**π‘ Problem Formulation:** Imagine weβre tasked with verifying a transportation schedule where a series of passengers need to be picked up and then dropped off at various locations. Given a list of passenger operations, where a positive number indicates a pickup and a negative number a dropoff, we want to check whether we can successfully pick up and drop off all the passengers accordingly. The list [1, -1, 2, -2] represents picking up passenger 1, dropping them off, then picking up passenger 2 and dropping them off, and so on, and we would like a program to validate such sequences.

## Method 1: Brute Force Check

This method iterates through the list of passenger operations and keeps track of the current number of passengers in the vehicle. If it ever tries to drop off a passenger that wasn’t picked up, the method will return false. This is straightforward and suitable for small lists.

Here’s an example:

def can_complete_rides(operations): passengers = 0 for op in operations: passengers += op if passengers < 0: return False return passengers == 0 print(can_complete_rides([1, -1, 2, -2]))

Output: `True`

This function, `can_complete_rides()`

, checks each operation in the sequence. It increments or decrements a passenger count and verifies that it doesnβt go negative, which would indicate a drop-off without a pickup. It also ensures that the vehicle is empty at the end by checking if the passenger count returns to zero.

## Method 2: Using a Set to Track Passengers

This approach uses a set to keep track of the unique passengers currently in the vehicle. Passengers are added when picked up and removed when dropped off. The method ensures a passenger cannot be dropped off if they have not been picked up first.

Here’s an example:

def can_complete_rides_with_set(operations): passengers = set() for op in operations: if op > 0: passengers.add(op) elif op < 0 and -op not in passengers: return False else: passengers.remove(-op) return not passengers print(can_complete_rides_with_set([1, -1, 2, -2]))

Output: `True`

The function `can_complete_rides_with_set()`

uses the properties of a set to ensure we only drop off passengers that have been recorded as picked up. It’s more robust than the first method, as it handles the case where there are multiple operations for the same passenger.

## Method 3: Sort and Validate

This method first sorts the operations list to process all pickups before drop-offs. If pickups and drop-offs are not in pairs of equal and opposite numbers, the schedule is invalid. Sorting helps in identifying unpaired operations.

Here’s an example:

def can_complete_rides_sorted(operations): sorted_ops = sorted(operations, key=abs) return all(sorted_ops[i] == -sorted_ops[i+1] for i in range(0, len(sorted_ops), 2)) print(can_complete_rides_sorted([1, -1, 2, -2]))

Output: `True`

In `can_complete_rides_sorted()`

, the sorted operations list should have each pickup operation followed by its corresponding dropoff. If at any point this is not the case, it returns false, ensuring a valid pickup/dropoff sequence.

## Method 4: Using a Counter

Using Python’s collections.Counter, we tally the pickups and drop-offs separately. The schedule is valid if for every passenger the number of pickups equals the number of drop-offs.

Here’s an example:

from collections import Counter def can_complete_rides_counter(operations): counter = Counter(operations) return all(counter[op] == counter[-op] for op in counter if op > 0) print(can_complete_rides_counter([1, -1, 2, -2]))

Output: `True`

The function `can_complete_rides_counter()`

leverages `Counter`

to count instances of pickups and drop-offs. It then checks for each operation if the count equals the corresponding drop-off, ensuring that each passenger that was picked up was also dropped off.

## Bonus One-Liner Method 5: Using a Python Generator

For the aficionados of Python’s succinctness, a one-liner generator expression can similarly validate the transportation schedule. This method leans on the fact that pickups and drop-offs must cancel each other out.

Here’s an example:

can_complete_rides_one_liner = lambda ops: not sum(1 for op in ops if (ops.count(op) != ops.count(-op) and op > 0)) print(can_complete_rides_one_liner([1, -1, 2, -2]))

Output: `True`

The one-liner function `can_complete_rides_one_liner()`

uses a generator expression to count how many times a pickup does not have a corresponding drop-off. If this sum is zero, it implies all passengers have been picked up and dropped off correctly.

## Summary/Discussion

**Method 1: Brute Force Check.**Easy to implement. Handles simple cases well. May not scale efficiently with very large lists.**Method 2: Using a Set to Track Passengers.**Robust and handles multiple passengers. More memory intensive due to storing unique elements.**Method 3: Sort and Validate.**Easy to reason about. Requires sorting which adds O(n log n) complexity.**Method 4: Using a Counter.**Efficient for large data sets with repeated elements. May be overkill for small lists.**Bonus Method 5: One-Liner.**Concise and elegant, but potentially less efficient and harder to read for beginners.