Much of the algorithms we’ll be discussing in this series will require us to efficiently pull the lowest values in a set of unsorted numbers without looking at every number in the list.

While sorting or traversing a list may appear to be efficient, it gets rather expensive when we have to do these multiple times, especially when we’re constantly updating or adding new elements to the list.

This is where heaps come into play in helping us get the lowest (or highest) values in a much faster way and in this post, we’ll discuss how.

What is a heap?

First, let’s talk discuss…

One of the difficulties in dealing with directed acyclic graphs (DAGs) is that they can look complicated and messy. This makes it difficult to see the relationships that vertices have with each other.

In this post, we’re going to discuss and learn how to rearrange the vertices of DAGs in such a way that will allow us to simplify these graphs and see possible patterns much easier.

Source and Sink Vertices

Before we start, we need to be familiar with some terms: source and sink vertices.

Source Vertex

A source vertex is simply a vertex where no edges point towards it. For example:

Vertex A has…

By now, we have an understanding of what a graph is and learned some of the methods in traversing them.

While, we’ve already seen directed graphs, it’s time to get a formal understanding of them and uncover exciting properties that come along with their nature.

In this post, we’ll be exploring directed graphs along with learning how to determine if they have cycles within them.

Let’s first start off with learning what a directed graph is.

Directed Graphs

Directed graphs are graphs where edges go in one direction. Here’s an example.

As we can see, we use arrows to indicate that an…

One thing that we’ll be doing a lot with the algorithms in this series is graph traversal. What does this mean exactly?

Basically, the idea is that we’ll be moving around the graph from one vertex to another and discovering the properties of their interconnected relationships.

Two of the most commonly used algorithms that we’ll use a lot is: Depth-First Search (DFS) and Breadth-First Search (BFS).

While both these algorithms allow us to traverse graphs, they differ in varying ways. Let’s start with DFS.

Depth-First Search (BFS)

DFS utilizes the “go deep, head first” philosophy in its implementation. The idea is that starting…

To simply put it, a graph is a collection of vertices and a collection of edges such that each edge connects a pair of vertices together. A visual representation would be:

However, graphs can come with various properties and varying sizes. Here are a few examples:

Since as far back as I could remember, I’ve always wanted to learn Chinese Mandarin. As a kid speaking the Teochew dialect, I always felt left out whenever my dad watched Chinese dramas and I couldn’t understand a single word. It was difficult just getting started in learning as a kid because classes were inconveniently far and I lacked the discipline to keep up with my studies. It wasn’t until a volunteer teaching program in China sparked my interest in learning it again. This time I was dedicated.

So it came as a huge surprise to me when I learned…