12

CHAPTER

we choose to hold a collection of data objects play an
important role in the design process. In the last two chapters, we dis-
cussed the one-dimensional array and its use in problems where the log-
ical representation of the data is a list of objects. The choice of data
structure directly affects the design, because it determines the algo-
rithms used to process the data objects. For example, if the data items are
stored in sorted order within the array, we can apply a binary search al-
gorithm to them rather than a linear search.
In many problems, however, the relationships between data items are
more complex than can be represented in a simple list. For example, we
need a more sophisticated data structure when simulating board games
(such as chess, Tic-Tac-Toe, or Scrabble), computer graphics (where points
on the screen are arranged as a two-dimensional object), or matrix op-
erations in mathematics. In this chapter we examine the two-dimen-
sional array, which is useful when we need to organize data in two
dimensions. We usually call these dimensions rowsand columns.
In addition, we extend the definition of an array to allow arrays with
any number of dimensions, called multidimensional arrays. Each dimen-
sion represents a different feature of the data objects in the structure. For
example, we might use a three-dimensional array to store objects repre-
senting sales figures by (1) store number, (2) month, and (3) item number.
Finally, we take a closer look at the limitations of the computer in do-
ing calculations, noting how these limitations can cause numerical errors
and how we can avoid such errors. This discussion relates directly to the
Case Study, in which we examine arrays as implementation structures for
two mathematical objects, vector and matrix.

The structures that

1985

Microsoft releases

Windows 1.0. It is

their first in a series

of widely-used

operating systems

1985

Intel introduces the

80386, a 32-bit

processing chip with

on-chip memory

management

1985

Paul Brainard

creates PageMaker,

and launches the

world of PC desktop

publishing

1986

The Cray XMP

supercomputer

executes 713 million

floating-point

calculations per

second

1988

Microprocessor

speeds reach 17

million instructions

per second with

Motorola’s 88000

chip

1988

Robert Morris Jr.

releases a worm

program into the

Internet,

demonstrating the

need for greater

network security