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

where n is the number of elements in the list. The worst case for this kind of
search occurs when
r= n/2.
Thus, the running time is still O(n).
Operations add(i,e) and remove(i) also must perform link hopping to
locate the node storing the element with index i, and then insert or delete a node.
The running times of these implementations of add(i,e) and remove(i) are
likewise
O(min(i+ 1, n−i+1)),
which is O(n). One advantage of this approach is that, if i = 0 or i = n − 1, as is the
case in the adaptation of the array list ADT to the deque ADT given in Section
6.1.1, then add and remove run in O(1) time. But, in general, using array-list
methods with a java.util. LinkedList object is inefficient.
6.4.3 Sequences
A sequence is an ADT that supports all of the methods of the deque ADT (Section
5.3), the array list ADT (Section 6.1), and the node list ADT (Section 6.2). That is,
it provides explicit access to the elements in the list either by their indices or by
their positions. Moreover, since it provides this dual access capability, we also
include, in the sequence ADT, the following two "bridging" methods that provide
connections between indices and positions:
atIndex(i): Return the position of the element with index i; an error
condition occurs if i < 0 or i > size() − 1.
indexOf(p): Return the index of the element at position p.
Multiple Inheritance in the Sequence ADT
The definition of the sequence ADT as including all the methods from three
different ADTs is an example of multiple inheritance (Section 2.4.2). That is, the
sequence ADT inherits methods from three "super" abstract data types. In other
words, its methods include the union of the methods of these super ADTs. See
Code Fragment 6.18 for a Java specification of the sequence ADT as a Java
interface.
Code Fragment 6.18: The Sequence interface
defined via multiple inheritance. It includes all the
methods of the Deque, IndexList, and
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