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.

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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.

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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

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