Graph Theory Based Methods
A maze can be generated by starting with a predetermined arrangement of cells (most commonly a rectangular grid but other arrangements are possible) with wall sites between them. This predetermined arrangement can be considered as a connected graph with the edges representing possible wall sites and the nodes representing cells. The purpose of the maze generation algorithm can then be considered to be making a subgraph where it is challenging to find a route between two particular nodes.
If the subgraph is not connected, then there are regions of the graph that are wasted because they do not contribute to the search space. If the graph contains loops, then there may be multiple paths between the chosen nodes. Because of this, maze generation is often approached as generating a random spanning tree. Loops which can confound naive maze solvers may be introduced by adding random edges to the result during the course of the algorithm.
Read more about this topic: Maze Generation Algorithm
Famous quotes containing the words graph, theory, based and/or methods:
“In this Journal, my pen is a delicate needle point, tracing out a graph of temperament so as to show its daily fluctuations: grave and gay, up and down, lamentation and revelry, self-love and self-disgust. You get here all my thoughts and opinions, always irresponsible and often contradictory or mutually exclusive, all my moods and vapours, all the varying reactions to environment of this jelly which is I.”
—W.N.P. Barbellion (1889–1919)
“The theory [before the twentieth century] ... was that all the jobs in the world belonged by right to men, and that only men were by nature entitled to wages. If a woman earned money, outside domestic service, it was because some misfortune had deprived her of masculine protection.”
—Rheta Childe Dorr (1866–1948)
“Language makes it possible for a child to incorporate his parents’ verbal prohibitions, to make them part of himself....We don’t speak of a conscience yet in the child who is just acquiring language, but we can see very clearly how language plays an indispensable role in the formation of conscience. In fact, the moral achievement of man, the whole complex of factors that go into the organization of conscience is very largely based upon language.”
—Selma H. Fraiberg (20th century)
“We are lonesome animals. We spend all our life trying to be less lonesome. One of our ancient methods is to tell a story begging the listener to say—and to feel—”Yes, that’s the way it is, or at least that’s the way I feel it. You’re not as alone as you thought.””
—John Steinbeck (1902–1968)