Introduction

A hands-on workbook for mastering data structures and algorithms from first principles. Each topic is a fill-in-yourself lecture page (concept → complexity → implementation walkthrough) paired with a Java skeleton, JUnit 5 tests, and a problem set. Everything ships blank: you implement the skeletons until the tests pass and grind the problems until the patterns are automatic.

🗺️ Roadmap

Work the modules in this order — each phase assumes the vocabulary of the ones above it. Inside a phase, order is flexible.

graph TD
    F["00 · Foundations"]
    F --> A["01 · Arrays"]
    F --> LL["02 · Linked Lists"]
    F --> SQ["03 · Stacks & Queues"]
    F --> HT["12 · Hash Tables"]
    A --> RC["04 · Recursion &<br/>Divide and Conqueror"]
    RC --> SS["05 · Searching & Sorting"]
    SS --> TR["06 · Trees"]
    TR --> HE["07 · Heaps"]
    TR --> TRI["16 · Tries"]
    TR --> SPT["08 · Spatial Trees"]
    HT --> DSU["09 · Disjoint Sets"]
    TR --> DSU
    DSU --> GF["10 · Graph Fundamentals"]
    GF --> GA["11 · Graph Algorithms"]
    SS --> DP["13 · Dynamic Programming"]
    SS --> GR["14 · Greedy"]
    TRI --> STR["15 · String Algorithms"]
    HE --> ADV["17 · Advanced"]
    GA --> ADV
    DP --> ADV

The path

Phase	Modules	What you learn	What it unlocks
0 · Foundations	`00`	Big-O, recurrences, amortized analysis	The language to reason about every later structure: don’t skip it
1 · Linear structures	`01` Arrays · `02` Linked Lists · `03` Stacks & Queues · `12` Hash Tables	contiguous vs linked memory, LIFO/FIFO, O(1) hashing, prefix sums, monotonic stack	the containers every algorithm is built on (pull Hash Tables forward: it’s used everywhere)
2 · Recursion & Order	`04` Recursion / Divide and Conqueror · `05` Searching and Sorting	recursion/backtracking, divide-and-conquer, the comparison sorts, binary search (incl. on the answer), quickselect	recursive thinking + the sort/search toolkit trees, graphs, and DP all lean on
3 · Hierarchical	`06` Trees · `07` Heaps · `16` Tries · `08` Spatial Trees	BSTs and Balance (i.e. AVL/RB/B-tree), priority queues, prefix trees, k-d/quad trees	logarithmic ordered / priority / prefix queries
4 · Graphs	`09` Disjoint Sets · `10` Graph Fundamentals · `11` Graph Algorithms	union-find, BFS/DFS/topo/SCC, Dijkstra/Bellman-Ford/Floyd-Warshall, MST, max-flow/min-cut	modeling the huge class of problems that are secretly graphs
5 · Paradigms	`13` Dynamic Programming · `14` Greedy	state/transition design, the classic DPs, exchange-argument greedy	optimization problems — the hardest, most rewarding tier
6 · Strings	`15` String Algorithms	KMP, Rabin–Karp, Z-algorithm	linear-time pattern matching (pairs with Tries from Phase 3)
7 · Advanced	`17`	segment/Fenwick trees, lazy propagation, sparse tables, suffix arrays/trees, treaps, vEB	competitive-programming range-query power — a capstone

How to work a module / topic

Best done with an AI coding agent as a tutor — see Learning with AI for the full setup. Per topic:

Learn it section by section — /teach <topic> (or “teach me <topic>”). The agent teaches one section, then stops until you understand it and have written that section’s notes in your own words.
Implement the code/ skeleton until the tests/concepts tests go green.
Grind the problem set — Foundational first (write them cold), then Applied (recognize the pattern, no peeking). They self-grade via tests, and LeetCode ones link out.
Drill more when you want extra reps — /extra-practice <module> generates fresh problems + stubs + tests in the same format.

The agent never hands over answers — it teaches, grades, and drills; you write every note, skeleton, and solution.

Pacing and Checkpoints

~1 module/week solo. Don’t advance until the Foundational problems are automatic; re-do a few old Applied ones weekly so earlier patterns stay sharp.
After Phase 2 → most easy/medium array & sorting problems are comfortable.
After Phase 4 → you can model and solve graph problems (a major interview gate).
After Phase 5 → DP isn’t scary; you derive recurrences yourself.
After Phase 7 → ready for competitive programming and the hardest interviews.

Keyboard shortcuts

Data Structures and Algorithms

Introduction

🗺️ Roadmap

The path

How to work a module / topic

Pacing and Checkpoints