Graph Theory for Competitive Programmers

Definitions

Graph theory is a fundamental concept in computer science, especially for competitive programming. Here’s an overview of essential graph concepts:

Key Concepts

• Vertices and Edges: Graphs consist of nodes (vertices) connected by edges.
• Directed vs. Undirected Graphs: Directed graphs have edges with a direction, while undirected graphs do not.

Common Algorithms

1. Depth-First Search (DFS): Explore as far as possible along a branch before backtracking.
2. Breadth-First Search (BFS): Explore all neighbors at the present depth before moving on to nodes at the next depth level.

Understanding these concepts will enhance your ability to tackle graph-related problems in contests.