Implement a Reusable Locker Allocation System

Problem Statement

Design a locker management system for an automated delivery kiosk. The kiosk contains a fixed number of lockers numbered 1 through capacity.

Implement the LockerSystem class with the following methods:

• __init__(self, capacity: int): Initializes the locker bank with capacity lockers, indexed from 1 to capacity. Initially, all lockers are empty.
• store(self, package_id: str) -> int: Assigns the lowest-numbered available locker to hold package_id. If all lockers are occupied or if package_id is already currently stored in another locker, the operation is invalid and must return -1. Otherwise, returns the assigned locker_id.
• pickup(self, locker_id: int, package_id: str) -> bool: Releases the specified locker if locker_id is valid, is currently occupied, and contains package_id. If released, the locker immediately becomes available for reuse by future store operations, and the method returns True. If locker_id is invalid, not currently occupied, or the stored package does not match package_id, the operation fails and returns False.
• get_last_stored(self, locker_id: int) -> str | None: Returns the package_id of the package most recently stored in locker_id, even if the locker is currently empty. If locker_id is invalid or no package has ever been stored in that locker, returns None.

Example

lockers = LockerSystem(3)

lockers.store("PKG-A")        # returns 1 (locker 1 is lowest available)
lockers.store("PKG-B")        # returns 2 (locker 2 is lowest available)
lockers.store("PKG-A")        # returns -1 (PKG-A is already in the system)

lockers.pickup(1, "PKG-A")    # returns True (locker 1 is now empty)
lockers.pickup(1, "PKG-A")    # returns False (locker 1 is already empty)

lockers.store("PKG-C")        # returns 1 (locker 1 was released and is lowest available)

lockers.get_last_stored(1)    # returns "PKG-C"
lockers.pickup(1, "PKG-C")    # returns True
lockers.get_last_stored(1)    # returns "PKG-C" (retained after pickup)
lockers.get_last_stored(3)    # returns None (locker 3 never had a package)

Constraints

• 1 <= capacity <= 10^5
• 1 <= len(package_id) <= 32, containing alphanumeric characters only.
• At most 2 * 10^5 total calls across store, pickup, and get_last_stored.

Edge Cases to Consider

• Attempting to store when the locker bank is full.
• Attempting to store an item whose package_id is currently in another locker versus one that was previously picked up.
• Invalid locker_id values (e.g., capacity).
• Querying get_last_stored before any item has been stored in a locker.