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Topics/Graphs & Graph Algorithms
intermediate level

Graphs & Graph Algorithms

Quick Answer

What is Graphs & Graph Algorithms?

Graphs model relationships: cities connected by roads, users connected by friendships, tasks connected by dependencies. Understanding graph algorithms is essential for competitive programming and real-world engineering. RunTimeFix covers graph fundamentals systematically: adjacency lists vs matrices, depth-first and breadth-first search, connected components, cycle detection, bipartite checking, topological sorting for DAGs, Dijkstra's shortest path, 0-1 BFS, and Kruskal's MST. We extend into tree-specific algorithms: rooting, subtree sizes, diameter, binary lifting, LCA, and Euler tour techniques.

  • graphs
  • DFS
  • BFS
  • Dijkstra
  • shortest path
  • MST
  • Kruskal
  • topological sort
  • graph algorithms

Study Material for Graphs & Graph Algorithms

Ch 21: Graph Representation, DFS & BFS

Graph Terminology · Graph Representation · DFS on Graphs · BFS on Graphs · Connected Components · Grid Traversal

Ch 22: Cycle Detection, Bipartite Checking & Topological Sort

Cycle Detection in Undirected Graphs · Cycle Detection in Directed Graphs · Bipartite Checking · Topological Sort · DAG Reasoning · Functional Graphs

Ch 23: Dijkstra, 0-1 BFS & Kruskal's MST

Dijkstra's Algorithm · 0-1 BFS · Minimum Spanning Tree — Kruskal's Algorithm

Ch 24: Rooted Trees — DFS, Subtree Size & Diameter

Tree Terminology · Rooting a Tree · Tree Diameter · Distance Between Two Vertices · Tree Algorithms: Summary of Techniques

Ch 25: Binary Lifting, LCA & Euler Tour

Binary Lifting · Lowest Common Ancestor (LCA) · Euler Tour

Related Topics

Competitive ProgrammingDynamic ProgrammingData Structures
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