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Mazes date back to antient Greece. Nowadays they are a common game in children's books and magazines. Moreover, they are very popular in robotics. There are numerious competitions around the world for robots solving mazes. 

Now we will focus on some different types of mazes and strategies to solve them.

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  • #930
  • 26 Sep 2018

In general, a maze is a puzzle where you need to find a path from an entrance to a finish or a goal among multiple given paths. Mazes are categorized based on their features and now we will take a look at some of the most common types of mazes.

First of all we will start with one term that is commonly confused with maze.

Labyrinth

Labyrinth originates from ancient Greek mythology. Nowadays it is commonly used as a synonym of maze. However, there is a distinction between the two terms in specialized literature. A maze refers to a complex branching puzzle where you need to make multiple correct choices of path and direction in order to get to the goal, while a labyrinth has just one path. You do not need to make choices, just follow the path until you reach the goal. The only problem is that you may need to make a lot of turns along the way.

Simply-connected maze

A simply-connected maze may have multiple paths, unlike the labyrinth, but it does not have detached walls. So, when you choose a path, while going forward you may face branching, but you will never return to a previous position, i.e. there are no closed paths - ones that you may loop in forever. Such mazes may be solved by the "hand rule" - go forward with your hand against the wall. If you traverse the mase without detaching your hand from the wall, you will eventualy reach the goal.

Multiply-connected maze

As with simply-connected mazes, multiply-connected mazes may have multiple paths, but unlike them, multiply-connected mazes may have enclosed paths. There may be one or more paths that loop back to a previous point of the path. The easiest way to find such enclosed paths is to find disjoint walls (the ones collered in red on the image above). Such mazes may be quite hard to solve and usually are the ones given in robotics competitions. There are multiple strategies to tackle such mazes such as the Pledge algorithm, Trémaux's algorithm, Recursive algorithm etc. However, we will not cover them in this tutorial.

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