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Car Pooling

Updated on 19 May, 2025
Car Pooling header image

Problem Statement

In the given problem, a car with a specified number of empty seats (capacity) is tasked with transporting passengers Eastward without the option of turning West. Each trip, characterized by a number of passengers (numPassengersi), a pickup location (fromi), and drop off location (toi), is detailed within an array trips. Each element in this trips array represents a single journey, where the locations (fromi and toi) are distances measured in kilometers east from the starting point of the car.

The challenge lies in determining if the car can manage all scheduled trips without exceeding its passenger capacity at any given point in the journey. The objective is to return true if the car can accommodate all passengers for every trip as per their requirements; otherwise, return false.

Examples

Example 1

Input:

trips = [[2,1,5],[3,3,7]], capacity = 4

Output:

false

Example 2

Input:

trips = [[2,1,5],[3,3,7]], capacity = 5

Output:

true

Constraints

  • 1 <= trips.length <= 1000
  • trips[i].length == 3
  • 1 <= numPassengersi <= 100
  • 0 <= fromi < toi <= 1000
  • 1 <= capacity <= 105

Approach and Intuition

To solve this problem, we need to track the number of passengers in the vehicle at each point in the journey based on the trips' pickup and drop-off events. Here’s a step-by-step breakdown:

  1. First, understand the number of changes in passenger count at each event (pickup or dropoff). This can be done by creating a list or array where each index represents a point (kilometer) in the journey, and the value at each index alters based on passenger events happening at that location.

  2. Initialize a list with a length equal to the furthest distance (toi) in trips plus one (to accommodate zero indexing), filled initially with zeros. This array will represent passenger changes at each kilometer of the journey.

  3. For each trip in trips, increment the passenger count at the index representing the pickup location (fromi) by the number of passengers (numPassengersi), and decrement it at the index representing one past the drop-off location (toi) as passengers will be leaving the car.

  4. Walk through the passenger change array cumulatively to calculate the total number of passengers in the car at each kilometer. This is akin to applying the prefix sum technique where each value in the accumulation array changes based on the net effect of passenger pickups and drop-offs up to that point.

  5. During this walk, if at any point the number of passengers in the car exceeds the capacity, immediately return false. If you complete the walk without exceeding the car's capacity, return true.

By applying this approach, we can efficiently determine if the car can manage all the scheduled trips within the given passenger capacity constraints.

Solutions

  • Java
  • Python
java 
class Solution {
    public boolean canCarPool(int[][] rides, int maxCapacity) {
        int[] timeStamps = new int[1001];
        for (int[] ride : rides) {
            timeStamps[ride[1]] += ride[0];
            timeStamps[ride[2]] -= ride[0];
        }
        int currentLoad = 0;
        for (int load : timeStamps) {
            currentLoad += load;
            if (currentLoad > maxCapacity) {
                return false;
            }
        }
        return true;
    }
}

In the given Java solution for the Car Pooling problem, the goal is to determine if a car with a specified maximum capacity can successfully transport all passengers based on their respective trips without exceeding this capacity at any time.

  • Start by initializing an array timeStamps with a size sufficient to cover all minutes in which rides can start or end, defaulting to 1001 elements to encapsulate times from minute 0 to 1000.
  • Traverse through each ride in the provided rides array. Each ride is represented as an array where:
    • The first element indicates the number of passengers,
    • The second element specifies the start time,
    • The third element provides the end time.
  • For each ride, increase the passenger count at the start time index in the timeStamps array and decrease it at the end time index. This increment and decrement approach helps track how passenger load changes over time.
  • Initialize currentLoad to zero to represent the starting condition with an empty car.
  • Iterate over each load in the timeStamps:
    • Update currentLoad by adding the load. This effectively accumulates the total number of passengers in the car at each time.
    • If currentLoad exceeds maxCapacity at any point, return false indicating that the carrying capacity is insufficient at that moment.
  • If the loop completes without exceeding the capacity, return true, indicating that the car can handle all trips within the given capacity constraints.

The method effectively determines car pooling feasibility by simulating the ride's impact on car capacity across each timestamp, ensuring that capacity limitations are respected at all times.

python 
class Solution:
    def canCarPool(self, trips: List[List[int]], max_capacity: int) -> bool:
        time_line = [0] * 1001
        for t in trips:
            time_line[t[1]] += t[0]
            time_line[t[2]] -= t[0]

        current_load = 0
        for change in time_line:
            current_load += change
            if current_load > max_capacity:
                return False

        return True

The Python code provided determines if it's possible to carpool all trips under a given vehicle capacity constraint. Review the code to understand the approach:

  • The canCarPool method within the Solution class takes a list of trips and an max_capacity as input. All trips are represented as lists containing three integers: the number of passengers, the start location, and the end location.
  • A time_line array with a pre-defined size (1001) initializes all indices to zero. This structure is employed to efficiently track changes to the number of passengers over time as trips start and finish.
  • For each trip:
    • Increment the start position in time_line by the number of passengers.
    • Decrement the end position in time_line by the number of passengers.
  • Track the current_load of the car as the timeline progresses. This variable accumulates the net change in the number of passengers at each point in time.
  • If at any point the current_load exceeds max_capacity, the method returns False, indicating it's not possible to carpool within the given constraints.
  • If the loop completes without the current_load ever exceeding max_capacity, the method returns True, indicating all trips can be successfully pooled under the provided capacity.

This approach efficiently assesses the feasibility of carpooling by leveraging a timeline simulation to manage changes in the number of passengers carried, ensuring that the vehicle's capacity is not exceeded at any point.

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