A* Pathfinding for Beginners
Updated July 18, 2005
The A* (pronounced A-star) algorithm can be complicated for beginners. While there are many articles on the web that explain A*, most are written for people who understand the basics already. This article is for the true beginner.
This article does not try to be the definitive work on the subject. Instead it describes the fundamentals and prepares you to go out and read all of those other materials and understand what they are talking about. Links to some of the best are provided at the end of this article, under Further Reading.
Finally, this article is not program-specific. You should be able to adapt what's here to any computer language. As you might expect, however, I have included a link to a sample program at the end of this article. The sample package contains two versions: one in C++ and one in Blitz Basic. It also contains executables if you just want to see A* in action.
But we are getting ahead of ourselves. Let's start at the beginning ...
Introduction: The Search Area
Let's assume that we have someone who wants to get from point A to point B. Let's assume that a wall separates the two points. This is illustrated below, with green being the starting point A, and red being the ending point B, and the blue filled squares being the wall in between.
The first thing you should notice is that we have divided our search area into a square grid. Simplifying the search area, as we have done here, is the first step in pathfinding. This particular method reduces our search area to a simple two dimensional array. Each item in the array represents one of the squares on the grid, and its status is recorded as walkable or unwalkable. The path is found by figuring out which squares we should take to get from A to B. Once the path is found, our person moves from the center of one square to the center of the next until the target is reached.
These center points are called "nodes". When you read about pathfinding elsewhere, you will often see people discussing nodes. Why not just call them squares? Because it is possible to divide up your pathfinding area into something other than squares. They could be rectangles, hexagons, triangles, or any shape, really. And the nodes could be placed anywhere within the shapes – in the center or along the edges, or anywhere else. We are using this system, however, because it is the simplest.
Starting the Search
Once we have simplified our search area into a manageable number of nodes, as we have done with the grid layout above, the next step is to conduct a search to find the shortest path. We do this by starting at point A, checking the adjacent squares, and generally searching outward until we find our target.
We begin the search by doing the following:
At this point, you should have something like the following illustration. In this illustration, the dark green square in the center is your starting square. It is outlined in light blue to indicate that the square has been added to the closed list. All of the adjacent squares are now on the open list of squares to be checked, and they are outlined in light green. Each has a gray pointer that points back to its parent, which is the starting square.
Next, we choose one of the adjacent squares on the open list and more or less repeat the earlier process, as described below. But which square do we choose? The one with the lowest F cost.