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Key Graph Algorithms

Key Algorithms on Graphs

Section titled “Key Algorithms on Graphs”

Essential graph algorithms for shortest paths, minimum spanning trees, and more. Each major algorithm now has its own detailed page.

Dedicated Pages

Section titled “Dedicated Pages”

Each algorithm is explained in depth on its own page:

AlgorithmPageBest For
DijkstraDijkstra’s Algorithm →Shortest path, non-negative weights
Bellman-FordBellman-Ford Algorithm →Shortest path, handles negative weights
Floyd-WarshallFloyd-Warshall Algorithm →All-pairs shortest path
Topological SortTopological Sort →Ordering DAGs (dependencies, build systems)
Union-Find (DSU)Union-Find (Disjoint Set) →Track connected components, detect cycles
MST (Kruskal & Prim)Minimum Spanning Tree →Kruskal vs Prim for MST
Cycle DetectionCycle Detection →Detect cycles in directed/undirected graphs

Choosing the Right Algorithm

Section titled “Choosing the Right Algorithm”
flowchart TD
    Q1{What problem?}
    Q1 --> SP[Shortest Path]
    Q1 --> MST[Minimum Spanning Tree]
    Q1 --> Other[Structure / Order]


    SP --> SP1{Edge weights?}
    SP1 -->|Unweighted| BFS["BFS O(V+E)"]
    SP1 -->|Non-negative| DIJK["Dijkstra O((V+E) log V)"]
    SP1 -->|Negative edges| BF["Bellman-Ford O(V×E)"]
    SP1 -->|All pairs| FW["Floyd-Warshall O(V³)"]


    MST --> MST1{Graph density?}
    MST1 -->|Sparse| KRUS["Kruskal's O(E log E)"]
    MST1 -->|Dense| PRIM["Prim's O((V+E) log V)"]


    Other --> O1{Detect cycles?}
    Other --> O2{Order dependencies?}
    Other --> O3{Connected components?}
    O1 --> CYCLE["Cycle Detection →"]
    O2 --> TOPO["Topological Sort →"]
    O3 --> UF["Union-Find (DSU) →"]


    style BFS fill:#4f46e5,color:#fff
    style DIJK fill:#7c3aed,color:#fff
    style BF fill:#4f46e5,color:#fff
    style FW fill:#6366f1,color:#fff
    style KRUS fill:#059669,color:#fff
    style PRIM fill:#059669,color:#fff
    style CYCLE fill:#dc2626,color:#fff
    style TOPO fill:#dc2626,color:#fff
    style UF fill:#dc2626,color:#fff

Next Steps

Section titled “Next Steps”

Apply these algorithms using our Problem-Solving Approach and check the Code Examples for implementations.

Section titled “Related Topics”