Next: 4. Skiplists Up: 3. Linked Lists Previous: 3.3 : A Space-Efficient Contents
Both singly-linked and doubly-linked lists are folklore, having been
used in programs for over 40 years. They are discussed, for example,
by Knuth [41, Sections 2.2.3-2.2.5]. Even the
data
structure seems to be a well-known data structures exercise.
to use a dummy node to avoid
all the special cases that occur in the operations
,
,
, and
?
method,
, that returns
the second-last element of an
. Do this without using the
member variable,
, that keeps track of the size of the list.
operations
,
,
and
on an
. Each of these operations
should run in
time.
method,
that reverses the
order of elements in an
. This method should run in
time, should not use recursion, should not use any secondary data
structures, and should not create any new nodes.
and
methods called
.
These methods walk through the list and count the number of nodes to
see if this matches the value,
, stored in the list. These methods
return nothing, but throw an exception if the size they compute does
not match the value of
.
operation, that creates a node,
, and adds it just
before the node
in a
. If your code does not exactly match
the code given in this book it may still be correct. Test it and see
if it works.
The next few exercises involve performing manipulations on
s.
These should all be done without allocating any new nodes or temporary
arrays. More specifically, they can all be done only by changing
the
and
values of existing nodes.
method
that returns
if the
list is a palindrome, i.e., the element at position
is equal to
the element at position
for all
.
Your code should run in
time.
that ``rotates'' a
so that list
item
becomes list item
. This method should
run in
time and should not modify any nodes in
the list.
, that truncates a
at position
. After the execution of this method, the size of the list is
and it contains only the elements at indices
. The
return value is another
that contains the elements at indices
. This method should run in
time.
method,
, that takes as an argument
a
,
, empties it and appends its contents, in order,
to the receiver. For example, if
contains 
and
contains 
, then after calling
,
will contain
and
will be empty.
that removes all the elements with odd-numbered
indices from a
and return a
containing these elements.
For example, if
, contains the elements
, then after
calling
,
should contain 
and a list containing
should be returned.
, that reverses the order of elements in
a
.
, as discussed in Section 11.1.1.
method called
.
This method takes the first node from
and appends it to the the
receiving list. This is equivalent to
,
except that it should not create a new node.
static method,
, that takes two
sorted lists
and
, merges them, and returns a new sorted
list containing the result. This causes
and
to be emptied
in the proces. For example, if
contains 
and
contains
, then this method returns a new list containing
.
method
that sorts the elements contained
in the list using the merge sort algorithm. This recursive algorithm works as following:
and
using the
method;
;
; and, finally,
and
into a single sorted list.
The next few exercises are more advanced and require a clear
understanding of what happens to the minimum value stored in a
or
as items are added and removed.
data structure that can store
comparable elements and supports the stack operations
,
, and
, as well as the
operation, which
returns the minimum value currently stored in the data structure.
All operations should run in constant time.
data structure that can store
comparable elements and supports the queue operations
,
, and
, as well as the
operation, which
returns the minimum value currently stored in the data structure.
All operations should run in constant amortized time.
data structure that can store
comparable elements and supports the queue operations
,
,
and
, as well
as the
operation, which returns the minimum value currently
stored in the data structure. All operations should run in constant
amortized time.
The next exercises are designed to test the reader's understanding of
the implementation an analysis of the space-efficient
:
is used like a
(so that the
modifications are done using
and
) then these operations run in
constant amortized time, independent of the value of
.
that supports all
the
operations in constant amortized time per operation,
independent of the value of
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