• A linked data structure consists of capsules of data known as nodes that are connected via links

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Chapter 15

Linked Data SStructures

Introduction to Linked Data Structures Introduction to Linked Data Structures

A li k d d t t t i t f l f d t k

• A linked data structure consists of capsules of data known as nodes that are connected via links

– Links can be viewed as arrows and thought of as one way passages

f d t th

from one node to another

• In Java, nodes are realized as objects of a node class

• The data in a node is stored via instance variables The data in a node is stored via instance variables

• The links are realized as references

– A reference is a memory address, and is stored in a variable of a class type

type

– Therefore, a link is an instance variable of the node class type itself

Java Linked Lists Java Linked Lists

h i l ki d f li k d d i

• The simplest kind of linked data structure is a linked list

• A linked list consists of a single chain of nodes, each connected to the next by a link y

– The first node is called the head node

– The last node serves as a kind of end marker The last node serves as a kind of end marker

Nodes and Links in a Linked List

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A Simple Linked List Class A Simple Linked List Class

I li k d li t h d i bj t f d l

• In a linked list, each node is an object of a node class

– Note that each node is typically illustrated as a box containing one or more pieces of data

• Each node contains data and a link to another node

– A piece of data is stored as an instance variable of the node – Data is represented as information contained within the node "box" p – Links are implemented as references to a node stored in an instance

variable of the node type

– Links are typically illustrated as arrows that point to the node to which yp y p they "link"

A Node Class (Part 1 of 3) A Node Class (Part 1 of 3)

A Node Class (Part 2 of 3) A Node Class (Part 2 of 3)

A Node Class (Part 3 of 3) A Node Class (Part 3 of 3)

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A Simple Linked List Class A Simple Linked List Class

Th fi t d t t d i li k d li t i ll d

• The first node, or start node in a linked list is called the head node

– The entire linked list can be traversed by starting at the The entire linked list can be traversed by starting at the head node and visiting each node exactly once

• There is typically a variable of the node type (e.g.,

) h f h f d

head ) that contains a reference to the first node in the linked list

However it is not the head node nor is it even a node – However, it is not the head node, nor is it even a node – It simply contains a reference to the head node

A Simple Linked List Class A Simple Linked List Class

A li k d li t bj t t i th i bl h d

• A linked list object contains the variable head as an instance variable of the class

• A linked list object does not contain all the nodes in

• A linked list object does not contain all the nodes in the linked list directly

– Rather, it uses the instance variable head , to locate the head node of the list

– The head node and every node of the list contain a link instance variable that provides a reference to the next instance variable that provides a reference to the next node in the list

– Therefore, once the head node can be reached, then every

th d i th li t b h d

other node in the list can be reached

An Empty List Is Indicated by null An Empty List Is Indicated by null

Th h d i i bl i f

• The head instance variable contains a reference to the first node in the linked list

If th li t i t thi i t i bl i t t ll – If the list is empty, this instance variable is set to null – Note: This is tested using ==, not the equals method

• The linked list constructor sets the head instance

• The linked list constructor sets the head instance variable to null

This indicates that the newly created linked list is empty – This indicates that the newly created linked list is empty

A Linked List Class (Part 1 of 6) A Linked List Class (Part 1 of 6)

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A Linked List Class (Part 2 of 6) A Linked List Class (Part 2 of 6)

A Linked List Class (Part 3 of 6) A Linked List Class (Part 3 of 6)

A Linked List Class (Part 4 of 6) A Linked List Class (Part 4 of 6)

A Linked List Class (Part 5 of 6) A Linked List Class (Part 5 of 6)

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A Linked List Class (Part 6 of 6) A Linked List Class (Part 6 of 6)

Indicating the End of a Linked List Indicating the End of a Linked List

• The last node in a linked list should have its link instance variable set to null

– That way the code can test whether or not a node is the last node

is the last node

– Note: This is tested using == , not the equals method

method

Traversing a Linked List Traversing a Linked List

If li k d li l d i d i b

• If a linked list already contains nodes, it can be traversed as follows:

S t l l i bl l t th l t d b th h d

– Set a local variable equal to the value stored by the head node (its reference)

– This will provides the location of the first node This will provides the location of the first node

– After accessing the first node, the accessor method for the link instance variable will provide the location of the next node

– Repeat this until the location of the next node is equal to null

null

Traversing a Linked List g

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Adding a Node to a Linked List Adding a Node to a Linked List

• The method add adds a node to the start of the linked list

– This makes the new node become the first node on the list

• The variable head gives the location of the current first node of the list

– Therefore, when the new node is created, its link field is set equal to head

– Then head is set equal to the new node

Adding a Node at the Start

Deleting the Head Node from a Linked Li

List

Th th d d l t H dN d th fi t

• The method deleteHeadNode removes the first node from the linked list

– It leaves the It leaves the head head variable pointing to (i e containing a variable pointing to (i.e., containing a reference to) the old second node in the linked list

• The deleted node will automatically be collected and

l d l h h d h

its memory recycled, along with any other nodes that are no longer accessible

In Java this process is called automatic garbage collection – In Java, this process is called automatic garbage collection

A Linked List Demonstration

( f )

(Part 1 of 3)

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A Linked List Demonstration

( f )

(Part 2 of 3)

A Linked List Demonstration

( f )

(Part 3 of 3)

Node Inner Classes Node Inner Classes

N h h li k d li l di d f i d d

• Note that the linked list class discussed so far is dependent on an external node class

• A linked list or similar data structure can be made self‐ A linked list or similar data structure can be made self contained by making the node class an inner class

• A node inner class so defined should be made private, unless used elsewhere

– This can simplify the definition of the node class by eliminating the need for accessor and mutator methods

need for accessor and mutator methods

– Since the instance variables are private, they can be accessed directly from methods of the outer class without causing a privacy leak

Pitfall: Privacy Leaks Pitfall: Privacy Leaks

Th i i l d d li k d li l i d

• The original node and linked list classes examined so far have a dangerous flaw

Th d l th d t f t

– The node class accessor method returns a reference to a node

– Recall that if a method returns a reference to an instance Recall that if a method returns a reference to an instance variable of a mutable class type, then the private restriction on the instance variables can be easily defeated – The easiest way to fix this problem would be to make the

node class a private inner class in the linked list class

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A Linked List Class with a Node Inner Class (Part 1 f 6)

1 of 6)

A Linked List Class with a Node Inner Class (Part 2 f 6)

2 of 6)

A Linked List Class with a Node Inner Class (Part 3 f 6)

3 of 6)

A Linked List Class with a Node Inner Class (Part 4 f 6)

4 of 6)

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A Linked List Class with a Node Inner Class (Part 5 f 6)

5 of 6)

A Linked List Class with a Node Inner Class (Part 6 f 6)

6 of 6)

A Generic Linked List A Generic Linked List

A li k d li t b t d h N d l h t

• A linked list can be created whose Node class has a type parameter T for the type of data stored in the node

– Therefore, it can hold objects of any class type, including types that

t i lti l i t i bl

contain multiple instance variable

– The type of the actual object is plugged in for the type parameter T

• For the most part, this class can have the same methods, p coded in basically the same way, as the previous linked list example

– The only difference is that a type parameter is used instead of an y yp p actual type for the data in the node

• Other useful methods can be added as well

A Generic Linked List Class

( f )

(Part 1 of 9)

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A Generic Linked List Class

( f )

(Part 2 of 9)

A Generic Linked List Class

( f )

(Part 3 of 9)

A Generic Linked List Class

( f )

(Part 4 of 9)

A Generic Linked List Class

( f )

(Part 5 of 9)

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A Generic Linked List Class

( f )

(Part 6 of 9)

A Generic Linked List Class

( f )

(Part 7 of 9)

A Generic Linked List Class

( f )

(Part 8 of 9)

A Generic Linked List Class

( f )

(Part 9 of 9)

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A Sample Class for the Data in a Generic Linked List (Part 1 of 2)

A Sample Class for the Data in a Generic Linked List (Part 2 of 2)

A Generic Linked List Demonstration (Part 1 of 2)

A Generic Linked List Demonstration (Part 2 of 2)

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Pitfall: Using Node instead of Node<T>

N Thi i f ll i l i d b l

• Note: This pitfall is explained by example – any names can be substituted for the node Node and its parameter <T>

• When defining the When defining the LinkedList3<T> LinkedList3<T> class the type for a class, the type for a node is Node<T>, not Node

– If the <T> is omitted, this is an error for which the compiler may or

i (d di h d il f h

may not issue an error message (depending on the details of the code), and even if it does, the error message may be quite strange – Look for a missing <T> when a program that uses nodes with type

parameters gets a strange error message or doesn't run correctly

A Generic Linked List: the equals Method A Generic Linked List: the equals Method

Lik th l li k d li t l h ld ll h

• Like other classes, a linked list class should normally have an equals method

• The equals q method can be defined in a number of reasonable ways

– Different definitions may be appropriate for different situations

• Two such possibilities are the following: Two such possibilities are the following:

1. They contain the same data entries (possibly in different orders) 2. They contain the same data entries in the same order

Of th t l d i f T t l h d fi d

• Of course, the type plugged in for T must also have redefined the equals method

An equals Method for the Linked List in Display 15.7 (Part 1 of 2)

An equals Method for the Linked List in Display 15.7 (Part 2 of 2)

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Simple Copy Constructors and clone Methods

Methods

Th i i l d fi d h

• There is a simple way to define copy constructors and the clone method for data structures such as linked lists

– Unfortunately, this approach produces only shallow copies Unfortunately, this approach produces only shallow copies

• The private helping method copyOf is used by both the copy constructor and the clone method

• The copy constructor uses copyOf to create a copy of the list of nodes

• The clone method first invokes its superclass clone

method, and then uses copyOf to create a clone of the list of nodes

A Generic Linked List: the private method copyOf

Th i t h l i th d Of t k t th t

• The private helping method copyOf takes an argument that is a reference to a head node of a linked list, and returns a reference to the head node of a copy of that list py

– It goes down the argument list one node at a time and makes a copy of each node

The new nodes are added to the end of the linked list being built – The new nodes are added to the end of the linked list being built

• However, although this produces a new linked list with all new nodes, the new list is not truly independent because the data object is not cloned

A Copy Constructor and clone Method for a Generic Linked List (Part 1 of 6)

A Copy Constructor and clone Method for a Generic Linked List (Part 2 of 6)

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A Copy Constructor and clone Method for a Generic Linked List (Part 3 of 6)

A Copy Constructor and clone Method for a Generic Linked List (Part 4 of 6)

A Copy Constructor and clone Method for a Generic Linked List (Part 5 of 6)

A Copy Constructor and clone Method for a Generic Linked List (Part 6 of 6)

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Pitfall: The clone Method Is Protected in Object

• It would have been preferable to clone the data belonging to the list being copied in the copyOf method as follows:

method as follows:

nodeReference = new

Node((T)(position.data).clone(), null);

• However, this is not allowed, and this code will not compile

The error message generated will state that clone is protected – The error message generated will state that clone is protected

in Object

– Although the type used is T , not Object , any class can be plugged in for T

plugged in for T

– When the class is compiled, all that Java knows is that T is a descendent class of Object

Exceptions Exceptions

A i d i lik l h h d h h

• A generic data structure is likely to have methods that throw exceptions

• Situations such as a Situations such as a null null argument to the copy constructor argument to the copy constructor may be handled differently in different situations

– If this happens, it is best to throw a NullPointerException, and

l h h i i h li k d li h dl h i

let the programmer who is using the linked list handle the exception, rather than take some arbitrary action

– A NullPointerException is an unchecked exception: it need not be caught or declared in a throws clause

Tip: Use a Type Parameter Bound for a Better clone

• One solution to this problem is to place a bound on the type parameter T so that it must satisfy a suitable interface

– Although there is no standard interface that does this, it is easy to define one

• For example, a PubliclyCloneable interface could be defined

Tip: Use a Type Parameter Bound for a Better clone

• Any class that implements the

PubliclyCloneable interface would

h h h i

have these three properties:

1. It would implement the Cloneable interface because PubliclyCloneable extends because PubliclyCloneable extends Cloneable

2. It would have to implement a public clone p p method

3. Its clone method would have to make a deep copy

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The PubliclyCloneable Interface The PubliclyCloneable Interface

A Generic Linked List with a Deep Copy clone Method (Part 1 of 8)

A Generic Linked List with a Deep Copy clone Method (Part 2 of 8)

A Generic Linked List with a Deep Copy clone Method (Part 3 of 8)

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A Generic Linked List with a Deep Copy clone Method (Part 4 of 8)

A Generic Linked List with a Deep Copy clone Method (Part 5 of 8)

A Generic Linked List with a Deep Copy clone Method (Part 6 of 8)

A Generic Linked List with a Deep Copy clone Method (Part 7 of 8)

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A Generic Linked List with a Deep Copy clone Method (Part 8 of 8)

A Linked List with a Deep Copy clone Method A Linked List with a Deep Copy clone Method

• Some of the details of the clone method in the previous linked list class may be puzzling, since the following code would also return a deep copy:

would also return a deep copy:

public LinkedList<T> clone() {

return new LInkedList<T>(this);

}

• However because the class implements

• However, because the class implements

PubliclyCloneable which, in turn, extends Cloneable, it must implement the Cloneable interface as specified in the Java documentation

A PubliclyCloneable Class (Part 1 of 4) A PubliclyCloneable Class (Part 1 of 4)

A PubliclyCloneable Class (Part 2 of 4) A PubliclyCloneable Class (Part 2 of 4)

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A PubliclyCloneable Class (Part 3 of 4) A PubliclyCloneable Class (Part 3 of 4)

A PubliclyCloneable Class (Part 4 of 4) A PubliclyCloneable Class (Part 4 of 4)

Demonstration of Deep Copy clone (Part 1 of 3)

Demonstration of Deep Copy clone (Part 2 of 3)

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Demonstration of Deep Copy clone (Part 3 of 3)

Tip: Cloning is an "All or Nothing"

Affair

• If a clone method is defined for a class, then it should follow the official Java guidelines g

– In particular, it should implement the Cloneable interface

Cloneable interface

Iterators Iterators

• A collection of objects, such as the nodes of a linked list, must often be traversed in order to perform some action on each object j

– An iterator is any object that enables a list to be traversed in this way

• A linked list class may be created that has an iterator inner A linked list class may be created that has an iterator inner class

– If iterator variables are to be used outside the linked list class, then the iterator class would be made public

the iterator class would be made public

– The linked list class would have an iterator method that returns an iterator for its calling object

– Given a linked list named Given a linked list named list, this can be done as follows: list, this can be done as follows:

LinkedList2.List2Iterator i = list.iterator();

Iterators Iterators

• The basic methods used by an iterator are as follows:

– restart: Resets the iterator to the beginning of the list

– hasNext: Determines if there is another data item on the list

– next: Produces the next data item on the list

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A Linked List with an Iterator (Part 1 of 6)

A Linked List with an Iterator (Part 2 of 6)

A Linked List with an Iterator (Part 3 of 6)

A Linked List with an Iterator (Part 4 of 6)

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A Linked List with an Iterator (Part 5 of 6)

A Linked List with an Iterator (Part 6 of 6)

Using an Iterator (Part 1 of 6) Using an Iterator (Part 1 of 6)

Using an Iterator (Part 2 of 6) Using an Iterator (Part 2 of 6)

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Using an Iterator (Part 3 of 6) Using an Iterator (Part 3 of 6)

Using an Iterator (Part 4 of 6) Using an Iterator (Part 4 of 6)

Using an Iterator (Part 5 of 6) Using an Iterator (Part 5 of 6)

Using an Iterator (Part 6 of 6) Using an Iterator (Part 6 of 6)

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The Java Iterator Interface The Java Iterator Interface

• Java has an interface named Iterator that specifies how Java would like an iterator to p behave

– Although the iterators examined so far do not – Although the iterators examined so far do not

satisfy this interface, they could be easily redefined to do so

redefined to do so

Adding and Deleting Nodes Adding and Deleting Nodes

• An iterator is normally used to add or delete a node in a linked list

• Given iterator variables position and previous, the following two lines of code will delete the node at location position :

previous.link = position.link;

position = position.link;

– Note: previous points to the node before position

Deleting a Node (Part 1 of 2) Deleting a Node (Part 1 of 2)

1. Existing list with the iterator positioned at “shoes”

"orange juice" "shoes" "socks " null

"coat"

head previous position

2. Bypass the node at position from previous

previous.link = position.link;

"orange juice" "shoes" "socks" null

"coat"

Deleting a Node (Part 2 of 2) Deleting a Node (Part 2 of 2)

3. Update position to reference the next node p pos t o

position = position.link;

"orange juice" "shoes" "socks" null

"coat "

Since no variable references the node "shoes" Java will automatically recycle the memory allocated for it .

4. Same picture with deleted node not shown

"orange juice" "socks" null

"coat"

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Adding and Deleting Nodes Adding and Deleting Nodes

N h J h i b ll i

• Note that Java has automatic garbage collection

– In many other languages the programmer has to keep track of deleted nodes and explicitly return their memory for recycling

– This procedure is called explicit memory management

• The iterator variables position and previous can be used to add a node as well

used to add a node as well

– previous will point to the node before the insertion point, and position will point to the node after the insertion point

Node temp = new Node(newData,position);

previous.link = temp;

Adding a Node between Two Nodes (Part 1 of 2)

1. Existing list with the iterator positioned at “shoes”

"orange juice" "shoes" null

"coat"

2 Create new Node with "socks" linked to "shoes"

2. Create new Node with "socks" linked to "shoes"

temp = new Node(newData, position); // newData is "socks"

"coat"

" k "

t "socks"

temp

Adding a Node between Two Nodes (Part 2 of 2)

3. Make previous link to the Node temp

previous.link = temp;

"coat"coat orange juice shoes null

"socks"

temp

4. Picture redrawn for clarity, but structurally identical to picture 3

"orange juice" "socks "

"coat" "shoes" null

head previous temp position

Variations on a Linked List Variations on a Linked List

• An ordinary linked list allows movement in one direction only

• However, a doubly linked list has one link that references the next node, and one that references the previous node

• The node class for a doubly linked list can begin as follows:

private class TwoWayNode {

private String item;

private TwoWayNode previous;

private TwoWayNode next;

. . .

• In addition, the constructors and methods in the doubly linked list class would be modified to accommodate the extra link

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A Doubly Linked List

Adding a Node to the Front of a Doubly Linked List

Deleting a Node from a Doubly Linked List (1 of 2)

null

1. Existing list with an iterator referencing "shoes"

"coat" "shoes” "socks” null

head position

2. Bypass the "shoes" node from the next link of the previous node

position.previous.next = position.next;

null "coat" "shoes” "socks” null

head position

Deleting a Node from a Doubly Linked List (2 of 2)

3. Bypass the "shoes" node from the previous link of the next node and move position off the deleted node

position.next.previous = position.previous;

p p p p ;

position = position.next;

null "coat"

head

"shoes "socks null

position

4. Picture redrawn for clarity with the "shoes" node removed since there are no longer references pointing to this node .

null "coat"

head

"socks”

position

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Inserting a Node Into a Doubly Linked List (1 of 2)

null

1. Existing list with an iterator referencing "shoes"

"coat" "shoes” "socks” null

head position

2. Create new TwoWayNode with previous linked to "coat" and next to "shoes"

TwoWayNode temp = new TwoWayNode(newData, position.previous, position);

// newData = "shirt"

//

head "shirt"

position temp

Inserting a Node Into a Doubly Linked List (2 of 2)

The Stack Data Structure The Stack Data Structure

• A stack data structure is not necessarily a linked data structure, but can be implemented p as one

– A stack is a data structure that removes items in – A stack is a data structure that removes items in

the reverse order of which they were inserted (LIFO: Last In First Out)

(LIFO: Last In First Out)

– A linked list that inserts and deletes only at the h d f th li t i t k

head of the list is a stack

The Queue Data Structure The Queue Data Structure

A i d t t t th t h dl d t i

• A queue is a data structure that handles data in a first‐in/first‐out fashion (FIFO) like a line at a bank

– Customers add themselves to the end of the line and are Customers add themselves to the end of the line and are served from the front of the line

• A queue can be implemented with a linked list

– However, a queue needs a pointer at both the head and tail (the end) of the linked list

– Nodes are removed from the front (head end) and are – Nodes are removed from the front (head end), and are

added to the back ( tail end)

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A Queue Class (Part 1 of 5) A Queue Class (Part 1 of 5)

A Queue Class (Part 2 of 5) A Queue Class (Part 2 of 5)

A Queue Class (Part 3 of 5) A Queue Class (Part 3 of 5)

A Queue Class (Part 4 of 5) A Queue Class (Part 4 of 5)

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A Queue Class (Part 5 of 5) A Queue Class (Part 5 of 5)

Demonstration of the Queue Class (Part 1 of 2)

Demonstration of the Queue Class (Part 2 of 2)

Running Times Running Times

H f i ?

• How fast is program?

– "Seconds"?

C id l i ? ll i ?

– Consider: large input? .. small input?

• Produce "table"

d i i

– Based on input size

– Table called "function" in math

• With arguments and return values!

– Argument is input size:

T(10), T(10,000), … ( ) ( )

• Function T is called "running time"

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Table for Running Time Function:

Display 15 31 Some Values Display 15.31 Some Values of a Running Time Function

Consider Sorting Program Consider Sorting Program

• Faster on smaller input set?

– Perhaps p

– Might depend on "state" of set

• "Mostly" sorted already?

• Mostly sorted already?

• Consider worst‐case running time

– T(N) is time taken by "hardest" list

• List that takes longest to sort

Counting Operations Counting Operations

• T(N) given by formula, such as:

T(N) = 5N + 5 ( )

– "On inputs of size N program runs for 5N + 5 time units"

5N + 5 time units

• Must be "computer‐independent"

– Doesn’t matter how "fast" computers are – Can’t count "time"

– Instead count "operations"

Counting Operations Example Counting Operations Example

i i 0

• int i = 0;

Boolean found = false;

while (( i < N) && !found) (( ) ) if (a[I] == target)

found = true;

else else

i++;

• 5 operations per loop iteration: p p p

<, &&, !, [ ], ==, ++

• After N iterations, final three: <, &&, !

• So: 6N+5 operations when target not found

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Big O Notation Big‐O Notation

• Recall: 6N+5 operations in "worst‐case"

• Expressed in "Big‐O" notation

– Some constant "c" factor where c(6N+5) is actual running time

• c different on different systems

– We say code runs in time O(6N+5)

– But typically only consider "highest term"

• Term with highest exponent

– O(N) here

Big O Terminology Big‐O Terminology

i i i

• Linear running time:

– O(N)—directly proportional to input size N

• Quadratic running time:

– O(N O(N ) ² )

• Logarithmic running time:

O(l N) – O(log N)

• Typically "log base 2"

V f t l ith !

• Very fast algorithms!

Display 15.32

Comparison of Running Times

Efficiency of Linked Lists Efficiency of Linked Lists

• Find method for linked list

– May have to search entire list y

– On average would expect to search half of the list, or n/2

or n/2

– In big‐O notation, this is O(n)

• Adding to a linked list

– When adding to the start we only reassign some g y g references

– Constant time or O(1) Constant time or O(1)

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Hash Tables Hash Tables

• A hash table or hash map is a data structure that efficiently stores and retrieves data from y memory

• Here we discuss a hash table that uses an

• Here we discuss a hash table that uses an array in combination with singly linked lists

• Uses a hash function

– Maps an object to a key Maps an object to a key

– In our example, a string to an integer

Simple Hash Function for Strings Simple Hash Function for Strings

S th ASCII l f h t i th

• Sum the ASCII value of every character in the string and then compute the modulus of the sum using the size of the fixed array.

private int computeHash(String s) private int computeHash(String s) {

int hash = 0;

for (int i = 0; i < s.length(); i++) {

hash += s.charAt(i);

}

return hash % SIZE; // SIZE = 10 in example return hash % SIZE; // SIZE = 10 in example }

Example: “dog” = ASCII 100, 111, 103

Hash = (100 + 111 + 103) % 10 = 4

Hash Table Idea Hash Table Idea

• Storage Storage

– Make an array of fixed size, say 10

h l l k d l

– In each array element store a linked list

– To add an item, map (i.e. hash) it to one of the 10 array elements, then add it to the linked list at that location

• Retrieval

To look up an item determine its hash code then – To look up an item, determine its hash code then

search the linked list at the corresponding array slot for the item

slot for the item

Constructing a Hash Table (1 of 2) Constructing a Hash Table (1 of 2)

1. Existing hash table initialized with ten empty linked lists hashArray = new LinkedList3[SIZE]; // SIZE = 10

empty empty empty empty empty empty empty empty empty empty

0 1 2 3 4 5 6 7 8 9

hashArray

2. After adding "cat" with hash of 2

0 1 2 3 4 5 6 7 8 9

empty empty empty empty null empty empty empty empty

hashArray

t cat

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Constructing a Hash Table (2 of 2) Constructing a Hash Table (2 of 2)

3 After adding "dog" with hash of 4 and "bird" with hash of 7 3. After adding dog with hash of 4 and bird with hash of 7

empty empty empty empty empty empty empty

0 1 2 3 4 5 6 7 8 9

hashArray

cat dog bird

4. After adding "turtle" with hash of 2 – collision and chained to linked list with "cat"

empty empty empty empty empty empty empty

0 1 2 3 4 5 6 7 8 9

hashArray empty empty empty empty empty empty empty

hashArray

turtle dog bird

cat

A Hash Table Class (1 of 3) A Hash Table Class (1 of 3)

1 public class HashTable

2 { {

3 // Uses the generic LinkedList2 class from Display 15.7

4 private LinkedList2[] hashArray;

5 private static final int SIZE = 10;

6 public HashTable()

7 {

8 hashArray = new LinkedList2[SIZE];

9 for (int i=0; i < SIZE; i++) ( ; ; )

10 hashArray[i] = new LinkedList2();

11 }

12 private int computeHash(String s) p p ( g )

13 {

14 int hash = 0;

15 for (int i = 0; i < s.length(); i++)

16 { {

17 hash += s.charAt(i);

18 }

19 return hash % SIZE;

20 }

}

A Hash Table Class (2 of 3) A Hash Table Class (2 of 3)

21 /**

22 Returns true if the target is in the hash table, g ,

23 false if it is not.

24 */

25 public boolean containsString(String target)

26 { {

27 int hash = computeHash(target);

28 LinkedList2 list = hashArray[hash];

29 if (list.contains(target))

30 return true; ;

31 return false;

32 }

A Hash Table Class (3 of 3) A Hash Table Class (3 of 3)

33 /**

34 Stores or puts string s into the hash table p g

35 */

36 public void put(String s)

37 {

38 int hash = computeHash(s); p ( ); // Get hash value //

39 LinkedList2 list = hashArray[hash];

40 if (!list.contains(s))

41 {

42 // Only add the target if it's not already // y g y

43 // on the list.

44 hashArray[hash].addToStart(s);

45 }

46 } }

47 } // End HashTable class

(35)

Hash Table Demonstration (1 of 2) Hash Table Demonstration (1 of 2)

1 public class HashTableDemo

2 { {

3 public static void main(String[] args)

4 {

5 HashTable h = new HashTable();

6 System.out.println("Adding dog, cat, turtle, bird");

7 h.put("dog");

8 h.put("cat");

9 h.put("turtle"); p ( );

10 h.put("bird");

11 System.out.println("Contains dog? " +

12 h.containsString("dog"));

13 System.out.println("Contains cat? " + y p (

14 h.containsString("cat"));

15 System.out.println("Contains turtle? " +

16 h.containsString("turtle"));

17 System.out.println("Contains bird? " + y p (

18 h.containsString("bird"));

Hash Table Demonstration (2 of 2) Hash Table Demonstration (2 of 2)

19 System.out.println("Contains fish? " + 20 h.containsString("fish")); g( ));

21 System.out.println("Contains cow? " +

22 h.containsString("cow"));

23 }

24 } }

SAMPLE DIALOGUE

Adding dog, cat, turtle, bird Contains dog? true

Contains cat? true Contains turtle? true Contains bird? true Contains fish? false Contains cow? false

Hash Table Efficiency Hash Table Efficiency

• Worst Case

– Every item inserted into the table has the same hash key, the find operation may have to search through all items

( ( ) )

every time (same performance as a linked list, O(n) to find)

• Best Case

– Every item inserted into the table has a different hash key, the find operation will only have to search a list of size 1,

f t O(1) t fi d very fast, O(1) to find.

• Can decrease the chance of collisions with a better hash function

• Tradeoff: Lower chance of collision with bigger hash table, but more wasted memory space

Set Template Class Set Template Class

• A set is a collection of elements in which no element occurs more than once

• We can implement a simple set that uses a linked list to store the items in the set

linked list to store the items in the set

• Fundamental set operations we will support:

– Add – Contains Contains – Union – Intersection

(36)

Sets Using Linked Lists Sets Using Linked Lists

A Set Class (1 of 5) A Set Class (1 of 5)

1 // Uses a linked list as the internal data structure 2 // to store items in a set. //

3 public class Set<T>

4 {

5 private class Node<T>

6 { {

7 private T data;

8 private Node<T> link;

9 public Node( ) p ( )

10 {

11 data = null;

12 link = null;

13 } }

14 public Node(T newData, Node<T> linkValue)

15 {

16 data = newData;

17 link = linkValue; ;

18 }

19 }//End of Node<T> inner class 20 private Node<T> head;

p

A Set Class (2 of 5) A Set Class (2 of 5)

21 public Set()

22 { {

23 head = null;

24 }

25 /**

26 Add a new item to the set. If the item 27 is already in the set, false is returned,

28 otherwise true is returned.

29 */

30 public boolean add(T newItem) p ( )

31 {

32 if (!contains(newItem))

33 {

34 head = new Node<T>(newItem, head); ( , );

35 return true;

36 }

37 return false;

38 } }

A Set Class (3 of 5) A Set Class (3 of 5)

39 public boolean contains(T item)

40 {

41 Node<T> position = head;

42 T itemAtPosition;

43 while (position != null)

44 {

45 itemAtPosition = position.data;

46 if (itemAtPosition.equals(item))

47 return true;

48 position = position.link;

49 }

50 return false; //target was not found

51 }

52 public void output( )

53 {

54 Node position = head;

55 while (position != null)

56 {

57 System.out.print(position.data.toString() + " ");

58 position = position.link;

59 }

60 System.out.println();

61 }

(37)

A Set Class (4 of 5) A Set Class (4 of 5)

62 /**

63 Returns a new set that is the union

64 of this set and the input set.

65 */

66 public Set<T> union(Set<T> otherSet)

67 {

68 Set<T> unionSet = new Set<T>();

69 // Copy this set to unionSet

70 Node<T> position = head;

71 while (position != null)

72 {

73 unionSet.add(position.data);

74 position = position.link;

75 }

//

76 // Copy otherSet items to unionSet.

77 // The add method eliminates any duplicates.

78 position = otherSet.head;

79 while (position != null)

80 {

81 unionSet.add(position.data);

82 position = position.link;

83 }

84 return unionSet;

85 }

A Set Class (5 of 5) A Set Class (5 of 5)

86 /**

87 Returns a new that is the intersection

88 of this set and the input set.

89 */

90 public Set<T> intersection(Set<T> otherSet)

91 {

92 Set<T> interSet = new Set<T>();

93 // Copy only items in both sets

94 Node<T> position = head;

95 while (position != null)

96 {

97 if (otherSet.contains(position.data))

98 interSet.add(position.data);

99 position = position.link;

100 }

101 return interSet;

102 }

103 }

The clear, size, and isEmpty methods are identicalto those in Display 15.8 for the LinkedList3 class.

A Set Class Demo (1 of 3) ( )

1 class SetDemo

2 {

3 public static void main(String[] args)

4 {

5 // Round things

6 Set round = new Set<String>();

7 // Green things

8 Set green = new Set<String>();

9 // Add some data to both sets

10 round.add("peas");

11 d dd( b ll )

11 round.add("ball");

12 round.add("pie");

13 round.add("grapes");

14 dd( )

14 green.add("peas");

15 green.add("grapes");

16 green.add("garden hose");

17 green.add("grass");

18 System.out.println("Contents of set round: ");

19 round.output();

20 System.out.println("Contents of set green: ");

21 t t()

21 green.output();

22 System.out.println();

A Set Class Demo (2 of 3) A Set Class Demo (2 of 3)

23 System.out.println("ball in set round? " +

24 round.contains("ball"));

25 System.out.println("ball in set green? " +

26 green.contains("ball"));

27 System.out.println("ball and peas in same set? " + 28 ((round.contains("ball") &&

29 (round.contains("peas"))) ||

30 (green.contains("ball") &&

31 (green.contains("peas")))));

32 System.out.println("pie and grass in same set? " + 33 ((round.contains("pie") &&

34 (round.contains("grass"))) ||

35 (green.contains("pie") &&

36 (green.contains("grass")))));

(38)

A Set Class Demo (3 of 3) A Set Class Demo (3 of 3)

37 System.out.print("Union of green and round: ");

38 round.union(green).output();

39 System.out.print("Intersection of green and round: ");

40 round.intersection(green).output();

41 }

42 }

SAMPLE DIALOGUE

Contents of set round:

grapes pie ball peas Contents of set green:

Grass garden hose grapes peas Grass garden hose grapes peas

ball in set round? true ball in set green? false ball and peas in same set? true ball and peas in same set? true pie and grass in same set? false

Union of green and round: garden hose grass peas ball pie grapes Intersection of green and round: peas grapes

Trees Trees

T i d id l d d

• Trees are a very important and widely used data structure

Lik li k d li h b d d

• Like linked lists, they are a structure based on nodes and links, but are more complicated than linked lists

All t h d ll d th t

– All trees have a node called the root

– Each node in a tree can be reached by following the links from the root to the node

from the root to the node

– There are no cycles in a tree: Following the links will always lead to an "end"

Trees Trees

A bi t i th t ki d f t

• A binary tree is the most common kind of tree

– Each node in a binary tree has exactly two link instance variables – A binary tree must satisfy the Binary Search Tree Storage Rule

• The root of the tree serves a purpose similar to that of the instance variable head in a linked list

– The node whose reference is in the The node whose reference is in the root root instance variable is called instance variable is called the root node

• The nodes at the "end" of the tree are called leaf nodes

Both of the link instance variables in a leaf node are null – Both of the link instance variables in a leaf node are null

A Binary Tree (Part 1 of 2)