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Stacks
Goodrich, Tamassia
Linked Lists
1
Abstract Data Types (ADTs)
An abstract data
type (ADT) is an
abstraction of a
data structure
An ADT specifies:



Data stored
Operations on the
data
Error conditions
associated with
operations
Goodrich, Tamassia
Example: ADT modeling a
simple stock trading system


The data stored are buy/sell
orders
The operations supported are
 order buy(stock, shares, price)
 order sell(stock, shares, price)
 void cancel(order)

Error conditions:
 Buy/sell a nonexistent stock
 Cancel a nonexistent order
Linked Lists
2
The Stack ADT (§4.2)
The Stack ADT stores
arbitrary objects
Insertions and deletions
follow the last-in first-out
scheme
Think of a spring-loaded
plate dispenser
Main stack operations:


push(object): inserts an
element
object pop(): removes and
returns the last inserted
element
Goodrich, Tamassia
Linked Lists
Auxiliary stack
operations:



object top(): returns the
last inserted element
without removing it
integer size(): returns the
number of elements
stored
boolean isEmpty():
indicates whether no
elements are stored
3
Stack Interface in Java
Java interface
corresponding to
our Stack ADT
Requires the
definition of class
EmptyStackException
Different from the
built-in Java class
java.util.Stack
public interface Stack {
public int size();
public boolean isEmpty();
public Object top()
throws EmptyStackException;
public void push(Object o);
public Object pop()
throws EmptyStackException;
}
Goodrich, Tamassia
Linked Lists
4
Exceptions
Attempting the
execution of an
operation of ADT may
sometimes cause an
error condition, called
an exception
Exceptions are said to
be “thrown” by an
operation that cannot
be executed
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Linked Lists
In the Stack ADT,
operations pop and
top cannot be
performed if the
stack is empty
Attempting the
execution of pop or
top on an empty
stack throws an
EmptyStackException
5
Applications of Stacks
Direct applications



Page-visited history in a Web browser
Undo sequence in a text editor
Chain of method calls in the Java Virtual
Machine
Indirect applications


Auxiliary data structure for algorithms
Component of other data structures
Goodrich, Tamassia
Linked Lists
6
Method Stack in the JVM
The Java Virtual Machine (JVM)
keeps track of the chain of
active methods with a stack
When a method is called, the
JVM pushes on the stack a
frame containing
main() {
int i = 5;
foo(i);
}
foo(int j) {
int k;
 Local variables and return value
 Program counter, keeping track of
k = j+1;
the statement being executed
bar(k);
When a method ends, its frame
}
is popped from the stack and
control is passed to the method bar(int m) {
on top of the stack
…
}
Allows for recursion
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bar
PC = 1
m=6
foo
PC = 3
j=5
k=6
main
PC = 2
i=5
7
Array-based Stack
A simple way of
implementing the
Stack ADT uses an
array
We add elements
from left to right
A variable keeps
track of the index of
the top element
Algorithm size()
return t + 1
Algorithm pop()
if isEmpty() then
throw EmptyStackException
else
tt1
return S[t + 1]
…
S
0 1 2
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t
Linked Lists
8
Array-based Stack (cont.)
The array storing the
stack elements may
become full
A push operation will
then throw a
FullStackException


Algorithm push(o)
if t = S.length  1 then
throw FullStackException
else
tt+1
Limitation of the arrayS[t]  o
based implementation
Not intrinsic to the
Stack ADT
…
S
0 1 2
Goodrich, Tamassia
t
Linked Lists
9
Performance and Limitations
Performance



Let n be the number of elements in the stack
The space used is O(n)
Each operation runs in time O(1)
Limitations


The maximum size of the stack must be defined a
priori and cannot be changed
Trying to push a new element into a full stack
causes an implementation-specific exception
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Linked Lists
10
Array-based Stack in Java
public class ArrayStack
implements Stack {
// holds the stack elements
private Object S[ ];
// index to top element
private int top = -1;
// constructor
public ArrayStack(int capacity) {
S = new Object[capacity]);
}
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public Object pop()
throws EmptyStackException {
if isEmpty()
throw new EmptyStackException
(“Empty stack: cannot pop”);
Object temp = S[top];
// facilitates garbage collection
S[top] = null;
top = top – 1;
return temp;
}
Linked Lists
11
Parentheses Matching
Each “(”, “{”, or “[” must be paired with
a matching “)”, “}”, or “[”





correct: ( )(( )){([( )])}
correct: ((( )(( )){([( )])}
incorrect: )(( )){([( )])}
incorrect: ({[ ])}
incorrect: (
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Linked Lists
12
Parentheses Matching Algorithm
Algorithm ParenMatch(X,n):
Input: An array X of n tokens, each of which is either a grouping symbol, a
variable, an arithmetic operator, or a number
Output: true if and only if all the grouping symbols in X match
Let S be an empty stack
for i=0 to n-1 do
if X[i] is an opening grouping symbol then
S.push(X[i])
else if X[i] is a closing grouping symbol then
if S.isEmpty() then
return false {nothing to match with}
if S.pop() does not match the type of X[i] then
return false {wrong type}
if S.isEmpty() then
return true {every symbol matched}
else
return false {some symbols were never matched}
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Linked Lists
13
HTML Tag Matching
For fully-correct HTML, each <name> should pair with a matching </name>
<body>
<center>
<h1> The Little Boat </h1>
</center>
<p> The storm tossed the little
boat like a cheap sneaker in an
old washing machine. The three
drunken fishermen were used to
such treatment, of course, but
not the tree salesman, who even as
a stowaway now felt that he
had overpaid for the voyage. </p>
<ol>
<li> Will the salesman die? </li>
<li> What color is the boat? </li>
<li> And what about Naomi? </li>
</ol>
</body>
Goodrich, Tamassia
The Little Boat
The storm tossed the little boat
like a cheap sneaker in an old
washing machine. The three
drunken fishermen were used to
such treatment, of course, but not
the tree salesman, who even as
a stowaway now felt that he had
overpaid for the voyage.
1. Will the salesman die?
2. What color is the boat?
3. And what about Naomi?
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14
Tag Matching Algorithm
Is similar to parentheses matching:
import java.util.StringTokenizer;
import datastructures.Stack;
import datastructures.NodeStack;
import java.io.*;
/** Simpli.ed test of matching tags in an HTML document. */
public class HTML { /** Nested class to store simple HTML tags */
public static class Tag { String name; // The name of this tag
boolean opening; // Is true i. this is an opening tag
public Tag() { // Default constructor
name = "";
opening = false;
}
public Tag(String nm, boolean op) { // Preferred constructor
name = nm;
opening = op;
}
}
/** Is this an opening tag? */
public boolean isOpening() { return opening; }
/** Return the name of this tag */
public String getName() {return name; }
/** Test if every opening tag has a matching closing tag. */
public boolean isHTMLMatched(Tag[ ] tag) {
Stack S = new NodeStack(); // Stack for matching tags
for (int i=0; (i<tag.length) && (tag[i] != null); i++) {
if (tag[i].isOpening())
S.push(tag[i].getName()); // opening tag; push its name on the stack
else {
if (S.isEmpty()) // nothing to match
return false;
if (!((String) S.pop()).equals(tag[i].getName())) // wrong match
return false;
}
}
Goodrich, Tamassia
}
if (S.isEmpty())
return true; // we matched everything
return false; // we have some tags that never were matched
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15
Tag Matching Algorithm, cont.
public final static int CAPACITY = 1000;
// Tag array size upper bound
/* Parse an HTML document into an array of html tags */
public Tag[ ] parseHTML(BufferedReader r) throws IOException {
String line; // a line of text
boolean inTag = false ;
// true iff we are in a tag
Tag[ ] tag = new Tag[CAPACITY]; // our tag array (initially all null)
int count = 0
;
// tag counter
while ((line = r.readLine()) != null) {
// Create a string tokenizer for HTML tags (use < and > as delimiters)
StringTokenizer st = new StringTokenizer(line,"<> \t",true);
while (st.hasMoreTokens()) {
String token = (String) st.nextToken();
if (token.equals("<")) // opening a new HTML tag
inTag = true;
else if (token.equals(">")) // ending an HTML tag
inTag = false;
else if (inTag) { // we have a opening or closing HTML tag
if ( (token.length() == 0) | | (token.charAt(0) != ’/’) )
tag[count++] = new Tag(token, true); // opening tag
else // ending tag
tag[count++] = new Tag(token.substring(1), false); // skip the
} // Note: we ignore anything not in an HTML tag
}
}
return tag; // our array of tags
}
/** Tester method */
public static void main(String[ ] args) throws IOException {
BufferedReader stdr;
// Standard Input Reader
stdr = new BufferedReader(new InputStreamReader(System.in));
HTML tagChecker = new HTML();
if (tagChecker.isHTMLMatched(tagChecker.parseHTML(stdr)))
System.out.println("The input file is a matched HTML document.");
else
System.out.println("The input file is not a matched HTML document.");
}
}
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Goodrich, Tamassia
16
Computing Spans (not in book)
7
We show how to use a stack 6
as an auxiliary data structure 5
in an algorithm
4
Given an an array X, the span
3
S[i] of X[i] is the maximum
2
number of consecutive
elements X[j] immediately
1
preceding X[i] and such that 0
X[j]  X[i]
Spans have applications to
financial analysis

E.g., stock at 52-week high
Goodrich, Tamassia
Linked Lists
0
X
S
1
6
1
3
1
2
3
4
2
5
3
4
2
1
17
Quadratic Algorithm
Algorithm spans1(X, n)
Input array X of n integers
Output array S of spans of X
S  new array of n integers
for i  0 to n  1 do
s1
while s  i  X[i  s]  X[i]
ss+1
S[i]  s
return S
#
n
n
n
1 + 2 + …+ (n  1)
1 + 2 + …+ (n  1)
n
1
Algorithm spans1 runs in O(n2) time
Goodrich, Tamassia
Linked Lists
18
Computing Spans with a Stack
We keep in a stack the
indices of the elements
visible when “looking
back”
We scan the array from
left to right




Let i be the current index
We pop indices from the
stack until we find index j
such that X[i]  X[j]
We set S[i]  i  j
We push x onto the stack
Goodrich, Tamassia
Linked Lists
7
6
5
4
3
2
1
0
0 1 2 3 4 5 6 7
19
Linear Algorithm
Each index of the
array


Is pushed into the
stack exactly one
Is popped from
the stack at most
once
The statements in
the while-loop are
executed at most
n times
Algorithm spans2
runs in O(n) time
Goodrich, Tamassia
Algorithm spans2(X, n)
#
S  new array of n integers n
A  new empty stack
1
for i  0 to n  1 do
n
while (A.isEmpty() 
X[A.top()]  X[i] ) do n
A.pop()
n
if A.isEmpty() then
n
S[i]  i + 1
n
else
S[i]  i  A.top()
n
A.push(i)
n
return S
1
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20
Queues
Goodrich, Tamassia
Linked Lists
21
The Queue ADT (§4.3)
The Queue ADT stores arbitrary
objects
Insertions and deletions follow
the first-in first-out scheme
Insertions are at the rear of the
queue and removals are at the
front of the queue
Main queue operations:


enqueue(object): inserts an
element at the end of the
queue
object dequeue(): removes and
returns the element at the front
of the queue
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Linked Lists
Auxiliary queue
operations:



object front(): returns the
element at the front without
removing it
integer size(): returns the
number of elements stored
boolean isEmpty(): indicates
whether no elements are
stored
Exceptions

Attempting the execution of
dequeue or front on an
empty queue throws an
EmptyQueueException
22
Queue Example
Operation
enqueue(5)
enqueue(3)
dequeue()
enqueue(7)
dequeue()
front()
dequeue()
dequeue()
isEmpty()
enqueue(9)
enqueue(7)
size()
enqueue(3)
enqueue(5)
dequeue()
Goodrich, Tamassia
Output
–
–
5
–
3
7
7
“error”
true
–
–
2
–
–
9
Q
(5)
(5, 3)
(3)
(3, 7)
(7)
(7)
()
()
()
(9)
(9, 7)
(9, 7)
(9, 7, 3)
(9, 7, 3, 5)
(7, 3, 5)
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23
Applications of Queues
Direct applications



Waiting lists, bureaucracy
Access to shared resources (e.g., printer)
Multiprogramming
Indirect applications


Auxiliary data structure for algorithms
Component of other data structures
Goodrich, Tamassia
Linked Lists
24
Array-based Queue
Use an array of size N in a circular fashion
Two variables keep track of the front and rear
f index of the front element
r index immediately past the rear element
Array location r is kept empty
normal configuration
Q
0 1 2
f
r
wrapped-around configuration
Q
0 1 2
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r
f
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25
Queue Operations
We use the
modulo operator
(remainder of
division)
Algorithm size()
return (N  f + r) mod N
Algorithm isEmpty()
return (f = r)
Q
0 1 2
f
0 1 2
r
r
Q
Goodrich, Tamassia
f
Linked Lists
26
Queue Operations (cont.)
Operation enqueue
throws an exception if
the array is full
This exception is
implementationdependent
Algorithm enqueue(o)
if size() = N  1 then
throw FullQueueException
else
Q[r]  o
r  (r + 1) mod N
Q
0 1 2
f
0 1 2
r
r
Q
Goodrich, Tamassia
f
Linked Lists
27
Queue Operations (cont.)
Operation dequeue
throws an exception
if the queue is empty
This exception is
specified in the
queue ADT
Algorithm dequeue()
if isEmpty() then
throw EmptyQueueException
else
o  Q[f]
f  (f + 1) mod N
return o
Q
0 1 2
f
0 1 2
r
r
Q
Goodrich, Tamassia
f
Linked Lists
28
Queue Interface in Java
Java interface
corresponding to
our Queue ADT
Requires the
definition of class
EmptyQueueException
No corresponding
built-in Java class
public interface Queue {
public int size();
public boolean isEmpty();
public Object front()
throws EmptyQueueException;
public void enqueue(Object o);
public Object dequeue()
throws EmptyQueueException;
}
Goodrich, Tamassia
Linked Lists
29
Application: Round Robin
Schedulers
We can implement a round robin scheduler using a
queue, Q, by repeatedly performing the following
steps:
1.
2.
3.
e = Q.dequeue()
Service element e
Q.enqueue(e)
The Queue
1. Deque the
next element
2 . Service the
next element
3. Enqueue the
serviced element
Shared
Service
Goodrich, Tamassia
Linked Lists
30
Linked Lists
Goodrich, Tamassia
Linked Lists
31
Singly Linked List (§ 4.4.1)
A singly linked list is a
concrete data structure
consisting of a sequence
of nodes
Each node stores


next
element
link to the next node
node
elem

A
Goodrich, Tamassia
B
C
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D
32
The Node Class for List Nodes
public class Node
{
// Instance variables:
private Object element;
private Node next;
/** Creates a node with null references to its element and next node. */
public Node()
{
this(null, null);
}
/** Creates a node with the given element and next node. */
public Node(Object e, Node n) {
element = e;
next = n;
}
// Accessor methods:
public Object getElement() {
return element;
}
public Node getNext() {
return next;
}
// Modifier methods:
public void setElement(Object newElem) {
element = newElem;
}
public void setNext(Node newNext) {
next = newNext;
}
}
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Linked Lists
33
Inserting at the Head
1. Allocate a new
node
2. Insert new element
3. Have new node
point to old head
4. Update head to
point to new node
Goodrich, Tamassia
Linked Lists
34
Removing at the Head
1. Update head to
point to next node
in the list
2. Allow garbage
collector to reclaim
the former first
node
Goodrich, Tamassia
Linked Lists
35
Inserting at the Tail
1. Allocate a new
2.
3.
4.
5.
node
Insert new element
Have new node
point to null
Have old last node
point to new node
Update tail to point
to new node
Goodrich, Tamassia
Linked Lists
36
Removing at the Tail
Removing at the tail
of a singly linked list
is not efficient!
There is no
constant-time way
to update the tail to
point to the previous
node
Goodrich, Tamassia
Linked Lists
37
Stack with a Singly Linked List
We can implement a stack with a singly linked list
The top element is stored at the first node of the list
The space used is O(n) and each operation of the
Stack ADT takes O(1) time
nodes

t
elements
Goodrich, Tamassia
Linked Lists
38
Queue with a Singly Linked List
We can implement a queue with a singly linked list


The front element is stored at the first node
The rear element is stored at the last node
The space used is O(n) and each operation of the
Queue ADT takes O(1) time
r
nodes
f

elements
Goodrich, Tamassia
Linked Lists
39
Vectors and Array Lists
Goodrich, Tamassia
Linked Lists
40
The Vector ADT (§5.1)
The Vector ADT
extends the notion of
array by storing a
sequence of arbitrary
objects
An element can be
accessed, inserted or
removed by specifying
its rank (number of
elements preceding it)
An exception is
thrown if an incorrect
rank is specified (e.g.,
a negative rank)
Goodrich, Tamassia
Main vector operations:
 object elemAtRank(integer r):
returns the element at rank r
without removing it
 object replaceAtRank(integer r,
object o): replace the element at
rank with o and return the old
element
 insertAtRank(integer r, object o):
insert a new element o to have
rank r
 object removeAtRank(integer r):
removes and returns the element
at rank r
Additional operations size() and
isEmpty()
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41
Applications of Vectors
Direct applications

Sorted collection of objects (elementary
database)
Indirect applications


Auxiliary data structure for algorithms
Component of other data structures
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Linked Lists
42
Array-based Vector
Use an array V of size N
A variable n keeps track of the size of the vector
(number of elements stored)
Operation elemAtRank(r) is implemented in O(1)
time by returning V[r]
V
0 1 2
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n
r
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43
Insertion
In operation insertAtRank(r, o), we need to make
room for the new element by shifting forward the
n  r elements V[r], …, V[n  1]
In the worst case (r = 0), this takes O(n) time
V
0 1 2
r
n
0 1 2
r
n
0 1 2
o
r
V
V
Goodrich, Tamassia
Linked Lists
n
44
Deletion
In operation removeAtRank(r), we need to fill the
hole left by the removed element by shifting
backward the n  r  1 elements V[r + 1], …, V[n  1]
In the worst case (r = 0), this takes O(n) time
V
0 1 2
o
r
n
0 1 2
r
n
0 1 2
r
V
V
Goodrich, Tamassia
Linked Lists
n
45
Performance
In the array based implementation of a Vector



The space used by the data structure is O(n)
size, isEmpty, elemAtRank and replaceAtRank run in
O(1) time
insertAtRank and removeAtRank run in O(n) time
If we use the array in a circular fashion,
insertAtRank(0) and removeAtRank(0) run in
O(1) time
In an insertAtRank operation, when the array
is full, instead of throwing an exception, we
can replace the array with a larger one
Goodrich, Tamassia
Linked Lists
46
Growable Array-based Vector
In a push operation, when Algorithm push(o)
the array is full, instead of
if t = S.length  1 then
throwing an exception, we
A  new array of
can replace the array with
size …
a larger one
for i  0 to t do
A[i]  S[i]
How large should the new
SA
array be?


incremental strategy:
increase the size by a
constant c
doubling strategy: double
the size
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Linked Lists
tt+1
S[t]  o
47
Comparison of the Strategies
We compare the incremental strategy and
the doubling strategy by analyzing the total
time T(n) needed to perform a series of n
push operations
We assume that we start with an empty
stack represented by an array of size 1
We call amortized time of a push operation
the average time taken by a push over the
series of operations, i.e., T(n)/n
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Linked Lists
48
Incremental Strategy Analysis
We replace the array k = n/c times
The total time T(n) of a series of n push
operations is proportional to
n + c + 2c + 3c + 4c + … + kc =
n + c(1 + 2 + 3 + … + k) =
n + ck(k + 1)/2
Since c is a constant, T(n) is O(n + k2), i.e.,
O(n2)
The amortized time of a push operation is O(n)
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Linked Lists
49
Doubling Strategy Analysis
We replace the array k = log2 n
times
The total time T(n) of a series
of n push operations is
proportional to
n + 1 + 2 + 4 + 8 + …+ 2k =
n + 2k + 1 1 = 2n 1
T(n) is O(n)
The amortized time of a push
operation is O(1)
Goodrich, Tamassia
Linked Lists
geometric series
2
4
1
1
8
50
Lists
Goodrich, Tamassia
Linked Lists
51
Position ADT (§ 5.2.2)
The Position ADT models the notion of
place within a data structure where a
single object is stored
It gives a unified view of diverse ways
of storing data, such as


a cell of an array
a node of a linked list
Just one method:

object element(): returns the element
stored at the position
Goodrich, Tamassia
Linked Lists
52
List ADT (§ 5.2.3)
The List ADT models
a sequence of
positions storing
arbitrary objects
It establishes a
before/after relation
between positions
Generic methods:

Accessor methods:


Update methods:



size(), isEmpty()

Goodrich, Tamassia
Linked Lists
first(), last()
prev(p), next(p)
replace(p, e)
insertBefore(p, e),
insertAfter(p, e),
insertFirst(e),
insertLast(e)
remove(p)
53
Doubly Linked List
A doubly linked list provides a natural
implementation of the List ADT
Nodes implement Position and store:



element
link to the previous node
link to the next node
prev
next
elem
node
Special trailer and header nodes
nodes/positions
header
trailer
elements
Goodrich, Tamassia
Linked Lists
54
Insertion
We visualize operation insertAfter(p, X), which returns position q
p
A
B
C
p
A
q
B
C
X
p
A
Goodrich, Tamassia
q
B
Linked Lists
X
C
55
Insertion Algorithm
Algorithm insertAfter(p,e):
Create a new node v
v.setElement(e)
v.setPrev(p)
{link v to its predecessor}
v.setNext(p.getNext()) {link v to its successor}
(p.getNext()).setPrev(v) {link p’s old successor to v}
p.setNext(v)
{link p to its new successor, v}
return v {the position for the element e}
Goodrich, Tamassia
Linked Lists
56
Deletion
We visualize remove(p), where p = last()
p
A
B
C
A
B
C
D
p
D
A
Goodrich, Tamassia
B
Linked Lists
C
57
Deletion Algorithm
Algorithm remove(p):
t = p.element
{a temporary variable to hold the
return value}
(p.getPrev()).setNext(p.getNext())
{linking out p}
(p.getNext()).setPrev(p.getPrev())
p.setPrev(null) {invalidating the position p}
p.setNext(null)
return t
Goodrich, Tamassia
Linked Lists
58
Performance
In the implementation of the List ADT
by means of a doubly linked list




The space used by a list with n elements is
O(n)
The space used by each position of the list
is O(1)
All the operations of the List ADT run in
O(1) time
Operation element() of the
Position ADT runs in O(1) time
Goodrich, Tamassia
Linked Lists
59
Sequences and
Iterators
Goodrich, Tamassia
Linked Lists
60
Sequence ADT (§ 5.3)
The Sequence ADT is the
union of the Vector and
List ADTs
Elements accessed by


List-based methods:

Rank, or
Position
Generic methods:

size(), isEmpty()
Vector-based methods:

elemAtRank(r),
replaceAtRank(r, o),
insertAtRank(r, o),
removeAtRank(r)
Goodrich, Tamassia
Linked Lists
first(), last(), prev(p),
next(p), replace(p, o),
insertBefore(p, o),
insertAfter(p, o),
insertFirst(o),
insertLast(o),
remove(p)
Bridge methods:

atRank(r), rankOf(p)
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Applications of Sequences
The Sequence ADT is a basic, generalpurpose, data structure for storing an ordered
collection of elements
Direct applications:


Generic replacement for stack, queue, vector, or
list
small database (e.g., address book)
Indirect applications:

Building block of more complex data structures
Goodrich, Tamassia
Linked Lists
62
Linked List Implementation
A doubly linked list provides a
reasonable implementation of the
Sequence ADT
Nodes implement Position and store:



element
link to the previous node
link to the next node
Position-based methods
run in constant time
Rank-based methods
require searching from
header or trailer while
keeping track of ranks;
hence, run in linear time
Special trailer and header nodes
nodes/positions
header
trailer
elements
Goodrich, Tamassia
Linked Lists
63
Array-based Implementation
elements
We use a
circular array
storing
positions
A position
object stores:


Element
Rank
Indices f and l
keep track of
first and last
positions
0
1
3
positions
S
f
Goodrich, Tamassia
2
Linked Lists
l
64
Sequence Implementations
Operation
size, isEmpty
atRank, rankOf, elemAtRank
first, last, prev, next
replace
replaceAtRank
insertAtRank, removeAtRank
insertFirst, insertLast
insertAfter, insertBefore
remove
Goodrich, Tamassia
Linked Lists
Array
1
1
1
1
1
n
1
n
n
List
1
n
1
1
n
n
1
1
1
65
Iterators (§ 5.4)
An iterator abstracts the
process of scanning through
a collection of elements
Methods of the ObjectIterator
ADT:




object object()
boolean hasNext()
object nextObject()
reset()

ObjectIterator elements()
Two notions of iterator:
Extends the concept of
Position by adding a traversal
capability
Implementation with an array
or singly linked list
Goodrich, Tamassia
An iterator is typically
associated with an another
data structure
We can augment the Stack,
Queue, Vector, List and
Sequence ADTs with method:
Linked Lists


snapshot: freezes the
contents of the data
structure at a given time
dynamic: follows changes to
the data structure
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