Graph Fundamentals — ZeroCourse

reading · we frame, you read MIT or the canonical taught · we author, no canonical fits ↺ spirals back to earlier lessons

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Complete Hashing and Advanced Linear Structures first.

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Linear Data Structures not yet

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Hashing and Advanced Linear Structures not yet

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reading · 30 min + ~240 min canonical

Graphs and Their Representations: Adjacency List, Matrix, Edge List

A binary tree is a graph where every node has at most 2 children and exactly 1 parent. A linked list is a graph where every node has exactly 1 next and exactly 1 prev. A road netw…

primary UC Berkeley CS61B — Graph sections

preview →

reading · 40 min + ~240 min canonical L1

The Graph Search Mind-Shift: BFS, DFS, and Why They Are the Same Algorithm with Different Queues

You're about to meet two algorithms — Breadth-First Search and Depth-First Search — that are everywhere in graph theory. Every textbook treats them as a pair: "here are two import…

primary UC Berkeley CS61B — Graph sections

after L1 locked

reading · 30 min + ~240 min canonical L1

DFS in Depth: Topological Sort, Cycle Detection, and the Three-Colour Algorithm

DFS isn't useful because it visits vertices in a particular order — BFS does that too. DFS is useful because of when it finishes processing each vertex. Every vertex has two times…

primary UC Berkeley CS61B — Graph sections

after L2 locked

reading · 35 min + ~240 min canonical L1

BFS in Depth: Shortest Paths, Bipartiteness, and the Layer-by-Layer Lens

The last lesson said BFS is graph search with a queue, and that's all the algorithm is. But why does that queue give you shortest paths? Why doesn't a stack give them too? The ans…

primary UC Berkeley CS61B — Graph sections

after L3 locked

reading · 35 min + ~240 min canonical L1

Strongly Connected Components and Bridges: When the Graph Has Structure Inside

A graph isn't usually one undifferentiated mass of vertices. It has structure: clusters where everything reaches everything else, single edges whose removal disconnects regions, i…

primary UC Berkeley CS61B — Graph sections

after L4 locked

exercise reading · 15 min L1

Exercises: Easy (Warm-up)

- [ ] Number of Islands (#200) — NC/LC — BFS/DFS on 2D grid, mark visited - [ ] Max Area of Island (#695) — NC/LC — DFS counting cells per island - [ ] Clone Graph (#133) — NC/LC …

after L5 locked

exercise reading · 30 min L1

Exercises: Medium (Core)

- [ ] Course Schedule (#207) — NC/LC — Topological sort via DFS cycle detection - [ ] Course Schedule II (#210) — NC/LC — Return topological ordering - [ ] Pacific Atlantic Water …

after L6 locked

exercise reading · 45 min L1

Exercises: Hard (Stretch)

- [ ] Word Ladder (#127) — NC/LC — BFS with word transformation as edges - [ ] Alien Dictionary (#269) — NC/LC — Topological sort from character ordering constraints - [ ] Walls a…

after L7 locked

exercise reading · 60 min L1

Mini-Project

- [ ] Build a social network analyzer in Ruby — load a graph from file (adjacency list), find connected components, compute shortest path (BFS), detect communities (connected comp…

after L8 locked

L10

project reading · 300 min L1

Project: Dependency Resolver

Build a Ruby tool that reads a dependency graph (like a Gemfile) and outputs the installation order using topological sort. Detect circular dependencies and report them. Input: YA…

after L9 locked

L11

project reading · 600 min L1

Capstone: Route Planner and Map Navigator

- [ ] Milestone 1: Build the graph data structure in Ruby with adjacency list; load from CSV - [ ] Milestone 2: Implement Dijkstra's algorithm with min-heap; output shortest path …

after L10 locked

L12

assessment reading · 63 min L1

Self-Assessment: Graph Fundamentals

- [ ] What are the three ways to represent a graph in code? What are the tradeoffs? - [ ] Explain BFS and DFS. What data structure does each use? When would you choose one over th…

after L11 locked

12 lessons. Read in order; spiral back when you need to. By the end you'll have used the core ideas twice — once on the abstract, once on something you'll meet at work next week.