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Introduction

Introduction to Graph Algorithms Directed and Undirected Graphs Graph Terminology I Graph Terminology II Weighted Graphs Excursion: Algorithm Analysis Quiz: Introduction to Graph Algorithms

Graph Representations

Adjacency Matrix Adjacency List Representing Weighted Graphs Comparison of Graph Representations Quiz: Graph Representations Challenge: Converting Graph Representations

Graph Traversal

Depth-first Search (DFS)Implementation of DFS Breadth First Search (BFS)Implementation of BFS Application 1: Topological Sort Application 2: Strongly Connected Components Implementation of Kosaraju's Algorithm Quiz: Graph Traversal Challenge: Bipartite Graph Check

Shortest Paths

Shortest Path Problems Dijkstra's Algorithm for the SSSP Implementation of Dijkstra Floyd-Warshall Algorithm for the ASSP Implementation of Floyd-Warshall Quiz: Shortest Paths Challenge: Bellmann-Ford

Spanning Trees

The Minimum Spanning Tree Problem

Kruskal's Algorithm

Implementation of Kruskal's Algorithm

Quiz: Spanning Trees

Challenge: Maximum Spanning Trees

Flow Problems

The Max Flow Problem The Ford-Fulkerson Method Max Flow = Min Cut Implementation of Ford Fulkerson (Edmonds-Karp)Quiz: Flow Problems Challenge: Bipartite Matchings

Conclusion

Recap and Next Steps

Appendix

Disjoint Set Union Data Structure

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Quiz: Spanning Trees

Quiz: Spanning Trees

Quiz yourself on spanning trees.

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Quiz: Spanning trees

1.

What is the worst-case runtime of Kruskal’s algorithm?

A.

$\mathcal{O}(|V|\log|V|)$

B.

$\mathcal{O}(|E|\log|V|)$

C.

$\mathcal{O}(|E| + |V|)$

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