Apple Backend Engineer Coding Questions

Apple's AirPods need an intelligent system to maintain an active list of connections based on user movements and proximity. An efficient algorithm can help track active devices using the Sliding Window technique.Given an array of connection times and an integer k, return the maximum number of active connections at any given time within the last k seconds.- def max_active_connections(times: List[int], k: int) -> int: returns the maximum number of connections.Example 1:
Input: times = [1, 2, 5, 6, 7], k = 3
Output: 3
Explanation: At time 5, there are 3 active connections (from 3 to 5).Example 2:
Input: times = [1, 2, 3, 4, 5], k = 2
Output: 2
Explanation: At times 4 and 5, the number of active connections within k=2 seconds is 2.Constraints:
- 1 <= len(times) <= 10^5
- 1 <= k <= 10^3

In Apple Maps, it’s essential to provide users with the shortest and fastest routes possible. Efficiently calculating these routes involves analyzing weighted graphs to identify optimal paths between locations.Write a function that implements Dijkstra's algorithm to find the shortest path from a source node to all other nodes in a weighted graph represented by an adjacency list.- def dijkstra(graph: Dict[int, List[Tuple[int, int]]], source: int) -> Dict[int, int]: returns a dictionary mapping each node to its shortest distance from the source.Example 1:
Input: graph = {0: [(1, 4), (2, 1)], 1: [(3, 1)], 2: [(1, 2), (3, 5)], 3: []}, source = 0
Output: {0: 0, 1: 3, 2: 1, 3: 4}
Explanation: The shortest distances from the source node 0 to all other nodes are calculated.Example 2:
Input: graph = {0: [(1, 2)], 1: [(2, 5)], 2: []}, source = 0
Output: {0: 0, 1: 2, 2: 7}
Explanation: The shortest paths are derived from the source node 0.Constraints:
- 1 <= len(graph) <= 10^5
- 0 <= source < len(graph)