Course Overview

What this Data Structures and Algorithms course covers, how to use it, prerequisites.

About This Course

Course goal: Build a strong understanding of data structures, algorithm design, complexity analysis, problem-solving patterns, and interview-level implementation. Language examples: Core ideas are language-neutral. C++ examples are used for concise syntax, with Python versions of core algorithms and a cross-language table in Module 4. Learning rule: Every lesson covers prerequisites, intuitive explanation, a visual representation, the formal definition, operations, complexity, a complete worked example with its dry run, edge cases, common mistakes, practical use, an interview-style problem, practice questions and a quiz.

Learning Outcomes

Analyse the time and space complexity of iterative and recursive code, including amortized costs and recurrences.

Choose and implement arrays, linked lists, stacks, queues, hash tables, trees, heaps, tries and union-find for a given access pattern.

Apply searching, sorting, recursion, backtracking, divide and conquer, greedy algorithms and dynamic programming — and prove them correct.

Model problems as graphs and apply traversal, topological sorting, shortest paths, spanning trees, connectivity, flow and matching.

Use range-query structures (prefix sums, Fenwick and segment trees, sparse tables) and string algorithms (KMP, Z, hashing, suffix arrays, Manacher).

Recognise the 45 standard problem-solving patterns, select algorithms from constraints, and test solutions with brute-force stress tests.

How the Examples Were Checked

This course was written from the Data Structures and Algorithms blueprint: its outline, definitions, complexity tables and code snippets are kept, and each topic list was expanded into a full lesson. Every program in the course is complete and was actually run; the output printed under it is the real output.

C++ programs (C++17) were compiled with g++ 11.2 on Ubuntu 22.04 (WSL2) using -Wall -Wextra -Wshadow -Werror and both AddressSanitizer and UndefinedBehaviorSanitizer, so they compile cleanly and showed no memory errors, leaks or undefined behaviour on these runs.

Python versions of core algorithms ran on CPython 3.13.1.

Wherever a fast algorithm has an obvious slow counterpart, the program checks itself against it on hundreds or thousands of random inputs with a fixed seed (for example Dijkstra against Bellman–Ford, the AVL tree against std::set, Dinic against Edmonds–Karp, the segment tree against a plain array).

Two outputs depend on the machine and are labelled as such: the cache-locality timing ratio in Module 56 and the randomly based rolling hash in Module 44 (which prints only match positions).

The blueprint's own Part I (the website's UI and navigation requirements) describes how this course is presented rather than course content, so it is not repeated as a lesson. Its Part XI pattern library is Module 64, and its assessment and capstone material is Module 65.

Course Roadmap

Introduction to DSA Mathematics for DSA C++ Toolkit for DSA Arrays and Dynamic Arrays Queues, Deques, and Circular Buffers Hashing and Hash Tables Trees: Fundamentals Binary Search Trees Balanced Search Trees Heaps and Priority Queues Tries and Prefix Trees Disjoint Set Union (Union-Find) Recursion and Backtracking Divide and Conquer Dynamic Programming (DP)

Prefix Sums, Difference Arrays, and Range Queries Monotonic Stack and Monotonic Queue Bit Manipulation and Bitmasking Topological Sorting and DAG Algorithms Minimum Spanning Trees Cycle Detection and Connectivity Advanced Graph Algorithms Grid and State-Space Graphs Fenwick Tree (Binary Indexed Tree) Sparse Tables and RMQ Mo's Algorithm and Offline Queries Square Root Decomposition

Persistent and Functional Data Structures Advanced Trees and Specialized Structures Prefix Function, KMP, and Z Algorithm Rolling Hash and Rabin–Karp

Suffix Arrays, LCP, and Suffix Structures Manacher and Palindromic Structures Advanced Sequence Algorithms Combinatorics and Counting Geometry for DSA Probability and Randomized Algorithms Advanced Greedy and Exchange Proofs Advanced Dynamic Programming Branch and Bound and Exact Search

Randomized, Approximation, and Online Algorithms Parallel and Cache-Aware Algorithms Reading and Modeling a Problem Constraint-Driven Algorithm Selection Correctness and Proof Writing Debugging and Test Design C++ Implementation Safety Interview DSA Roadmap Problem Bank and Progression Problem-Solving Pattern Library Assessment and Capstone Projects

Prerequisites

Comfort with one programming language (variables, loops, functions, arrays). Reading C++ helps, and Module 4 covers the C++ features the course uses. School algebra is enough for the mathematics; Module 3 reviews logarithms, sums and modular arithmetic.