WEBINAR: On-demand webcast
How to Boost Database Development Productivity on Linux, Docker, and Kubernetes with Microsoft SQL Server 2017 REGISTER >
Some time ago, I had to make a project where I need to find the shorted path inside a matrix and I though "nothing better than use path finding for this."
There is lots of links and explanation about Path Finding, but Ididn't find a version written in C# that could meet my expectatations. So, I decided to make the A-star implementation in C#. This code was really useful for me and I bet it can be useful for many people too.
About the Application
A* is a generic algorithm and there are no perfect parameters to be set. The algorithm has many things that can be set, so the best way to know the best parameters that will fit in your project is to test the different combinations.
Note: Usually, a good A* implementation does not use a standard ArrayList or List for the open nodes. If a standard List is used, the algorithm will spend a huge amount of time searching for nodes in that list; instead, a priority queue should be used.
I borrow code from BenDi (http://www.codeproject.com/csharp/PriorityQueue.asp) for the priority queue implementation. I changed it a little bit and I changed the implementation to use generics instead ArrayList to make it run faster than before.
This project is really useful for two reasons:
- I followed the A* implementation and I tried to implement it to run with good performance, so the algorithm itself can be easily reused in any project.
- The front end gives a full chance to experiment with many variables where you can really watch and learn how it works. You also can change the heuristic, formula, or options to analyze the best setting for your project.
The call in the source code that does the entire job is the following:
public List<PathFinderNode> FindPath(Point start, Point end, byte[,] grid);
This method takes as parameters a start, end point, and the grid; it will return the path as a list of nodes with the coordinates. I made this call on a separate thread; this gives the chance to keep control of the application when PathFinder is working.
This is the rendering speed. Reducing the speed changes the look of how the algorithm opens and closes the nodes in real time.
This hint will tell the algorithm whether it is allowed to process diagonals as a valid path. If this checkbox is not set, the algorithm will process just four directions instead of eight.
If this check box is set, the cost of the diagonals will be bigger. That will make the algorithm avoid using diagonals.
Punish Change Direction
If this check box is set, every time the algorithm changes direction it will have a bigger cost. The end result is that, if the path is found, it will be a smoother path without too many changes in directions and look more natural. The con is that it will take more time because it searches for extra nodes.
This is a constant that will affect the estimated distance from the current position to the goal destination. A heuristic function creates this estimate of how long it will take to reach the goal state because the better the estimate, the better a short path will be found.
This is the equation used to calculate the heuristic. Different formulas give different results. Some will be faster and others slower. The end may vary, and the formula to be used depends strongly on what the A-star algorithm will be used for.
Use Tie Breaker
Sometimes when A* is finding the path, it will find many possible choices with the same cost and basically all of them could reach the destination. A tie breaker setting is a hint to tell the algorithm that when it has multiple choices to research, instead keeping going, to change those costs a little bit and apply a second formula to determinate what could be the best "guess" to follow. Usually, this formula increments the heuristic from the current position to the goal by multipling by a constant factor.
Heuristic = Heuristic + Abs(CurrentX * GoalY - GoalX * CurrentY) * 0.001
This is the limit of closed nodes to be researched before returning a "Path not found." This is a useful parameter because sometimes the grid can be too big and you need to know a path only if the goal is near from the current position or it can't spend too much time calculating the path.
This parameter just affects the front end. It will change the grid size; reducing the grid size gives a chance to create a bigger test, but it will take longer to render.
When unchecked, the implementation used is the algorithm as it usually appears in the books. When checked, it will use my own PathFinder implementation. It requires more memory. but it is about 300 to 1500 times faster or more, depending on the map complexity (See PathFinder Optimization below).
This allows seeing how the algorithm works in real time. If this box is checked, the completed time will be the calculation plus rendering time.
This is the time that the algorithm took to calculate the path. To know the real value, uncheck 'Show Progress'.
Path Finder Optimization
After I implemented the original algorithm, I got frustrated because of the amount of time it took to resolve paths, especially for bigger grids and also when there was no solution to the path. Basically. I noticed that the open and closing lists were killing the algorithm. The first optimization was to replace the open list by a sorted list and the close list by a hashtable. This made a good improvement in the calculation time, but still was not what I expected. Later, I replaced the open list from a sorted list to a priority queue; it made a change, but still was not a big difference.
The big problem was that when the grid was big (1000x1000), the number of open and close nodes in the list was huge and searching in those lists a took long time, whatever method I used. At first, I thought to use classes to keep the nodes' information, but that was going to make the garbage collection crazy between the nodes' memory allocation and releasing the memory for the nodes that were disposed. Instead of classes, I used structs and re-use them in the code. I got more improvements, but still nothing close to what StarCraft does to handle eight hundred units in real time.
My current application is like a Viso application where I need to find a path between objects. The objects are not moving, so I didn't need really a super-fast algorithm, but I needed something that can react in less than one second.
I needed to find a way to get nodes from the open list in O(1) or closer to that. I though the only way to get that was not having an open list at all. There is when I thought to use a calculation grid to store the nodes. If I knew the (X/Y) location, I could reach the node immediately O(1).
Because of this, I could get rid of the close list. I could mark a closed node directly in the calculation grid. Every node has a link to the parent node, so I did not need a close list at all. However, I could not get rid of the open list because I needed to keep getting the nodes with less total cost (F), and the second grid didn't help with that.
This time I kept using the open list (priority queue), but it was just to push and get the node with lowest cost. Priority queues are excellent to do that; they require no linear access at all.
The only cons are that the memory consumption was huge to keep a second grid, because every cell stores a node, and every node was 32 bytes long. Basically, for a map (1000x1000), I needed 32 Mb of RAM. Now I was accessing the second grid by coordinates (X/Y), so I didn't need those values in the node anymore. That reduced eight bytes, multiplied by 1,000,000. I saved 8 Mb of RAM.
Every node has a link to the parent nodes and those were int (32 bits). Because the grid can never be too big, I replaced them for ushort (16 bits). That saved another 2 bytes by node; that meant another 2 Mb of savings.
Also, I realize that the heuristic (H) is calculated for every node on the fly and it is not used any more for the algorithm, so I removed it from the node structure too. Heuristic was a int (4 bytes), so I saved another 4 Mb. Finally, I got a minimum node that took 13 bytes but, because of memory alignment, they took 16 bytes at run-time. I had to set the struct to use memory alignment for every byte.