README.md

Graph Algorithms

Articulation Points

An articulation Point (or a cut vertex) is a vertex. If we remove the vertex from a graph, it makes the graph disconnected. A graph may have zero or more articulation points. We can find all articulation points of a given graph in O(V + E). V is the number of nodes. E is the number of edges.

Articulation Points | C++ code

References in English

• Finding articulation points in a graph in O(N+M) | E-Maxx Algorithms in English

Challenges

• Articulation Points | AOJ GRL3A

Bridges

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Topological Sort

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Challenges

• AtCoder | E - League

Connected Components (Undirected Graph)

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Challenges

• D - Friend Suggestions

Strongly Connected Components (Directed Graph)

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Single-Source Shortest Paths

Dijkstra

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Bellman-Ford

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SPFA

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Challenges

• トレジャーハント - AtCoder ABC035D

All-Pairs Shortest Paths

Floyd-Warshall

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Challenges

• 正直者の高橋くん - AtCoder ABC021C
• Blue Bird - AtCoder ABC022C
• Travel by Car - AtCoder ABC143E

Bipartite

Bipartite Check

Check whether a given graph is bipartite or not. It can be computed in O(V). V is the number of vertices.

Bipartite Check | C++ code

Bipartite Maximum Matching

Find the maximum matching in a given bipartite graph G. Kuhn's algorithm can compute the maximum matching in O(VE). V is the number of vertices. E is the number of edges.

Bipartite Maximum Matching | C++ code

References in English

• Kuhn's Algorithm for Maximum Bipartite Matching - Competitive Programming Algorithms

Challenges

• GRL_7_A < Problems | Aizu Online Judge
• C - 2D Plane 2N Points

Cycle

Finding Cycle

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Finding Negative Cycle

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Minimum Spanning Tree

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Minimum Cost Arborescence

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Maximum Flow

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Minimum Cut

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Minimum Cost Flow

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