I have always loved solving mazes... so naturally I had to write a program to solve mazes for me!

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a black and white maze

Take a look at this maze; can you find a path from the upper left entrance in the maze to the lower right exit? Probably you can, and so does the program I wrote!

I wrote a program in Python (making use of pygame and Pillow) to solve any maze given. I did this project several years ago, after learning about Dijkstra's algorithm. I read about the algorithm and decided to implement it, to get a feel for it. I realized that I could apply it to a maze in a picture, if I took each pixel of the image to be a vertex in the graph where I'd apply the method.

I wanted to make my program fairly general, in terms of the mazes that could be given, and so I dwelled with a problem: how to tell if two adjacent pixels should be connected in the graph or not. I knew I only wanted to connect pixels that referred to the path, and not to the walls, so my idea was simple: I supposed that a picture of a maze would have mainly two colours, one for the walls and another for the paths. I leveraged on that to preprocess the image and turn it to a black and white picture, where each pixel would be either completely white or completely black (I did this by finding the average luminosity of a pixel in the image and used that as a threshold; a pixel with luminosity below the average becomes black, otherwise it becomes white). After processing, ask the user for the two points we want to connect; if they have the same colour (say it was white) then it must have been because the paths have been changed into white and thus I need only to consider white pixels.

After we know where to start, where to end, and which colour we care about (either black or white) I apply Dijkstra's algorithm on the graph of the vertices of that colour, where two vertices are connected if the two corresponding pixels are adjacent. Of course I didn't have to explicitly build the graph, as it was given by the pixels in the picture. After a path is found, a red line is drawn. The first version of the script would draw the absolute shortest path, and so it would mainly be adjacent to walls and I found it aesthetically unpleasing. To try and counter that I added a slight element of randomness when drawing the red path. Using my script to solve the maze above we get this drawing:

the maze above but solved with a red line showing the path

which looks like a line I could draw with my pencil, if I managed to not overlap my line with the walls of the maze by accident. The code can be found in this GitHub repo and a downloadable executable can be found here. In both places you can find a bin folder with a couple of maze examples.

Thanks for reading this far! If you would like to show your appreciation for my work and would like to contribute to the development of this project, consider buying me a slice of pizza 🍕.

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