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:
“When producers want to know what the public wants, they graph it as curves. When they want to tell the public what to get, they say it in curves.”
—Marshall McLuhan (1911–1980)
“By the “mud-sill” theory it is assumed that labor and education are incompatible; and any practical combination of them impossible. According to that theory, a blind horse upon a tread-mill, is a perfect illustration of what a laborer should be—all the better for being blind, that he could not tread out of place, or kick understandingly.... Free labor insists on universal education.”
—Abraham Lincoln (1809–1865)
“Because it is not always easy for an adult to predict what inaccurate ideas a child may have, it can help to answer questions first with one of your own: “What do you think?” Once you find out what a child is really asking, you’ll be in a better position to give a helpful answer based on the facts.”
—Joanna Cole (20th century)
“With a generous endowment of motherhood provided by legislation, with all laws against voluntary motherhood and education in its methods repealed, with the feminist ideal of education accepted in home and school, and with all special barriers removed in every field of human activity, there is no reason why woman should not become almost a human thing. It will be time enough then to consider whether she has a soul.”
—Crystal Eastman (1881–1928)