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

“Applets, Not Craplets tm ” (– ca. 1997)
c○: Michael Kohlhase 14
Thinking about a problem will involve thinking about the representations we want to use (after
all, we want to work on the computer), which computations these representations support, and
what constitutes a solutions to the problem.
This will also give us a foundation to talk about the problem with our peers and clients. Enabling
students to talk about CS problems like a computer scientist is another important learning goal
of this course.
We will now exemplify the process of “thinking about the problem” on our mazes example. It
shows that there is quite a lot of work involved, before we write our first line of code. Of course,
sometimes, explorative programming sometimes also helps understand the problem , but we would
consider this as part of the thinking process.
Thinking about the problem
Idea: Randomly knock out walls until
we get a good maze
Think about a grid of rooms separated
by walls.
Each room can be given a name.
Mathematical Formulation:
a set of rooms: {a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p}
Pairs of adjacent rooms that have an open wall between them.
Example 3 For example, 〈a, b〉 and 〈g, k〉 are pairs.
Abstractly speaking, this is a mathematical structure called a graph.
c○: Michael Kohlhase 15
Of course, the “thinking” process always starts with an idea of how to attack the problem. In our
case, this is the idea of starting with a grid-like structure and knocking out walls, until we have a
maze which meets our requirements.
Note that we have already used our first representation of the problem in the drawing above: we
have drawn a picture of a maze, which is of course not the maze itself.
Definition 4 A representation is the realization of real or abstract persons, objects, circumstances,
Events, or emotions in concrete symbols or models. This can be by diverse methods, e.g.
visual, aural, or written; as three-dimensional model, or even by dance.
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