Module Review: Graphs
[!NOTE] You have traversed the web, solved the maze, and optimized the grid. Time to consolidate your knowledge.
Key Takeaways
- Modeling: Almost any relationship problem can be modeled as a Graph.
- Traversal:
- BFS (Queue) finds shortest paths in unweighted graphs.
- DFS (Stack/Recursion) explores deep and is key for topological sort.
- Shortest Path:
- Dijkstra (Priority Queue) is standard for weighted graphs.
- Bellman-Ford handles negative weights.
- Connectivity:
- Union-Find is the fastest way to track connected components dynamically.
Complexity Cheat Sheet
| Algorithm | Time Complexity | Space Complexity | Use Case |
|---|---|---|---|
| BFS | O(V + E) | O(V) | Shortest Path (Unweighted) |
| DFS | O(V + E) | O(V) | Puzzles, Cycle Detection |
| Dijkstra | O(E log V) | O(V) | Shortest Path (Weighted) |
| Bellman-Ford | O(VE) | O(V) | Negative Weights |
| Prim’s | O(E log V) | O(V) | MST (Dense/General) |
| Kruskal’s | O(E log E) | O(V) | MST (Sparse) |
| Union-Find | O(α(N)) | O(N) | Dynamic Connectivity |
| Topo Sort | O(V + E) | O(V) | Dependency Resolution |
Interactive: Flashcards
Test your knowledge. Click to flip.
Question
What data structure does BFS use?
Click to flip
Answer
A Queue (FIFO).
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Next Steps
Now that you understand the connections, it’s time to learn how to solve problems efficiently. Next Module: Dynamic Programming
Course Glossary
Module Review: Graphs
[!NOTE] This module explores the core principles of Module Review: Graphs, deriving solutions from first principles and hardware constraints to build world-class, production-ready expertise.
1. Practice in the Vault
Looking to solidify your understanding? Head over to the Problem Vault to solve curated problems related to this module with detailed walkthroughs and optimal solutions.