xAI Hard Interview Questions

In xAI's data processing systems, we often encounter large arrays of user-generated metrics. Finding the maximum subarray sum quickly becomes essential to understand user behavior efficiently.
Problem Statement: Given an integer array nums, find the contiguous subarray (containing at least one number) which has the largest sum and return its sum.

• int max_sub_array_sum(List<int> nums): returns the maximum sum of the contiguous subarray.

Example 1:
Input: nums = [-2,1,-3,4,-1,2,1,-5,4]
Output: 6
Explanation: The contiguous subarray [4,-1,2,1] has the largest sum = 6.
Example 2:
Input: nums = [1]
Output: 1
Explanation: The contiguous subarray [1] has the largest sum = 1.
Constraints:

• 1 <= nums.length <= 3 * 10^4


• -10^4 <= nums[i] <= 10^4.

In xAI's recommendation system, we need to efficiently find the shortest path to similar items based on user interactions. This will help improve user engagement.
Problem Statement: Given a directed graph represented as an adjacency list, where each node represents an item and edges represent the relationship strength, implement a function that finds the shortest path from a start node to a target node using BFS. Return the list of nodes in the path from start to target, or an empty list if no path exists.

• List[int] bfs_shortest_path(int start, int target): returns the list of integers representing the path from start to target.

Example 1:
Input: start = 0, target = 4
Output: [0, 1, 2, 4]
Explanation: The shortest path from node 0 to 4 is through nodes 1 and 2.
Example 2:
Input: start = 0, target = 3
Output: []
Explanation: No path exists between node 0 and node 3.
Constraints:

• 1 <= start, target <= 10^4


• The graph can have up to 10^4 nodes and 2 * 10^4 edges.

For optimizing user interaction, xAI requires efficient routing through dialogue states in a conversation graph.
You have a directed graph where each node represents a dialogue state and edges represent possible transitions. Write a function to return the shortest path from the initial state to a target state.
Example method signature: def shortestPath(graph: Dict[int, List[int]], start: int, target: int) -> List[int]: returns a list of node values representing the shortest path.Example 1:
Input: graph = {0: [1, 2], 1: [3], 2: [3], 3: []}, start = 0, target = 3
Output: [0, 1, 3]
Explanation: One possible shortest path from the initial state (0) to target (3) is through state 1.Example 2:
Input: graph = {0: [1], 1: [2], 2: [3], 3: []}, start = 0, target = 2
Output: [0, 1, 2]
Explanation: This is a direct route from 0 to 2 passing through state 1.Constraints:

• 1 <= graph.length <= 1000


• Input graph is a directed acyclic graph (DAG).

In order to improve the efficiency of our AI models, xAI needs to analyze the time complexity of certain input sequences in real-time.
Given an array of integers nums, return the length of the longest increasing subsequence.
Example method signature: def lengthOfLIS(self, nums: List[int]) -> int: returns the length of the longest increasing subsequence found in nums.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 its 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 its length is 4.Constraints:

• 1 <= nums.length <= 2500


• -10^4 <= nums[i] <= 10^4

To enhance performance for xAI's machine learning algorithms, we need a fast, in-memory caching system to store frequently accessed data. This system should allow for efficient data retrieval and support for automatic eviction of old data.
Problem Statement: Design a custom cache that supports the following operations: put(key: int, value: int): void and get(key: int): int. When the cache reaches its capacity, it should invalidate the least recently used (LRU) item.

• class LRUCache:


• def __init__(self, capacity: int): Initializes the cache with a positive size capacity.


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


• def put(self, key: int, value: int) -> None: Updates or adds the value if the key is not present. When the cache reaches its capacity, it should invalidate the least recently used item before adding the new item.

Example 1:
Input:
LRUCache cache = new LRUCache(2);
cache.put(1, 1);
cache.put(2, 2);
cache.get(1); // returns 1
cache.put(3, 3); // evicts key 2
cache.get(2); // returns -1 (not found)
Example 2:
Input:
LRUCache cache = new LRUCache(1);
cache.put(1, 1);
cache.get(1); // returns 1
cache.put(2, 2); // evicts key 1
cache.get(1); // returns -1 (not found)
Constraints:

• 1 <= capacity <= 3000


• 0 <= key <= 10000


• 0 <= value <= 10^9.

To accelerate response times from our AI models, xAI needs to implement a caching mechanism for the frequently accessed data.
Design and implement a simple LRU Cache class that supports the following operations:

• get(key: int) -> int: Retrieve the value of the key if the key exists in the cache, otherwise return -1.


• put(key: int, value: int) -> None: Update the value of the key if the key exists. If the key does not exist, add the key-value pair to the cache. If the cache reaches its capacity, it should invalidate the least recently used item before inserting a new item.

Example Method Signatures:

• def get(self, key: int) -> int


• def put(self, key: int, value: int) -> None

Example 1:
Input: cache = LRUCache(2), cache.put(1, 1), cache.put(2, 2), cache.get(1)
Output: 1 Example 2:
Input: cache.put(3, 3), cache.get(2)
Output: -1
Explanation: The least recently used key (2) was removed because the cache reached its capacity.Constraints:

• capacity is at most 3000.