General Computer Science 320201 GenCS I & II Lecture ... - Kwarc

c○: Michael Kohlhase 17
Can be represented as
⎧
⎫
〈a, e〉, 〈e, i〉, 〈i, j〉,
⎪⎨
〈f, j〉, 〈f, g〉, 〈g, h〉, ⎪⎬
〈d, h〉, 〈g, k〉, 〈a, b〉
⎪⎩
〈m, n〉, 〈n, o〉, 〈b, c〉
〈k, o〉, 〈o, p〉, 〈l, p〉
, a, p
⎪⎭
Mazes as Graphs (Visualizing Graphs via Diagrams)
Graphs are very abstract objects, we need a good, intuitive way of thinking about them. We
use diagrams, where the nodes are visualized as dots and the edges as lines between them.
Our maze
⎧
⎫
〈a, e〉, 〈e, i〉, 〈i, j〉,
⎪⎨
〈f, j〉, 〈f, g〉, 〈g, h〉, ⎪⎬
〈d, h〉, 〈g, k〉, 〈a, b〉
⎪⎩
〈m, n〉, 〈n, o〉, 〈b, c〉
〈k, o〉, 〈o, p〉, 〈l, p〉
, a, p
⎪⎭
can be visualized as
Note that the diagram is a visualization (a representation intended for humans to process
visually) of the graph, and not the graph itself.
c○: Michael Kohlhase 18
Now that we have a mathematical model for mazes, we can look at the subclass of graphs that
correspond to the mazes that we are after: unique solutions and all rooms are reachable! We will
concentrate on the first requirement now and leave the second one for later.
Unique solutions
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