Graph Algorithms — ZeroCourse

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

Course locked

Complete Dynamic Programming first.

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Prerequisites

Trees and Priority Queues not yet

Graph Fundamentals not yet

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reading · 35 min + ~250 min canonical

Shortest Paths: Dijkstra, Bellman-Ford, and What "Negative Edges" Actually Break

Course 3.1 lesson 4 ended with a promise: Dijkstra's algorithm is BFS with a priority queue, same invariant under weighted-cost ordering. This lesson is where that promise gets ca…

primary MIT 6.006 — Shortest Paths, MST lectures

preview →

reading · 35 min + ~250 min canonical L1

Floyd-Warshall and the All-Pairs Mind-Shift: Why Three Nested Loops Beat Running Dijkstra V Times

The previous lesson gave you Dijkstra and Bellman-Ford for single-source shortest paths — find the shortest path from one fixed vertex to every other. The natural next question: w…

primary MIT 6.006 — Shortest Paths, MST lectures

after L1 locked

reading · 30 min + ~250 min canonical L1

Minimum Spanning Trees: Kruskal's and Prim's, and Why Greedy Works Here

You've got a graph of cities with roads of various lengths. You want to build the cheapest network that connects every city — no isolated nodes, no unnecessary loops. The result i…

primary MIT 6.006 — Shortest Paths, MST lectures

after L2 locked

reading · 40 min + ~250 min canonical L1

Network Flow: The Max-Flow Min-Cut Duality

Three problems that look unrelated:

primary MIT 6.006 — Shortest Paths, MST lectures

after L3 locked

reading · 30 min + ~250 min canonical L1

Euler Paths, Hamiltonian Paths, and the LP Frontier

Two questions that look almost identical:

primary MIT 6.006 — Shortest Paths, MST lectures

after L4 locked

exercise reading · 15 min L1

Exercises: Easy (Warm-up)

- [ ] Network Delay Time (#743) — NC/LC — Dijkstra's algorithm, return max distance - [ ] Min Cost to Connect All Points (#1584) — NC/LC — Prim's or Kruskal's MST

after L5 locked

exercise reading · 30 min L1

Exercises: Medium (Core)

- [ ] Cheapest Flights Within K Stops (#787) — NC/LC — Modified Bellman-Ford with stop limit - [ ] Swim in Rising Water (#778) — NC/LC — Binary search + BFS, or Dijkstra on grid -…

after L6 locked

exercise reading · 45 min L1

Exercises: Hard (Stretch)

- [ ] Alien Dictionary (#269) — NC/LC — Topological sort from character constraints - [ ] Implement Floyd-Warshall all-pairs shortest path in Ruby — O(V^3) triple loop - [ ] Imple…

after L7 locked

exercise reading · 60 min L1

Mini-Project

- [ ] Build a route planner in Ruby — load a city graph (weighted edges = distances), implement Dijkstra for shortest route, A with heuristic, and MST for minimum network; output …

after L8 locked

L10

project reading · 360 min L1

Project: Network Flow Visualizer

Implement Ford-Fulkerson (Edmonds-Karp) max flow in Ruby. Given a flow network, compute max flow and output the residual graph at each step. Visualize the augmenting paths in ASCI…

after L9 locked

L11

assessment reading · 63 min L1

Self-Assessment: Graph Algorithms

- [ ] Explain Dijkstra's algorithm. Why does it not work with negative edge weights? - [ ] Explain Bellman-Ford. How does it detect negative cycles? - [ ] What is a minimum spanni…

after L10 locked

11 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.