Foundations
Big-O, Omega and Theta notation kept properly distinct from best, average and worst case analysis — plus amortized analysis and where asymptotics stop predicting real performance.
An Extensive Reference of Commonly Used Algorithms
Mastering Algorithms is a free, structured guide to the algorithms and data structures that actually come up — in coursework, in technical interviews, and in production code. It covers 36 topics across nine areas, each with a plain-language explanation, a complexity analysis, a worked example traced step by step, and Python you can run.
What distinguishes it is the verification. Every code listing on this site is executed before it is
published. Sorting algorithms are tested against Python's own sorted() across thousands
of randomised inputs; pattern-matching algorithms are checked against brute force; the neural
network's backpropagation is validated against numerically estimated gradients. Every worked example
is traced from the algorithm printed on the same page, so the numbers in the walkthrough are the
numbers the code actually produces.
That sounds like a low bar. It is not one most algorithm tutorials clear — and when a trace is wrong or an implementation does not match its stated complexity, the reader who is trying hardest to follow along is the one who gets stuck. In August 2026 the entire site was re-audited line by line and 58 corrections were applied. You can read more about that process on the about page.
What's Covered
Sorting
Eight algorithms from bubble sort to a complete Timsort with run detection, galloping and the merge-stack invariants — plus what standard libraries actually run, which is none of the eight.
Searching
Linear and binary search with the off-by-one traps spelled out, plus hash tables — the structure most real lookup code actually uses.
Graphs
Traversal, shortest paths and connectivity: DFS and BFS through to Dijkstra's, Bellman-Ford, Floyd-Warshall, A*, topological sort and strongly connected components.
- Dijkstra's · A* · Bellman-Ford
- Union-Find · SCC
Trees
Traversals, binary search trees, and the balancing machinery underneath them — rotations, AVL, red-black, and the B+ trees that every database index is built on.
DP & Greedy
Memoization versus tabulation, the standard DP patterns, and the matroid theory that actually answers when a greedy algorithm is guaranteed to be optimal.
Strings
KMP with its failure function derived, Rabin-Karp rolling hashes, Boyer-Moore, the Z-algorithm, and Manacher's for palindromes in linear time.
Cryptography
AES, RSA, SHA and their broken predecessors — with current guidance, including why TLS 1.3 dropped RSA key exchange and what the 2024 post-quantum standards change.
Machine Learning
From linear regression to gradient boosting and transformers, with an honest treatment of evaluation — including calibration, which most introductions skip entirely.
What Each Chapter Gives You
- A plain-language explanation of what the algorithm does and why it works, before any code appears.
- Pseudocode and runnable Python. Pseudocode for the idea, Python for the details — tested, not just typed.
- Complexity analysis for time and space, including the cases where the stated bound depends on the implementation shown.
- A worked example traced step by step, generated from the algorithm on that page.
- The failure modes. Where an implementation breaks — negative numbers, duplicate keys, adversarial input — the limitation is stated rather than skipped.
- Practice problems linked to the relevant LeetCode exercises, with the pattern explained rather than just the answer.
Where To Start
The chapters are ordered so each builds on the last, but nothing stops you jumping straight to what you need.
- New to algorithms? Begin with the introduction, then complexity analysis — almost everything else assumes it.
- Preparing for interviews? Trees, graphs and dynamic programming are where most of the questions live.
- Looking something specific up? The chapter index lists all 36 topics.
Browse All 36 Chapters →
Free to read in full. No account, no paywall, no signup.