Frequency Tracker

Let’s design a FrequencyTracker class to keep track of numbers and their frequencies.

We’ll use two dictionaries:

number_frequency: to track the frequency of each number.
frequency_count: to track the count of frequencies.

Here’s the code implementation:

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class FrequencyTracker:

    def __init__(self):
        self.number_frequency = {}  # Keeps track of frequency for each number
        self.frequency_count = {}  # Keeps track of count of frequencies

    def add(self, number: int) -> None:
        old_freq = self.number_frequency.get(number, 0)
        new_freq = old_freq + 1

        # Update the number_frequency dictionary
        self.number_frequency[number] = new_freq

        # Update the frequency_count dictionary
        if old_freq > 0:
            self.frequency_count[old_freq] -= 1
            if self.frequency_count[old_freq] == 0:
                del self.frequency_count[old_freq]

        self.frequency_count[new_freq] = self.frequency_count.get(new_freq, 0) + 1

    def deleteOne(self, number: int) -> None:
        if number in self.number_frequency:
            old_freq = self.number_frequency[number]
            new_freq = old_freq - 1
            
            # Update the number_frequency dictionary
            if new_freq == 0:
                del self.number_frequency[number]
            else:
                self.number_frequency[number] = new_freq

            # Update the frequency_count dictionary
            self.frequency_count[old_freq] -= 1
            if self.frequency_count[old_freq] == 0:
                del self.frequency_count[old_freq]

            if new_freq > 0:
                self.frequency_count[new_freq] = self.frequency_count.get(new_freq, 0) + 1

    def hasFrequency(self, frequency: int) -> bool:
        return self.frequency_count.get(frequency, 0) > 0

Explanation

In the add method, we increase the frequency of the given number and update both dictionaries accordingly.
In the deleteOne method, we decrease the frequency of the given number and update both dictionaries. We also handle the case where the frequency becomes zero, and we remove the entry from the dictionaries.
In the hasFrequency method, we simply check if the given frequency exists in the frequency_count dictionary.

Key Takeaways

The code is efficient as it allows constant time complexity for all operations (O(1)).
The space complexity is O(N), where N is the number of unique elements added to the tracker.

For “2671. Frequency Tracker”, the following is a good preparation:

“380. Insert Delete GetRandom O(1)” - This problem involves maintaining a data structure that supports insert, delete and getRandom operations efficiently.
“146. LRU Cache” - This problem involves designing a data structure (a type of cache) which has certain operations. It helps understand the design considerations required in building a custom data structure like the Frequency Tracker.
“460. LFU Cache” - This problem is about designing and implementing a data structure for Least Frequently Used (LFU) cache, which is similar to the FrequencyTracker problem where you need to keep track of frequencies.
“355. Design Twitter” - This problem is about designing a simplified version of Twitter where tweets have to be ordered by recency. It will help to understand design considerations in managing and maintaining data.
“895. Maximum Frequency Stack” - This problem requires you to design a stack-like data structure that supports push, pop, and maxFrequency operations.
“211. Design Add and Search Words Data Structure” - This problem requires designing a data structure to support add and search operations. It’s a good problem for understanding how to design and implement a data structure.
“716. Max Stack” - This problem involves designing a max stack that supports push, pop, top, peekMax and popMax operations.
“232. Implement Queue using Stacks” - This problem involves designing a queue using stacks. It helps to understand how to implement one data structure using another.
“225. Implement Stack using Queues” - Similarly, this problem requires designing a stack using queues. It’s a good problem to understand how to manage data in one structure using a different one.
“705. Design HashSet” - This problem involves designing a HashSet without using any built-in hash table libraries. It is a good problem for understanding design of basic data structures.

These cover how to design custom data structures to perform specific operations and how to manage data within them, which are crucial for solving the Frequency Tracker problem.

Frequency Tracker Design a data structure that keeps track of the values in it and answers some queries regarding their frequencies.

Implement the FrequencyTracker class.

FrequencyTracker(): Initializes the FrequencyTracker object with an empty array initially. void add(int number): Adds number to the data structure. void deleteOne(int number): Deletes one occurrence of number from the data structure. The data structure may not contain number, and in this case nothing is deleted. bool hasFrequency(int frequency): Returns true if there is a number in the data structure that occurs frequency number of times, otherwise, it returns false.

Example 1:

Input [“FrequencyTracker”, “add”, “add”, “hasFrequency”] [[], [3], [3], [2]] Output [null, null, null, true]

Explanation FrequencyTracker frequencyTracker = new FrequencyTracker(); frequencyTracker.add(3); // The data structure now contains [3] frequencyTracker.add(3); // The data structure now contains [3, 3] frequencyTracker.hasFrequency(2); // Returns true, because 3 occurs twice

Example 2:

Input [“FrequencyTracker”, “add”, “deleteOne”, “hasFrequency”] [[], [1], [1], [1]] Output [null, null, null, false]

Explanation FrequencyTracker frequencyTracker = new FrequencyTracker(); frequencyTracker.add(1); // The data structure now contains [1] frequencyTracker.deleteOne(1); // The data structure becomes empty [] frequencyTracker.hasFrequency(1); // Returns false, because the data structure is empty

Example 3:

Input [“FrequencyTracker”, “hasFrequency”, “add”, “hasFrequency”] [[], [2], [3], [1]] Output [null, false, null, true]

Explanation FrequencyTracker frequencyTracker = new FrequencyTracker(); frequencyTracker.hasFrequency(2); // Returns false, because the data structure is empty frequencyTracker.add(3); // The data structure now contains [3] frequencyTracker.hasFrequency(1); // Returns true, because 3 occurs once

Constraints:

1 <= number <= 105 1 <= frequency <= 105 At most, 2 * 105 calls will be made to add, deleteOne, and hasFrequency in total.

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class FrequencyTracker:
    def __init__(self):
        self.map = {} 
        self.frequency = [0] * (10**5 + 1) 

    def add(self, number):
        freq = self.map.get(number, 0) 
        if freq > 0 and self.frequency[freq] > 0: 
            self.frequency[freq] -= 1
        self.map[number] = freq + 1 
        self.frequency[self.map[number]] += 1 

    def deleteOne(self, n):
        count = self.map.get(n, 0) 
        if count > 0:
            self.frequency[count] -= 1 
            if count == 1:
                del self.map[n] 
            else:
                self.map[n] = count - 1 
                self.frequency[self.map[n]] += 1 

    def hasFrequency(self, number):
        return number < len(self.frequency) and self.frequency[number] > 0

Problem Classification

Domain Categorization: This problem falls under the category of “Data Structures and Algorithms” - more specifically, it deals with the implementation of a custom data structure to perform specific operations efficiently. This kind of problem is often seen in interviews for software engineering roles where a good grasp of basic data structures, their properties, and their manipulation is essential.

‘What’ Components:

Data Structure Creation: We need to create a data structure - the FrequencyTracker class. This involves defining certain methods that operate on this structure.
Adding Elements: The add method should add a number to the data structure.
Deleting Elements: The deleteOne method should delete one occurrence of a number from the data structure. If the number is not present, no operation is performed.
Frequency Query: The hasFrequency method should return a boolean value depending on whether any number in the data structure occurs a given number of times.

Problem Classification: This is a data structure design problem, which requires the design of a data structure that supports specific operations. The solution needs to take into account the constraints and requirements of these operations in order to provide the most efficient implementation. This may involve combining existing data structures in novel ways, or coming up with entirely new structures. As such, it requires a solid understanding of existing data structures and algorithms, as well as creativity and problem-solving skills.

The problem can also be classified as a frequency count problem, which is a common type of problem in the field of data structures and algorithms. These types of problems involve keeping track of the frequency of elements in a data structure. They often require the use of hash tables or similar data structures to track frequencies.

Language Agnostic Coding Drills

Distinct Concepts:
a. Class and Object-Oriented Programming: This code defines a class FrequencyTracker that contains methods and data members. Understanding the concept of classes, objects, and encapsulation is fundamental to understanding this code.
b. Using Dictionaries: Dictionaries (also known as hash maps or associative arrays) are used to store the frequency of numbers in the input.
c. Using Arrays: An array is used to store the counts of frequencies. The code uses array indexing to access elements.
d. Method Definitions and Invocations: Methods are defined within the class to perform specific operations. Understanding how to define and call methods is vital.
e. Conditional Statements: The if statement is used to check conditions and alter the program flow based on those conditions.
Coding Drills in Order of Difficulty:
a. Class and Object-Oriented Programming: Understanding how to create classes and define methods inside them is a basic skill required for object-oriented programming. It allows encapsulating data and the methods that operate on them together.
b. Using Dictionaries: Using dictionaries is a fundamental skill in Python and many other languages. It is more difficult than the previous concept because dictionaries can be complex and require understanding hashing and key-value storage.
c. Using Arrays: Using arrays is a slightly more complex concept, as it involves understanding how arrays are indexed and how to manipulate array elements.
d. Method Definitions and Invocations: Understanding how to define methods and call them is essential in any programming language. It is more complex than the previous concepts because it requires an understanding of how methods are scoped and how parameters are passed.
e. Conditional Statements: Understanding conditional statements and control flow is slightly more complex, as it involves understanding how to alter the flow of a program based on certain conditions.
Problem-solving Approach:
a. Understand the Problem: The first step is to understand the problem statement. We need to design a class that can add elements, remove elements, and check whether an element with a certain frequency exists.
b. Design the Data Structures: We need two data structures: a dictionary to store the frequency of each element, and an array to store the frequency of frequencies.
c. Implement the Methods: Implement methods for adding, deleting, and querying elements. The ‘add’ method increases the frequency count of a number, the ‘deleteOne’ method decreases it, and the ‘hasFrequency’ method checks whether any number exists with a specific frequency. We need to ensure that both our dictionary and our frequency array are updated correctly with each operation.
d. Test the Implementation: Once the methods have been implemented, we need to test them to ensure they work as expected. This involves creating an instance of our class and invoking its methods with various inputs.

The understanding and implementation of these concepts lead to the final solution of the problem.

Targeted Drills in Python

Coding Drills:

a. Class and Object-Oriented Programming:

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class SimpleClass:
    def __init__(self):
        self.data = []
    def add(self, item):
        self.data.append(item)
my_object = SimpleClass()
my_object.add("Hello")
print(my_object.data)

b. Using Dictionaries:

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my_dict = {}
my_dict['apple'] = 1
my_dict['banana'] = 2
print(my_dict)

c. Using Arrays:

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my_array = [1, 2, 3, 4, 5]
print(my_array[2])
my_array.append(6)
print(my_array)

d. Method Definitions and Invocations:

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def my_function(arg):
    print(arg)
my_function("Hello World")

e. Conditional Statements:

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value = 10
if value > 5:
    print("Value is greater than 5")
else:
    print("Value is not greater than 5")

Problem-Specific Drills:

a. Handling Frequencies with Dictionaries and Arrays:

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frequency_map = {}
frequency_map['apple'] = 1
frequency_map['banana'] = 2
frequency_array = [0] * 5
frequency_array[frequency_map['apple']] += 1
print(frequency_map)
print(frequency_array)

In our problem, we need to maintain the count of each number and how many numbers have a certain count. This is crucial to be able to perform operations like adding, deleting and checking frequencies quickly.

Assembly:
The above coding drills collectively create the entire functionality of the FrequencyTracker class.
a. Firstly, initialize the class with a map and frequency array (as shown in the Class and Object-Oriented Programming drill).
b. Then, when adding a number, use the drills related to dictionaries and arrays to update the frequency map and frequency array correctly.
c. Similarly, when deleting a number, reduce its count in the frequency map and frequency array using the concepts of dictionaries and arrays.
d. Finally, for checking the existence of a frequency, the knowledge of array indexing and condition checking comes into play.

These pieces, when integrated in the right order, can be used to construct the FrequencyTracker class that solves our initial problem.