Minimum Delivery Agents to Meet All Deadlines

Problem You have n delivery orders. Each order has an arrivalTime (when it becomes available) and a deliveryDeadline by which it must be completed. A single agent handles one order at a time and takes exactly travelTime minutes per delivery. Determine the minimum number of agents required so that every order is delivered on or before its deadline.

Input / Output

• Input: a list of orders, each {arrivalTime, deliveryDeadline}, and an integer travelTime.
• Output: the minimum number of agents needed to meet all deadlines.

Constraints

• 1 ≤ n ≤ 10^5.
• An agent starting an order at time t finishes at t + travelTime; it cannot start before the order's arrivalTime.
• An order is feasible only if it can finish by its deadline.

Example

• orders = [{arrival:0, deadline:10}, {arrival:1, deadline:10}, {arrival:0, deadline:10}], travelTime = 8 → 2.