Input: arr = [1, 2, 3, 4, 5], k = 3
Output: 12
Explanation: The maximum sum subarray of size 3 is [3, 4, 5] with a sum of 12.

Example 2:

Input: arr = [2, 3, 4, 1, 5], k = 2
Output: 7
Explanation: The maximum sum is from the subarray [4, 1].

Constraints:

• 0 < len(arr) <= 1000


• 1 <= k <= len(arr)

OpenAI's text completion models require efficient algorithms to generate responses in real-time while minimizing computational cost.
Given an array of integers representing the tokens in a sequence, you need to calculate the maximum non-adjacent sum of tokens that can be chosen from this array.

Function Signature

• def max_non_adjacent_sum(tokens: List[int]) -> int: Returns the maximum sum of non-adjacent integers.

Example 1:

Input: [3, 2, 5, 10, 7]
Output: 15
Explanation: The optimal choice is to take tokens 3, 10, and 2 which gives the maximum sum 15 without selecting adjacent values.

Example 2:

Input: [9, 1, 2, 8, 3]
Output: 17
Explanation: The optimal choice is to take tokens 9, 8, and 3.

Constraints:

• 0 < len(tokens) <= 1000


• 0 <= tokens[i] <= 1000

OpenAI often needs to compute the median of predicted metrics in real-time. This requires an efficient data structure to retrieve the median quickly while processing continuous streams of data.

Class Definition

Class MedianFinder should implement the following methods:

• addNum(num: int) -> None: Adds a number to the data structure.


• findMedian() -> float: Returns the median of all added numbers.

Example 1:

Input: medianFinder = MedianFinder(); medianFinder.addNum(1); medianFinder.addNum(2); medianFinder.findMedian()
Output: 1.5
Explanation: The median of [1,2] is 1.5

Example 2:

Input: medianFinder.addNum(3); medianFinder.findMedian()
Output: 2
Explanation: The median of [1,2,3] is 2.

Constraints:

• -10^5 <= num <= 10^5


• There will be at most 1,000,000 calls to addNum and findMedian.

OpenAI needs an efficient caching system to store previously computed model predictions, optimizing resource usage and response time.

Class Definition

Class LRUCache should implement the following methods:

• get(key: int) -> int: Returns the value of the key if the key exists, otherwise returns -1.


• put(key: int, value: int) -> None: Updates the value of the key if the key exists existing and moves the key to the front of the cache. Otherwise, it adds the key/value pair to the cache.

Example 1:

Input: cache = LRUCache(2); cache.put(1, 1); cache.put(2, 2); cache.get(1)
Output: 1
Explanation: Returns 1

Example 2:

Input: cache.put(3, 3); cache.get(2)
Output: -1
Explanation: Returns -1 since the cache reached its capacity; LRU (key = 2) was evicted.

Constraints:

• The capacity of the cache will be between 1 and 1000.


• All keys will be unique.