Introduction to Data Structures: Types and Algorithms

Introduction

Data structures are fundamental concepts in computer science that facilitate the organization, management, and storage of data in a way that enables efficient access and modification. They serve as the backbone of algorithms, which are step-by-step procedures or formulas for solving problems. Understanding various data structures, such as arrays, linked lists, stacks, queues, trees, and graphs, is crucial for any aspiring programmer or software engineer. Each data structure has its own strengths and weaknesses, and the choice of which to use can significantly affect the performance and efficiency of algorithms. For instance, while arrays offer fast access to elements due to their contiguous memory allocation, linked lists provide more flexibility in terms of insertion and deletion operations. This tutorial aims to introduce these essential concepts, providing you with a solid foundation for tackling more advanced topics in computer science and software development.

In this tutorial, we will explore the types of data structures and their respective algorithms, emphasizing practical applications and real-world examples. Starting with the basic types of data structures, we will delve into how they are implemented and utilized in various programming languages, especially focusing on languages like Python, Java, and C++. We will also examine algorithmic complexity, which is vital for evaluating the efficiency of different data structures and algorithms. By understanding Big O notation, you will be able to analyze how the performance of algorithms changes with input size. Furthermore, we will discuss common algorithms associated with each data structure, including searching and sorting algorithms, which are essential for data manipulation tasks. By the end of this tutorial, you will have a comprehensive understanding of data structures and algorithms, empowering you to make informed decisions in your programming endeavors.

Importance of Data Structures in Programming

Why Data Structures Matter

Data structures form the backbone of efficient programming, enabling developers to organize and manipulate data effectively. Their importance cannot be overstated, as they directly influence the performance and scalability of applications. When data is structured appropriately, tasks such as searching, sorting, and filtering become significantly faster and less resource-intensive. Conversely, poorly chosen data structures can lead to inefficiencies that can slow down programs and lead to increased costs in terms of time and computing power. Understanding the role of data structures is therefore crucial for any programmer aiming to build robust and efficient software solutions.

Using the right data structure can lead to optimal algorithm implementation. For instance, utilizing a hash table allows for average-case constant time complexity for lookups, while a linked list may offer better performance for frequent insertions and deletions. Additionally, different data structures come with unique strengths and weaknesses depending on the context of their use. For example, arrays provide fast access times at the cost of fixed size, while trees can represent hierarchical data efficiently but may introduce additional complexities in traversal and management. Understanding these trade-offs is essential in making informed decisions during the software development process.

In practice, real-world applications often demonstrate the importance of selecting appropriate data structures. For instance, a social media platform may use graphs to represent user connections, enabling efficient exploration of relationships. Alternatively, an e-commerce website might implement a priority queue for managing product recommendations based on user behavior. By analyzing case scenarios and selecting the right data structures, developers can significantly enhance application performance and user experience.

• Choose data structures based on use case requirements.
• Understand time and space complexities.
• Test performance with different data structures.
• Keep scalability in mind for future growth.
• Review and refactor code to improve efficiency.

This code snippet demonstrates a simple implementation of a singly linked list in Python. It includes methods for inserting elements and displaying the list contents.

class Node:
    def __init__(self, value):
        self.value = value
        self.next = None

class LinkedList:
    def __init__(self):
        self.head = None
    
    def insert(self, value):
        new_node = Node(value)
        if not self.head:
            self.head = new_node
        else:
            current = self.head
            while current.next:
                current = current.next
            current.next = new_node

    def display(self):
        current = self.head
        while current:
            print(current.value)
            current = current.next

# Example of usage
ll = LinkedList()
ll.insert(1)
ll.insert(2)
ll.display()

When the code is executed, it will display the values '1' and '2', showcasing how elements can be added and traversed in a linked list.

Feature	Description	Example
Efficiency	Reduces time for data operations	Using a hash table for fast lookups
Flexibility	Adapts to varying data sizes	Linked lists allow dynamic data storage
Organization	Organizes data logically	Trees represent hierarchical relationships
Accessibility	Facilitates quick data access	Arrays provide direct index-based access

Overview of Common Data Structures

Types of Data Structures

Data structures can be broadly classified into two categories: primitive and non-primitive. Primitive data structures, such as integers, floats, and characters, serve as the building blocks for more complex structures. Non-primitive data structures, on the other hand, include arrays, linked lists, stacks, queues, trees, and graphs. Each of these structures is designed to organize data in a specific way, addressing various problems faced in programming and data management. Understanding the distinctions between these categories is vital for selecting the appropriate structure for any given task.

Among the non-primitive data structures, arrays stand out for their simplicity and efficiency in storing fixed-size sequences of elements. They allow for quick access through indexing, making them suitable for scenarios where data size is known beforehand. Linked lists, in contrast, provide a more dynamic option, allowing for easy insertion and deletion of elements without the overhead of resizing. Stacks and queues, which are built on top of arrays or linked lists, introduce specific ordering rules, facilitating operations like backtracking in algorithms and managing tasks in a first-in-first-out manner, respectively.

Real-world applications of these data structures can be seen in various domains. For instance, arrays are commonly used in image processing to store pixel values, while linked lists may be employed in music playlist management, where users can easily add or remove songs. Stacks are crucial in undo operations in text editors, whereas queues can be found in web servers to handle incoming requests. By understanding these common data structures, developers can make informed decisions that lead to more efficient and maintainable code.

• Familiarize yourself with basic data structures.
• Understand when to use each structure.
• Practice implementing data structures from scratch.
• Analyze real-world applications of data structures.
• Review common algorithms associated with each structure.

This Python code snippet illustrates a simple stack implementation. It allows for pushing and popping elements while checking if the stack is empty.

class Stack:
    def __init__(self):
        self.stack = []

    def push(self, item):
        self.stack.append(item)

    def pop(self):
        if not self.is_empty():
            return self.stack.pop()
        return None

    def is_empty(self):
        return len(self.stack) == 0

# Example of usage
s = Stack()
s.push(1)
s.push(2)
print(s.pop())  # Outputs: 2
print(s.pop())  # Outputs: 1

When executed, the code will output '2' followed by '1', demonstrating the last-in-first-out (LIFO) behavior typical of stack structures.

Data Structure	Use Case	Advantages
Array	Storing fixed data collections	Fast access times and simple structure
Linked List	Dynamic data management	Efficient insertions and deletions
Stack	Managing function calls	LIFO order operations
Queue	Handling tasks in order	FIFO processing of data

Linear Data Structures: Arrays and Linked Lists

Understanding Arrays

Arrays are one of the most fundamental data structures in programming, providing a way to store a collection of elements of the same type in a contiguous block of memory. They allow for efficient access and manipulation of data, with the primary advantage being their ability to access elements in constant time due to direct indexing. However, arrays also have limitations, such as a fixed size that must be defined at the time of creation, which can lead to inefficiencies when the data size fluctuates significantly during runtime.

When working with arrays, it is crucial to consider both the time and space complexity of operations. For instance, accessing an element is O(1), while inserting or deleting an element can take O(n) time due to the need to shift elements. Best practices when using arrays include preallocating space when possible, minimizing resizing operations, and using dynamic arrays (like Python's list) which handle resizing automatically. Additionally, understanding when to use arrays versus other structures can significantly impact the performance of your application.

In practical applications, arrays are widely used in scenarios requiring fast access to elements, such as image processing, where pixel data is often stored in arrays for quick manipulation. For example, a common operation might involve flipping an image, where accessing pixel values directly via their indices makes the process highly efficient. Another example is sorting algorithms, which frequently utilize arrays to organize data due to their efficient access patterns. By mastering arrays, developers can build more responsive and efficient applications.

• Use arrays for fixed-size data collections.
• Leverage built-in functions for array manipulation.
• Minimize resizing to enhance performance.
• Understand array limitations regarding dynamic data.
• Utilize multi-dimensional arrays for complex data representation.

This code implements the merge sort algorithm using arrays in Python. It recursively divides the array into halves before merging them in sorted order.

def merge_sort(arr):
    if len(arr) > 1:
        mid = len(arr) // 2  # Finding the mid of the array
        left_half = arr[:mid]  # Dividing the elements into 2 halves
        right_half = arr[mid:]  

        merge_sort(left_half)  # Sorting the left half
        merge_sort(right_half)  # Sorting the right half

        i = j = k = 0

        while i < len(left_half) and j < len(right_half):
            if left_half[i] < right_half[j]:
                arr[k] = left_half[i]
                i += 1
            else:
                arr[k] = right_half[j]
                j += 1
            k += 1

        while i < len(left_half):
            arr[k] = left_half[i]
            i += 1
            k += 1

        while j < len(right_half):
            arr[k] = right_half[j]
            j += 1
            k += 1

# Example of usage
arr = [38, 27, 43, 3, 9, 82, 10]
merge_sort(arr)
print(arr)  # Outputs: [3, 9, 10, 27, 38, 43, 82]

Upon execution, the code will output the sorted array: [3, 9, 10, 27, 38, 43, 82], demonstrating the efficiency of the merge sort algorithm.

Array Type	Description	Use Case
Static Array	Fixed size with predefined length	Storing known quantities like days of the week
Dynamic Array	Resizes automatically as required	Storing user-generated content like comments
Multi-Dimensional Array	Array of arrays for complex data	Storing matrix data in scientific computations

Non-linear Data Structures: Trees and Graphs

Understanding Trees

Trees are hierarchical data structures that consist of nodes connected by edges. Unlike linear data structures such as arrays and linked lists, trees allow for more complex relationships among data. Each tree has a root node, from which all other nodes branch out, creating a parent-child relationship. This structure is particularly useful for representing data with a natural hierarchy, such as organizational charts or file systems. Trees can be classified into various types such as binary trees, binary search trees, and AVL trees, each serving distinct purposes and optimizing different operations.

Binary trees are perhaps the most commonly used type, where each node has at most two children. This property allows for efficient search, insertion, and deletion operations, typically in O(log n) time for balanced trees. Binary search trees, a subtype, maintain sorted order which facilitates quick look-up operations. For example, adding an integer to a binary search tree involves placing it in the correct position to maintain order. In contrast, AVL trees, which are self-balancing binary search trees, ensure that the tree remains balanced after every insertion or deletion, preventing performance degradation.

In practical applications, trees find use in various domains. For instance, in web browsers, the Document Object Model (DOM) represents the page’s structure as a tree, allowing scripts to manipulate HTML elements efficiently. Similarly, file systems use trees to organize directories and files hierarchically. Below is a simple implementation of a binary tree in Python, demonstrating how to insert nodes and perform in-order traversal.

• Hierarchical data representation
• Efficient searching
• Dynamic data structure
• Easy to implement with recursion
• Supports various traversal methods

This code snippet demonstrates a simple binary tree implementation in Python, including methods for insertion and in-order traversal.

class Node:
    def __init__(self, key):
        self.left = None
        self.right = None
        self.val = key

class BinaryTree:
    def __init__(self):
        self.root = None

    def insert(self, key):
        if self.root is None:
            self.root = Node(key)
        else:
            self._insert_rec(self.root, key)

    def _insert_rec(self, node, key):
        if key < node.val:
            if node.left is None:
                node.left = Node(key)
            else:
                self._insert_rec(node.left, key)
        else:
            if node.right is None:
                node.right = Node(key)
            else:
                self._insert_rec(node.right, key)

    def inorder_traversal(self, node):
        return self.inorder_traversal(node.left) + [node.val] + self.inorder_traversal(node.right) if node else []

bt = BinaryTree()
bt.insert(10)
bt.insert(5)
bt.insert(15)
print(bt.inorder_traversal(bt.root))

The output of the in-order traversal of the tree would be [5, 10, 15], representing the nodes in sorted order.

Feature	Description	Example
Node	Basic unit of a tree	Contains data and links to children
Root	Top node in a tree	The starting point of tree traversal
Leaf	Node with no children	End point in any path of the tree
Height	Longest path from root to leaf	Determines tree complexity

Exploring Graphs

Graphs are versatile data structures comprising nodes (or vertices) connected by edges. They can represent various systems, such as social networks, transportation systems, and interconnected web pages. A significant characteristic of graphs is that they can be directed or undirected: directed graphs have edges with a direction, while undirected graphs represent symmetric relationships. The flexibility of graphs allows for modeling complex relationships beyond hierarchical structures, making them a critical tool in computer science.

Graph traversal algorithms like Depth-First Search (DFS) and Breadth-First Search (BFS) are essential for exploring graph structures. DFS explores as far as possible along each branch before backtracking, making it useful for pathfinding and analyzing connectivity. On the other hand, BFS explores all neighbors at the present depth prior to moving on to nodes at the next depth level, which is useful for finding the shortest path in unweighted graphs. Understanding these algorithms is crucial for optimizing solutions in various applications, from routing on the internet to game development.

In real-world applications, graphs play a vital role in numerous domains. For example, social media platforms model user relationships as graphs, enabling features like friend recommendations. Additionally, search engines use graphs to rank web pages based on their interconnections. Below is a simple implementation of a graph in Python, showcasing how to add edges and perform BFS traversal to explore its structure.

• Model complex relationships
• Directed vs. undirected graphs
• Graph traversal techniques
• Applications in network analysis
• Support for weighted edges

This code snippet demonstrates a simple graph implementation in Python, including methods for adding edges and performing BFS traversal.

class Graph:
    def __init__(self):
        self.graph = {}

    def add_edge(self, u, v):
        if u not in self.graph:
            self.graph[u] = []
        self.graph[u].append(v)

    def bfs(self, start):
        visited = set()
        queue = [start]
        while queue:
            vertex = queue.pop(0)
            if vertex not in visited:
                visited.add(vertex)
                queue.extend(neighbor for neighbor in self.graph.get(vertex, []) if neighbor not in visited)
        return visited

g = Graph()
g.add_edge(1, 2)
g.add_edge(1, 3)
g.add_edge(2, 4)
g.add_edge(3, 4)
print(g.bfs(1))

The BFS traversal starting from vertex 1 would output {1, 2, 3, 4}, indicating all reachable nodes from the starting point.

Feature	Description	Example
Vertex	Basic unit of a graph	Represents an entity
Edge	Connection between vertices	Defines relationships
Directed Graph	Edges have direction	Modeling one-way relationships
Weighted Graph	Edges have weights	Cost or distance between nodes

Hash Tables and Their Applications

Introduction to Hash Tables

A hash table is a data structure that implements an associative array, a structure that can map keys to values. They are designed for efficient data retrieval, providing average-case constant time complexity O(1) for lookups, insertions, and deletions. This efficiency is achieved by employing a hash function to compute an index into an array of buckets or slots, from which the desired value can be found. The design of the hash function is critical, as it determines how well the keys are distributed across the available slots.

Despite their efficiency, hash tables can encounter issues such as collisions, where two keys hash to the same index. There are various strategies to resolve collisions, including chaining, where each slot contains a linked list of entries that hash to the same index, and open addressing, where a probing sequence is used to find the next available slot. Understanding these collision resolution techniques is essential for optimizing the performance of hash tables, especially in applications where the hash table may become densely populated.

Hash tables are widely used in various applications due to their efficiency and versatility. For instance, they are commonly used in implementing caches, databases, and sets. In programming languages, hash tables can be found in dictionaries or maps, enabling quick lookups of values based on keys. Below is an implementation of a simple hash table in Python, demonstrating basic operations such as insertion and retrieval of values.

• Fast data retrieval
• Efficient memory usage
• Handles dynamic data
• Supports associative arrays
• Useful in implementing caches

This code snippet illustrates a basic hash table implementation in Python, including methods for inserting values and retrieving them by key.

class HashTable:
    def __init__(self):
        self.size = 256
        self.table = [[] for _ in range(self.size)]

    def hash(self, key):
        return hash(key) % self.size

    def insert(self, key, value):
        index = self.hash(key)
        for kv in self.table[index]:
            if kv[0] == key:
                kv[1] = value
                return
        self.table[index].append([key, value])

    def get(self, key):
        index = self.hash(key)
        for kv in self.table[index]:
            if kv[0] == key:
                return kv[1]
        return None

ht = HashTable()
ht.insert('name', 'Alice')
ht.insert('age', 25)
print(ht.get('name'))

The output for the retrieval of the key 'name' would be 'Alice', showcasing the efficiency of hash tables.

Feature	Description	Example
Key	Identifier for value	A string or integer
Value	Data associated with key	User information, settings, etc.
Collision Resolution	Methods to handle key conflicts	Chaining or open addressing
Load Factor	Ratio of entries to slots	Determines resizing strategy

Algorithms: Introduction and Importance

Understanding Algorithms

Algorithms are a series of steps or procedures that provide a solution to a specific problem. They are integral to programming and computer science, enabling efficient data processing, manipulation, and analysis. An algorithm takes an input, processes it through defined steps, and produces an output. This systematic approach not only guides programmers in writing effective code but also helps in optimizing performance, making algorithms a cornerstone of software development.

The significance of algorithms extends beyond mere functionality; they influence the efficiency and scalability of applications. Different algorithms can yield different performance results depending on the size and nature of the input data. For instance, sorting algorithms like QuickSort and MergeSort each have distinct time and space complexities. Understanding these complexities is vital for selecting the right algorithm for a given situation, especially in resource-constrained environments where performance is crucial.

Real-world applications of algorithms are ubiquitous, from simple tasks like searching through a list to complex processes such as machine learning and data mining. For example, search engines utilize algorithms to rank web pages based on relevance and authority. Similarly, routing algorithms determine the most efficient paths in networks. Below is an implementation of a basic sorting algorithm (Bubble Sort) in Python, illustrating the concept of algorithms in action.

• Step-by-step problem solving
• Foundation of computer science
• Efficiency impacts performance
• Critical for data processing
• Variety of applications in tech

This code snippet demonstrates a basic Bubble Sort algorithm in Python for sorting an array.

def bubble_sort(arr):
    n = len(arr)
    for i in range(n):
        for j in range(0, n-i-1):
            if arr[j] > arr[j+1]:
                arr[j], arr[j+1] = arr[j+1], arr[j]
    return arr

numbers = [64, 34, 25, 12, 22, 11, 90]
sorted_numbers = bubble_sort(numbers)
print(sorted_numbers)

The output will be a sorted array: [11, 12, 22, 25, 34, 64, 90], illustrating how the algorithm processes input to produce the desired output.

Term	Definition	Example
Algorithm	Set of rules for solving a problem	Searching or sorting data
Complexity	Measure of resource usage	Time and space requirements
Recursive Algorithm	Solves problem by solving smaller instances	Factorial calculation
Iterative Algorithm	Repeats steps until a condition is met	Fibonacci sequence generation

Common Algorithms for Data Manipulation

Sorting Algorithms

Sorting algorithms are fundamental to data manipulation, allowing data to be organized in a specific order, which enhances data retrieval and analysis. Common sorting algorithms include Quick Sort, Merge Sort, and Bubble Sort. Each algorithm has unique characteristics, performance metrics, and scenarios where it excels or falters. Understanding these algorithms is essential for developers, as they directly impact the efficiency of applications that require data organization. For instance, sorting can improve search algorithms, enabling faster data access, which is critical in applications ranging from databases to user interfaces.

Quick Sort, a divide-and-conquer algorithm, is renowned for its efficiency with large datasets, boasting an average time complexity of O(n log n). In contrast, Merge Sort guarantees O(n log n) performance consistently, making it suitable for linked lists or when stability is a priority. Meanwhile, Bubble Sort, while intuitive and easy to implement, is often deemed inefficient for larger datasets due to its O(n²) average complexity. Understanding these nuances allows developers to select the most appropriate sorting algorithm based on specific data characteristics and application requirements.

In practical scenarios, sorting algorithms are frequently employed in applications like e-commerce platforms, where product listings need to be sorted based on price, ratings, or other attributes. For instance, in Python, one can easily implement a Quick Sort algorithm. Below is a simple code example showcasing how Quick Sort can be applied to sort a list of numbers. By optimizing the choice of pivot and employing recursion, developers can enhance performance and execution speed in real-world applications.

code_example

• Choose the right algorithm based on data size
• Consider stability requirements
• Optimize for best and worst-case scenarios
• Profile performance with real datasets
• Avoid unnecessary comparisons in Bubble Sort

This Python code snippet demonstrates the Quick Sort algorithm applied to a list of numbers. The function recursively divides the list based on a pivot element, ensuring efficient sorting.

def quick_sort(arr):
    if len(arr) <= 1:
        return arr
    pivot = arr[len(arr) // 2]
    left = [x for x in arr if x < pivot]
    middle = [x for x in arr if x == pivot]
    right = [x for x in arr if x > pivot]
    return quick_sort(left) + middle + quick_sort(right)

numbers = [3, 6, 8, 10, 1, 2, 1]
sorted_numbers = quick_sort(numbers)
print(sorted_numbers)

When executed, this code will output the sorted list: [1, 1, 2, 3, 6, 8, 10].

Algorithm	Time Complexity	Use Case
Quick Sort	O(n log n) average	Large datasets
Merge Sort	O(n log n)	Linked lists, stability required
Bubble Sort	O(n²)	Small datasets or educational purposes

Frequently Asked Questions

What is the best way to learn data structures and algorithms?

The best way to learn data structures and algorithms is through a combination of theory and practical application. Start with understanding the basic concepts through books or online courses. Once you grasp the fundamentals, practice regularly on coding platforms like LeetCode or HackerRank. Focus on solving a variety of problems to see how different data structures can be applied. Additionally, consider joining programming study groups or forums to discuss challenges and solutions with peers.

Can you explain time and space complexity in simple terms?

Time complexity refers to how the runtime of an algorithm grows with the size of the input data, usually expressed in Big O notation. Space complexity, on the other hand, measures how much additional memory an algorithm needs as the input size increases. For instance, a simple loop that goes through an array has a time complexity of O(n) and a space complexity of O(1) since it only uses a fixed amount of extra space regardless of the input size. Understanding these concepts helps you evaluate and choose more efficient algorithms.

What are some common mistakes to avoid when working with data structures?

Common mistakes include not considering edge cases, such as empty data sets or very large inputs, which can lead to unexpected behavior. Another mistake is using the wrong data structure for a problem; for example, using an array when a linked list would be more efficient for frequent insertions and deletions. Additionally, forgetting to account for time and space complexity can result in inefficient solutions. Always analyze your choices critically and run tests to validate your implementations.

How do I choose the right data structure for my project?

Choosing the right data structure depends on the specific requirements of your project. Consider factors such as the types of operations you need to perform (insertion, deletion, search), the frequency of these operations, and the size of the data. For example, if you need fast lookups, a hash table may be ideal, while a binary search tree could be better for maintaining sorted data. Evaluate the pros and cons of each structure in the context of your application to make an informed decision.

What resources can I use to practice my skills in data structures and algorithms?

Several excellent resources are available for practicing data structures and algorithms. Websites like GeeksforGeeks offer tutorials and coding challenges, while LeetCode provides a vast collection of problems sorted by difficulty and topic. Additionally, the free online course 'Data Structures and Algorithms' offered by Coursera can help you build a solid foundation. Exploring these resources will enhance your understanding and problem-solving abilities.

Conclusion

In this journey through data structures and algorithms, we've explored foundational concepts critical for effective programming and software development. We began by defining data structures, emphasizing their role in organizing and managing data efficiently. Understanding the various types, such as arrays, linked lists, stacks, queues, trees, and graphs, allows developers to choose the most suitable structure based on their specific needs. We then delved into algorithms, examining their importance in manipulating these structures to perform tasks such as searching, sorting, and traversing data. The interplay between data structures and algorithms is crucial; a well-chosen data structure can significantly optimize algorithm performance, leading to faster execution and reduced resource consumption. Additionally, we highlighted the significance of time and space complexity in evaluating algorithm efficiency, providing a framework for assessing trade-offs in performance. The knowledge acquired not only equips you with the tools to write effective code but also fosters a deeper understanding of computational theory that underpins modern computer science.

As we conclude this introduction to data structures and algorithms, several key takeaways can guide your next steps. First, practice is essential; apply the concepts learned by working on real-life coding problems or projects. Utilize platforms like LeetCode or HackerRank to hone your skills through practical challenges. Second, familiarize yourself with the implementation of various data structures in your preferred programming language, as this will deepen your understanding and enhance your problem-solving capabilities. Third, always consider the context of your data; the right data structure can lead to significant performance improvements. Lastly, stay curious and continue exploring advanced topics, such as graph algorithms or dynamic programming, to further elevate your programming prowess. By integrating these strategies into your learning process, you’ll be well-equipped to tackle complex programming challenges and contribute effectively to software development projects.

Further Resources

• GeeksforGeeks - This platform offers a wealth of tutorials, articles, and coding challenges covering a wide array of data structures and algorithms, making it an invaluable resource for learners of all levels.
• LeetCode - LeetCode is a popular online platform where you can practice coding problems specifically focused on data structures and algorithms, allowing you to sharpen your skills through hands-on experience.
• Coursera - Data Structures and Algorithms Specialization - This free online course offered by Coursera provides a structured approach to mastering data structures and algorithms, featuring video lectures, quizzes, and coding assignments.