My Calendar III

Identifying Problem Isomorphism

“My Calendar III” has an approximate isomorphic problem “My Calendar II”.

In both problems, the task is to design a booking system with the ability to add events to a calendar.

In “My Calendar III”, the focus is on handling overlapping events. The calendar should be able to keep track of the maximum number of simultaneous events and return that maximum number every time a new event is added.

In “My Calendar II”, the problem also deals with overlapping events. However, the constraint here is different: while an event can overlap (or be double booked) once, it cannot overlap twice.

The idea of managing time intervals and dealing with overlapping intervals makes these problems similar.

The two problems have different objectives: one is to count the maximum overlap (“My Calendar III”), and the other is to prevent an event from being triple booked (“My Calendar II”), which means the solutions to these two problems are not directly interchangeable.

Therefore, while the problems share similarities in their concept, they only represent an approximate isomorphic relation due to their differences in objectives.

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class MyCalendarThree:
    def __init__(self):
        self.timeline = {}

    def book(self, start, end):
        self.timeline[start] = self.timeline.get(start, 0) + 1
        self.timeline[end] = self.timeline.get(end, 0) - 1
        ongoing, k = 0, 0
        for t in sorted(self.timeline.items()):
            ongoing += t[1]
            k = max(k, ongoing)
        return k

Problem Classification

This problem falls into Interval Scheduling category. These are problems that involve managing and manipulating data using suitable data structures and finding solutions that pertain to scheduling of events in a certain way.

What: The ‘What’ components are:
- An event with a start time and end time.
- A booking system that accepts these events and tracks the maximum overlap or ‘k-booking’ between them.
- The goal is to find the maximum ‘k-booking’, i.e., the maximum number of overlaps at any given time.
Classification:
- Data Structures: We need to keep track of different events and their start and end times. Depending on how we approach the problem, various data structures might be used, including arrays, trees, or even simple variables.
- Interval Scheduling: The problem involves scheduling of events, which are represented by intervals (start time, end time). The task is to find the maximum overlap or ‘k-booking’, which requires analyzing the intervals in a specific way.

The problem requires not just the ability to store and manage data, but also to process it in a way that allows for determining overlaps between intervals. Therefore, the solution needs to consider both aspects - the appropriate data structures to store events, and the algorithm to process them and calculate the maximum ‘k-booking’.

Language Agnostic Coding Drills

Dissect the Code and Identify Each Distinct Concept:
1. Object-Oriented Programming (OOP): This code defines a class MyCalendarThree that has two methods, namely __init__ and book. This encapsulates the concept of classes, objects, and methods.
2. Dictionary in Python: The code uses a dictionary to keep track of start and end times of events. The dictionary is a key-value pair data structure in Python which stores information that can be quickly retrieved.
3. Python get method: The code uses the get method, which is a built-in method in Python to retrieve the value of a key from a dictionary. If the key does not exist, it provides a default value.
4. Sorting a dictionary: The code sorts the dictionary items before iterating over them. This concept involves sorting a dictionary by its keys.
5. Iteration: The code iterates over the items in the sorted dictionary, performing actions on each item.
List the Coding Concepts in Order of Increasing Difficulty:
1. Dictionary in Python: This is one of the basic concepts of Python where a user learns about storing data in key-value pairs. It’s easy because it’s similar to real-life scenarios where you use a unique key to get some value.
2. Python get method: This concept is relatively straightforward. It is a built-in function in Python for dictionaries which reduces the risk of key errors while trying to access dictionary values.
3. Iteration: While basic, the concept of iteration can be more difficult than the first two because it requires understanding of control flow and looping.
4. Sorting a dictionary: While Python provides built-in sorting, understanding how it works with complex data structures like dictionaries can be tricky.
5. Object-Oriented Programming (OOP): This is the most difficult concept as it requires understanding of objects, classes, encapsulation, and methods.
Problem-Solving Approach:
The problem is about finding the maximum number of overlapping events. The timeline dictionary keeps track of all the start times and end times. If a time point is a start time, it increments the counter for that point, if it is an end time, it decrements the counter.
When a new booking comes, the code updates the timeline and then checks the ongoing events by iterating over the timeline dictionary in ascending order, adding up the counts (which could be positive for start times or negative for end times).
It keeps track of the maximum count (k) during this process, which is the maximum k-booking between all the events. The book method then returns this maximum k-booking.
Each of the identified concepts (OOP, dictionary, get method, sorting, and iteration) come together to implement this logic and provide a solution to the problem.

Targeted Drills in Python

Python Coding Drills:

Dictionary in Python

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# Creation of a dictionary
dictionary = {"apple": 1, "banana": 2, "cherry": 3}

# Accessing values in a dictionary
print(dictionary["apple"])

# Adding new items to a dictionary
dictionary["date"] = 4
print(dictionary)

Python get method

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dictionary = {"apple": 1, "banana": 2, "cherry": 3}

# Using get method to access values
print(dictionary.get("apple"))

# Using get with a non-existent key and a default value
print(dictionary.get("orange", 0))

Iteration

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dictionary = {"apple": 1, "banana": 2, "cherry": 3}

# Iterating over dictionary items
for key, value in dictionary.items():
    print(f"Key: {key}, Value: {value}")

Sorting a dictionary

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dictionary = {"apple": 3, "banana": 1, "cherry": 2}

# Sorting dictionary items
sorted_items = sorted(dictionary.items())
print(sorted_items)

Object-Oriented Programming (OOP)

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# Defining a class with a constructor and a method
class Fruit:
    def __init__(self, name, quantity):
        self.name = name
        self.quantity = quantity

    def display(self):
        print(f"Fruit: {self.name}, Quantity: {self.quantity}")

# Creating an object of the class and calling its method
apple = Fruit("apple", 5)
apple.display()

Problem-Specific Concepts:
The main problem-specific concept here is the utilization of a dictionary to represent the timeline, where each key-value pair represents a time point and the change in the number of ongoing events at that point. This requires understanding of dictionary operations such as incrementing/decrementing a value and sorting the keys.
Integration of the Coding Drills:
To integrate these drills into a comprehensive solution, follow these steps:
- Define a class MyCalendarThree with an instance variable timeline which is an empty dictionary.
- Define a method book that takes start time and end time of an event. Use the get method to increment the value for start time and decrement the value for end time in timeline.
- Sort the timeline dictionary by keys and then iterate over its items. In each iteration, add the value to a variable ongoing and update k with the maximum of k and ongoing.
- Return k from the book method which represents the maximum k-booking between all events.