Theoretical and Experimental DNA Computation (Natural ...

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2.5 Data Structures 33
The description of the structure of the RAM and its instruction set constitutes
the machine model or model of computation. Thisisaformal,abstract
definition of a computer. Using a model of computation allows us to calculate
the resources (running time and memory space) required by algorithms,
without having to consider implementation issues. As we have seen, there are
many models of computation, each differing in computing power. In Chap.5
we consider models of computation using DNA.
2.5 Data Structures
So far, we have only considered very simple problems, such as computing
powers of integers. However, many “interesting” problems are concerned with
other mathematical constructs. The solution of a computational problem often
involves the determination of some property (or properties) of a given
mathematical structure. Such structures include lists, networks, and trees.
These are examples of data structures. A data structure is a way of organizing
information (usually, but not always, in computer memory) in a selfcontained
and organized fashion. Data structures have algorithms associated
with them to access and maintain the information they contain. For example,
one of the simplest data structures is the array. Arrays are used when we need
to store and manipulate a collection of items of similar type that may have
different attributes. Consider a set of mailboxes, or “pigeon-holes.” Each is
identical (i.e., of the same type), but may have different contents (attributes).
In addition, each mailbox has a unique number, or address. These principles
hold just as well if, for example, we wish to store a list of integers for use
within an algorithm. Rather than declaring an individual variable for each
integer stored, we simply declare an array of integers that is large enough for
our purposes.
Consider an example: we wish to store the average annual rainfall in our
country (rounded up to the nearest centimeter) over a ten-year period. We
could declare a separate variable for each year to store the rainfall over that
period, but this would be unwieldy and inefficient. A much better solution is
to declare an array of ten integers, each storing one year’s rainfall. Thus, we
may declare an array called rainfall, addressing the elements as rainfall[0],
rainfall[1], ..., rainfall[9]. Note how the first element of an n-element array
always has address 0, and the last has the address n-1.
Arrays may be multi-dimensional, allowing us to represent more complex
information structures. For example, we may wish to write an algorithm to calculate
the driving distances between several towns. The first problem we face
is how to represent the information about the towns and the roads connecting