A Guide to the Graph Data Structure
An effective programmer needs a solid understanding of data structures and algorithms. Technical interviews will often test your problem-solving and critical thinking skills.
Graphs are one of the many important data structures in programming. In most cases, understanding graphs and solving graph-based problems does not come easy.
What is a graph, and what do you need to know about it?
What Is a Graph?
A graph is a non-linear data structure that has nodes (or vertices) with edges that connect them. All trees are subtypes of graphs, but not all graphs are trees, and the graph is the data structure from which trees originated.
Although you canbuild data structures in JavaScriptand other languages, you’re able to implement a graph in various ways. The most popular approaches areedge lists,adjacency lists, andadjacency matrices.
TheKhan Academy guide to representing graphsis a great resource for learning about how to represent a graph.
There are many different types of graphs. One common distinction is betweendirectedandundirectedgraphs; these come up a lot in coding challenges and real-life uses.
Types of Graphs
Aloopin a graph is an edge that starts from a node and ends at the same node. Therefore, aself-loopis a loop over only one graph node, as seen in a pseudo graph.
Graph Traversal Algorithms
Being a type of non-linear data structure, traversing a graph is quite tricky. Traversing a graph means going through and exploring each node given there is a valid path through the edges. Graph traversal algorithms are mainly of two types.
Breadth-first search is the recommended algorithm to find paths between two nodes as quickly as possible, especially the shortest path.
Depth-first search is mostly recommended when you want to visit every node in the graph. Both traversal algorithms work fine in any case, but one might be simpler and more optimized than the other in selected scenarios.
A simple illustration can help understand both algorithms better. Think of the states of a country as a graph and strive to check if two states,XandY, are connected. A depth-first search might go on a path almost around the country without realizing early enough thatYis just 2 states away fromX.
The advantage of a breadth-first search is that it maintains closeness to the current node as much as possible before going to the next one. It will find the connection betweenXandYin a short time without having to explore the whole country.
Another major difference between these two algorithms is in the way they are implemented in code. Breadth-first search is aniterative algorithmand makes use of aqueue, while a depth-first search is usually implemented as arecursive algorithmthat leverages thestack.
Below is some pseudocode demonstrating the implementation of both algorithms.
Breadth-First Search
Depth-First Search
A few other graph-traversal algorithms derive from breadth-first and depth-first searches. The most popular ones are:
Common Interview Questions Based on Graphs
Graphs are among the importantdata structures every programmer should know. Questions often come up on this topic in technical interviews, and you may encounter some classic problems related to the topic. These include things like the “town judge”, “number of islands”, and “traveling salesman” problems.
These are just a few of the many popular graph-based interview problems. You can try them out onLeetCode,HackerRank, orGeeksforGeeks.
Understanding Graph Data Structures and Algorithms
Graphs aren’t just useful for technical interviews. They have real-world use cases as well, such as innetworking, maps,andairline systemsfor finding routes. They are also used in the underlying logic of computer systems.
Graphs are excellent for organizing data and for helping us visualize complex problems. Graphs should only be used when absolutely necessary, though, to prevent space complexity or memory issues.
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