Parking System Design

Problem Description

Design a parking system for a parking lot with three types of parking spaces: big, medium, and small. The system should initialize with a fixed number of slots for each size and allow cars to park based on their type. Implement the ParkingSystem class with the following methods:

• ParkingSystem(int big, int medium, int small): Initializes the object with the number of slots for each parking space size.
• bool addCar(int carType): Checks if a parking space of carType is available. carType can be 1 (big), 2 (medium), or 3 (small). If space is available, park the car and return true; otherwise, return false.

Naive Solution

A straightforward approach is to use three separate counters to keep track of the available slots for each car type. During initialization, the counters are set to the initial capacity of each type of parking space. The addCar method decrements the appropriate counter if space is available and returns true. Otherwise, it returns false.

Code (Java)

class ParkingSystem {
    private int big;
    private int medium;
    private int small;

    public ParkingSystem(int big, int medium, int small) {
        this.big = big;
        this.medium = medium;
        this.small = small;
    }

    public boolean addCar(int carType) {
        if (carType == 1) {
            if (big > 0) {
                big--;
                return true;
            } else {
                return false;
            }
        } else if (carType == 2) {
            if (medium > 0) {
                medium--;
                return true;
            } else {
                return false;
            }
        } else {
            if (small > 0) {
                small--;
                return true;
            } else {
                return false;
            }
        }
    }
}

Time Complexity

• ParkingSystem (constructor): O(1)
• addCar: O(1)

Space Complexity

O(1) - constant space is used to store the counts.

Optimal Solution

The optimal solution is essentially the same as the naive solution since the problem constraints are simple, and the number of car types is fixed. We can slightly optimize the code by using an array to store the counts, making the logic more concise.

Code (Java)

class ParkingSystem {
    private int[] spaces;

    public ParkingSystem(int big, int medium, int small) {
        spaces = new int[4]; // Index 0 is unused to match carType numbering
        spaces[1] = big;
        spaces[2] = medium;
        spaces[3] = small;
    }

    public boolean addCar(int carType) {
        if (spaces[carType] > 0) {
            spaces[carType]--;
            return true;
        } else {
            return false;
        }
    }
}

Time Complexity

• ParkingSystem (constructor): O(1)
• addCar: O(1)

Space Complexity

O(1) - constant space is used to store the counts.

Edge Cases

• The constructor receives negative values for big, medium, or small. The problem statement specifies that these values will be non-negative, so no explicit handling is needed.
• The carType is not 1, 2, or 3. The problem statement specifies that carType will always be one of these values, so no explicit handling is needed.
• Multiple calls to addCar exhaust all available spaces. The solution correctly handles this by returning false when there is no space available.