A Guide to Important Graph Algorithms for Competitive Programming

A Guide to Important Graph Algorithms for Competitive Programming

And how you can use DFS and BFS. If you’ve read an Introduction to Competitive Programming, then you’re probably familiar with why Competitive Programming is important.

If you’ve read an Introduction to Competitive Programming, then you’re probably familiar with why Competitive Programming is important. For those of you who haven’t, I believe that Competitive Programming is important because it helps you build your problem-solving skills and your technical knowledge of data structures and algorithms.

One of the biggest parts of Competitive Programming is learning the algorithms you need to succeed. I’ll be covering a large number of those algorithms in this post, specifically all the graph algorithms you’ll need to be successful in solving graph problems in Competitive Programming contests. Of course, just knowing the algorithms isn’t enough and you will have to complete a lot of practice problems on sites like Codeforces. However, this article will present you with the tools you need to master important graph algorithms.

What is a Graph?

In theoretical computer science, graphs are different from what you learned about in middle school. They are not bar charts.

Image for post

Graphs in theoretical Computer Science and Discrete Mathematics are an abstract way of representing various types of relationships such as roads connecting cities and other types of networks. Graphs are made up of two components: edges and vertices. A vertex is a point on a graph and an edge is what connects two points on a graph.

Image for post

An example of a graph

Graph problems in competitive programming will usually be talking about things like networks and grids in the problem statement.

Here’s a list of all the graph terminology you need to know:

  • *Path: *A sequence of edges which joins a sequence of distinct (different) vertices.
  • Walk: Walks are paths, but they don’t require a sequence of distinct vertices.
  • *Cycle: *A group of vertices linked together in a closed chain. In the picture above, [1,2,4] is a cycle.
  • *Connected Graph: *A graph where any pair of vertices have a path between them.
  • *Tree: *A connected graph that does not contain a cycle.
  • *Undirected Graph: *A graph where the edges have no direction, the picture above shows an undirected graph. In an undirected graph, you can travel in any direction along an edge.
  • *Directed Graph: *A graph where the edges have directions, the directions are represented by arrows. In a directed graph, you can only travel along an edge in the direction it goes.

computer-science programming coding technology algorithms algorithms

Bootstrap 5 Complete Course with Examples

Bootstrap 5 Tutorial - Bootstrap 5 Crash Course for Beginners

Nest.JS Tutorial for Beginners

Hello Vue 3: A First Look at Vue 3 and the Composition API

Building a simple Applications with Vue 3

Deno Crash Course: Explore Deno and Create a full REST API with Deno

How to Build a Real-time Chat App with Deno and WebSockets

Convert HTML to Markdown Online

HTML entity encoder decoder Online

Program a Quantum Computer Today

Your options on how to start with working with today’s quantum computers. Quantum computing is one of the most rapidly advancing technologies.

Coding 101: Programming Language Building Blocks

This article will introduce the concepts and topics common to all programming languages, that beginners and experts must know!

77 Programming Language Q&A (P4)

Check the bottom of the page for links to the other questions and answers I’ve come up with to make you a great Computer Scientist (when it comes to Programming Languages).

Common Misconceptions About Big-O & Algorithmic Complexity

Are you using Big-O incorrectly? Big-O is a simple and very general concept — the amount of primitive operations needed to complete the algorithm with some parameter.

13 Free/Low-Cost Sites to Supercharge Your Programming Self-Education

Although we still talk about programming as a standalone career, the dominance of technology in our lives makes it clear that coding is much more than a career path. In my opinion, computer science is more than a college major or a high-paid job; it’s a skill, essential for thriving in a modern-day economy. Whether you work in healthcare, marketing, business, or other fields, you will see more coding and have to deal with a growing number of technologies throughout your entire life.