Compute courier pay and implement load balancing

Problem 1: Compute courier (delivery driver) pay

You are given a sequence of delivery-related events for a courier during a day. Your task is to compute the courier’s total pay.

Inputs

• A list of pay-rate intervals for the day (rates can change over time):
  • Each interval is (start_minute, end_minute, rate_per_minute) where 0 <= start < end <= 1440 .
  • Intervals do not overlap and together may or may not cover the whole day.
• A list of delivery trips:
  • Each trip is (pickup_minute, dropoff_minute, per_trip_bonus) .
  • Trip time contributes time-based pay according to the rate schedule; bonus is added once per trip.

Output

Return the total pay for the courier for all trips combined.

Notes / constraints

• If a trip spans multiple rate intervals, split its time accordingly.
• If a trip overlaps a time range with no defined rate interval, assume rate is 0 for that portion.
• Minutes are integers; treat intervals as half-open: [start_minute, end_minute) .
• Constraints (typical): up to 1e5 intervals and 1e5 trips.

Problem 2: Implement request routing (Round Robin → Consistent Hashing)

Design a small in-memory request router for a set of backend servers.

Part A: Round Robin router

Implement a router that supports:

• addServer(serverId)
• removeServer(serverId)
• route(requestId) -> serverId

Behavior:

• route() should return servers in round-robin order over the current set of servers.
• The implementation should be robust to adds/removals between calls.

Part B: Consistent hashing router

Modify/replace the round-robin approach with consistent hashing so that:

• When a server is added/removed, only a small fraction of requests remap.
• You may use virtual nodes.

Notes / constraints

• serverId is a string.
• requestId is a string.
• Aim for near- O(log N) routing time.