Data Structures and Algorithms in Java[1].pdf - Fulvio Frisone

to that of the rank of an element in a list, which is usually defined to be one more
than its index; so the first element is at rank 1, the second is at rank 2, and so on.
A sequence that supports access to its elements by their indices is called an array list
(or vector, using an older term). Since our index definition is more consistent with the
way arrays are indexed in Java and other programming languages (such as C and
C++), we will be referring to the place where an element is stored in an array list as
its "index," not its "rank" (although we may use r to denote this index, if the letter "i"
is being used as a for-loop counter).
This index concept is a simple yet powerful notion, since it can be used to specify
where to insert a new element into a list or where to remove an old element.
6.1.1 The Array List Abstract Data Type
As an ADT, an array list S has the following methods (besides the standard
size() and isEmpty() methods):
get(i): Return the element of S with index i; an error condition
occurs if i < 0 or i > size() − 1.
set(i, e): Replace with e and return the element at index i; an error
condition occurs if i < 0 or i > size() − 1.
add(i, e): Insert a new element e into S to have index i; an error
condition occurs if i < 0 or i > size().
remove(i): Remove from S the element at index i; an error condition
occurs if i < 0 or i > size() − 1.
We do not insist that an array should be used to implement an array list, so that the
element at index 0 is stored at index 0 in the array, although that is one (very
natural) possibility. The index definition offers us a way to refer to the "place"
where an element is stored in a sequence without having to worry about the exact
implementation of that sequence. The index of an element may change whenever
the sequence is updated, however, as we illustrate in the following example.
Example 6.1: We show below some operations on an initially empty array list
S.
Operation
Output
S
add(0,7)
314