Data Structures & Algorithms

Complete syllabus

Every chapter and lesson

1. 01

   Chapter 1 · 3 lessons

   Algorithmic Foundations

   1. 1.1

      Algorithm analysis & Big-O

      9 min · Quick check

      Lesson goal: By the end you can analyze the efficiency of algorithms using Big-O notation.

      • Understand the definition of algorithm analysis.
      • Learn the concept of Big-O notation and its significance.
      • Identify different time complexities and their implications.
      • Compare the efficiency of various algorithms using Big-O.
   2. 1.2

      Recursion

      9 min · Quick check

      Lesson goal: By the end you can apply recursion to solve problems effectively.

      • Define recursion and understand its basic principles.
      • Identify base cases and recursive cases in recursive functions.
      • Explore common examples of recursive algorithms.
      • Analyze the performance and limitations of recursive solutions.
   3. 1.3

      Correctness & invariants

      8 min · Quick check

      Lesson goal: By the end you can demonstrate the correctness of algorithms using invariants.

      • Define correctness in the context of algorithms.
      • Understand the role of invariants in proving correctness.
      • Learn how to establish and use invariants in algorithm design.
      • Apply invariants to verify the correctness of specific algorithms.
2. 02

   Chapter 2 · 3 lessons

   Linear Structures

   1. 2.1

      Arrays & dynamic arrays

      9 min · Quick check

      Lesson goal: By the end you can define arrays and dynamic arrays, and explain their characteristics and uses.

      • Define arrays and dynamic arrays.
      • Explain the difference between static and dynamic arrays.
      • Discuss memory allocation for dynamic arrays.
      • Identify use cases for arrays and dynamic arrays.
   2. 2.2

      Linked lists

      8 min · Quick check

      Lesson goal: By the end you can define linked lists and describe their structure and advantages.

      • Define linked lists and their components (nodes, pointers).
      • Explain the advantages of linked lists over arrays.
      • Discuss different types of linked lists (singly, doubly, circular).
      • Identify use cases for linked lists.
   3. 2.3

      Stacks & queues

      8 min · Quick check

      Lesson goal: By the end you can define stacks and queues, and illustrate their operations and applications.

      • Define stacks and queues and their key operations (push, pop, enqueue, dequeue).
      • Explain the Last In First Out (LIFO) principle for stacks and the First In First Out (FIFO) principle for queues.
      • Discuss applications of stacks and queues in real-world scenarios.
      • Illustrate stack and queue implementations using arrays or linked lists.
3. 03

   Chapter 3 · 3 lessons

   Sorting & Searching

   1. 3.1

      Elementary sorts

      8 min · Quick check

      Lesson goal: By the end you can define elementary sorting algorithms and explain their basic principles.

      • Define elementary sorts such as Bubble Sort, Selection Sort, and Insertion Sort.
      • Explain the time complexity of each elementary sort.
      • Discuss the advantages and disadvantages of using elementary sorts.
   2. 3.2

      Merge & quicksort

      9 min · Quick check

      Lesson goal: By the end you can implement and compare the Merge Sort and Quick Sort algorithms.

      • Define Merge Sort and Quick Sort and their divide-and-conquer approach.
      • Implement Merge Sort and Quick Sort algorithms in code.
      • Compare the efficiency of Merge Sort and Quick Sort in terms of time complexity.
   3. 3.3

      Binary search

      8 min · Quick check

      Lesson goal: By the end you can describe the Binary Search algorithm and apply it to sorted data.

      • Define Binary Search and its requirements for operation.
      • Explain the time complexity of Binary Search.
      • Demonstrate how to implement Binary Search on a sorted array.
4. 04

   Chapter 4 · 3 lessons

   Trees

   1. 4.1

      Binary trees & traversals

      9 min · Quick check

      Lesson goal: By the end you can understand the structure and traversal methods of binary trees.

      • Define binary trees and their properties.
      • Explain different types of tree traversals: in-order, pre-order, and post-order.
      • Illustrate the process of traversing a binary tree using examples.
   2. 4.2

      Binary search trees

      9 min · Quick check

      Lesson goal: By the end you can identify and implement binary search trees.

      • Define binary search trees and their characteristics.
      • Discuss the importance of the binary search tree property for efficient searching.
      • Demonstrate insertion and deletion operations in a binary search tree.
   3. 4.3

      Balanced trees & heaps

      8 min · Quick check

      Lesson goal: By the end you can understand balanced trees and heaps, and their applications.

      • Define balanced trees and heaps, and explain their significance in data structures.
      • Describe common types of balanced trees, such as AVL trees and Red-Black trees.
      • Illustrate heap operations, including insertion and deletion, with examples.
5. 05

   Chapter 5 · 3 lessons

   Hashing & Maps

   1. 5.1

      Hash tables

      9 min · Quick check

      Lesson goal: By the end you can explain the concept of hash tables and their components.

      • Define what a hash table is and its purpose in data storage.
      • Explain the role of a hash function in mapping keys to indices.
      • Discuss the importance of load factor and resizing in hash tables.
   2. 5.2

      Collision handling

      8 min · Quick check

      Lesson goal: By the end you can describe various methods for handling collisions in hash tables.

      • Define what a collision is in the context of hash tables.
      • Explain separate chaining as a method for collision resolution.
      • Discuss open addressing techniques, including linear probing and quadratic probing.
   3. 5.3

      Sets & maps in practice

      8 min · Quick check

      Lesson goal: By the end you can apply sets and maps in practical scenarios.

      • Define sets and maps and their differences.
      • Demonstrate how to use sets for unique item storage.
      • Show how maps can be used for key-value pair storage in applications.
6. 06

   Chapter 6 · 3 lessons

   Graphs

   1. 6.1

      Graph representations

      8 min · Quick check

      Lesson goal: By the end you can explain the different ways to represent graphs in computer science.

      • Define a graph and its components (vertices and edges).
      • Describe the adjacency matrix representation and its characteristics.
      • Explain the adjacency list representation and its advantages.
      • Discuss other representations like edge lists and their use cases.
   2. 6.2

      BFS & DFS

      9 min · Quick check

      Lesson goal: By the end you can implement and differentiate between Breadth-First Search and Depth-First Search algorithms.

      • Define Breadth-First Search (BFS) and its use in traversing graphs.
      • Outline the steps involved in the BFS algorithm.
      • Define Depth-First Search (DFS) and its approach to graph traversal.
      • Compare and contrast BFS and DFS in terms of their applications and performance.
   3. 6.3

      Shortest paths & MSTs

      9 min · Quick check

      Lesson goal: By the end you can apply algorithms to find the shortest paths and minimum spanning trees in graphs.

      • Define shortest path and minimum spanning tree (MST) concepts.
      • Introduce Dijkstra's algorithm for finding the shortest path in weighted graphs.
      • Explain Prim's and Kruskal's algorithms for constructing minimum spanning trees.
      • Discuss the applications of shortest paths and MSTs in real-world scenarios.