Meta Data Scientist Coding Questions

Meta aims to improve communication speed on Messenger by analyzing network distances. You need to determine the shortest path between users based on a network graph where nodes represent users and edges represent direct communication paths with weights representing latency.
Problem statement: Implement Dijkstra's algorithm to find the shortest path from a given starting node to all other nodes in a weighted graph.
- Method Signature: def dijkstra(graph: Dict[int, List[Tuple[int, int]]], start: int) -> Dict[int, int]
Example 1:
Input: graph = {0: [(1, 1), (2, 4)], 1: [(2, 2)], 2: []}, start = 0
Output: {0: 0, 1: 1, 2: 3}
Explanation: The shortest path from node 0 to node 1 is 1 and to node 2 is 3 (0 -> 1 -> 2).
Constraints:
- 1 <= len(graph) <= 1000
- 0 <= weights <= 1000

Meta needs to optimize user engagement on Facebook Live. You are tasked with analyzing user interaction data in real-time to identify active segments of the audience during a live event.
Problem statement: Given an array of integers engagements where each integer represents the number of interactions at each timestamp, determine the maximum number of interactions in any k consecutive timestamps.
- Method Signature: def max_engagement(engagements: List[int], k: int) -> int
Example 1:
Input: engagements = [1, 2, 3, 4, 5], k = 2
Output: 9
Explanation: The maximum interactions in any 2 consecutive timestamps is 4 + 5 = 9.
Constraints:
- 1 <= len(engagements) <= 10^5
- 1 <= k <= len(engagements)