Data Structures 1

Basic Data StructuresElementary Structures• Arrays

• Lists

Search Structures• Binary search Tree• Hash Tables

Sequence Structures• Stacks• Queues

Graphs

Data Structures 2

What is a data structuredata structure?A data structure (DS) is essentially a device that collects and allows the manipulation of data within the structure.

•DS = Model (idea) + operations

•A DS is independent of its implementation.

•In Java, use interface to specify operations of DS

•The interface describes theoperation, but says nothingabout its implementation.

Example: A Stack • Model: A Stack•Operations:

•Add to stack•Remove from stack•check for empty•look into stack•empty the stack.

Functionality specified using interface

public interface Stack{ public void push(Object o); public Object pop(); public Object peek(); public boolean isEmpty(); public void makeEmpty();}

Data Structures 3

Stack Structure An array implementation of a Stack

public class StackArray impements Stack{

private Objects[] s;

private int top;

public StackArray(int size){

s = new Object[size];

top = -1;

}

public void push(Object item){ s[++top] = item;}

public Object pop(){return s[top--];}

public Object peek(){return s[top];}

public boolean isEmpty(){return (top==-1);}

public void makeEmpty(){top = -1;}

public boolean isFull(){return (top==s.length-1);}

}

max-1

0123

top

3

Data Structures 4

Queue Structure

DS: A Queue•Idea: A Queue or a line•Operations:

•Add to the Queue•Remove from the Queue•peek at front element•check for empty•Make empty

public interface Queue{

public void enQueue(Object x);

public Object deQueue();

public boolean isEmpty();

public void makeEmpty();

public Object peek();

}

0 1 2 3

front back

Implementation 1: Front always at array[0]

Implementation 2: With wrap around.

front back0 12

Can overflow

Data Structures 5

Queue Structure

public class QueueCircularArray implements Queue{ private Object[] q; private int front, back; private int usedSpace;

public QueueCircularArray(int size){ q = new Object[size]; front = 0; back = size-1; usedSpace=0; } public void enqueue(Object item){ back = (back+1)%q.length; q[back] = item; usedSpace++; } public Object dequeue(){ Object item = q[front]; q[front] = null; front = (front+1)%q.length; usedSpace--; return item; } public boolean isEmpty(){ (usedSpace==0); } public boolean isFull() { (usedSpace==q.length);} public Object peek(){return q[front];}}

Data Structures 6

What is a Dynamic Structure?

A data structure where there is “no” size limitation.

Characteristics of dynamic structures:

• Max size usually limited by machine memory

• Amount of memory used is a function of data stored in the structure.

• Data access is usually not random

• There is overhead involved in creating and maintaining such a structure

Data Structures 7

Fixed (or static) verses Dynamic structures

Disadvantages:• Fixed size results in either overflow or under use of internal resources.• Resizing is a computationally expensive operation.

Advantages:• Random/Direct access to data• Usually easy to develop data structures using static structures

Disadvantages:• Lose of random access.• Usually harder to implement.

Advantages:• No overflow or under use problems.• Resizing is usually not expensive.

Static structures:

Dynamic Structures:

Data Structures 8

Data Structure - a generic view:

method1()

method2()

method3()

method4()

ImplementationEither staticof Dynamic Interface

…dequeue(…)…

…enqueue(…)…

…isEmpty(…)…

…makeEmpty(…)

Methods of Queue

Example: Queue

Array or dynamicimplementation of queue

Data Structures 9

Dynamic Structures - preliminaries

Integer p;Integer q;

p

q

a1

?

p = new Integer(5);

5

a1

p = new Integer(6);

p a2 5

a1

6

a2

q = p;

p a2 6

a2

q a2

q = new Integer(9); 6

a2

a2p

9

a3

a3q

p = null; 6

a2

p

9

a3

a3q

q=p;6

a2

p

9

a3

q

Data Structures 10

Dynamic Structures - preliminaries

public class IntegerNode{ private int item; private IntegerNode next;

public IntegerNode(int item){ setItem(item); next =null; } public void setItem(int item){ this.item = item; } public int getItem(){ return item; } public void setNext(InegerNode next){ this.next = next; } public IntegerNode getNext(){ return next; }}

IntegerNode n1;

n1 ?

n1 = new IntegerNode(5);

n1 a1item next

a1

5

IntegerNode n2 = new IntegerNode(7);

n2 a2item next

a2

7

n1.setNext(n2);

n2 a2item next

a2

7

item next

a1

5 a2n1 a1

Data Structures 11

n2 =null;

n2 item next

a2

7

item next

a1

5 a2n1 a1

Dynamic Structures - preliminaries

n2 = n1.getNext();

n1 a15 a2

a1

7

a2

n2 a2

n2.setNext(new IntegerNode(9));

5 a2

a1

7 a3

a2

9

a3

n1 a1

n2 a2

IntegerNode n3 = n2;

n2 = n2.getNext();

5 a2

a1

7 a3

a2

9

a3

n1 a1

n3 a2 n2 a3

n2.setNext(new IntegerNode(3));n2 = null;

5 a2

a1

7 a3

a2

9 a4

a3

n1 a1

n3 a2 n2

3

a4

n3.setNext(null);

5 a2

a1

7

a2

9 a4

a3

n1 a1

n3 a2 n2

3

a4

Data Structures 12

A dynamic Stack

public class DStack implements Stack{ class StackNode{ int data; StackNode next; StackNode(int d){data = d; next = null;} }//inner class private StackNode top; private int size;

public DStack(){

Rules regarding Constructors:

ALWAYS initialize instance variables to null. }

public void push(int d){Rules regarding adding to dynamic structures:

Consider 2 cases Case 1: Adding to an empty structure Case 2: Adding to the front of structure (maybe covered in 1) Case 2: Inserting to an internal position.

}

Data Structures 13

A dynamic Stack

public int pop(){ Rules regarding removing from a dynamic structure:

Case 1: Deleting a “root” elementCase 2: Deleting an internal element

Data Structures 14

IntegerNode temp = front;

while(temp != null){

temp = temp.getNext();

}

temp a1

IntegerNode temp = front;while (temp!=null){ Integer item = temp.getItem(); System.out.println(item.toString()); temp = temp.getNext();}

Traversing a Structure

9 a4

a3 a4

#

an

5 a2

a1

7 a3

a2

front a13 …

Rules regarding traversing a structure:1. Never move the reference pointing to the root of the structure2. Check for null before moving.

Moving back and fourth along the structure.

Traversing the structure below:

Plain traversal: Printing the nodes in the structure:

view animation!

Data Structures 15

Dynamic Queue

9 a4

a3a4

#

an

5 a2

a1

7 a3

a2

front

a1

3 …

…enQueue(…)…

…deQueue(…)…

…isEmpty(…)…

…makeEmpty(…)back

an

… peek(…)…

Instance variables of class Queue

Data Structures 16

Dynamic Queue

public class DynamicQueue implements Queue{ class ListNode{ //inner class int data; ListNode next; ListNode(int d, ListNode n){ data = d; next = n; } } private ListNode front; back;

public Queue(){front = null;back = null;

}

RULEAlways initialize instance references

Data Structures 17

Dynamic Queue

public class DynamicQueue implements Queue{ class ListNode{ //inner class int data; ListNode next; ListNode(int d){ data = d; next = null; } } private ListNode front; back;

public void enQueue(Object o){ //Case 1- adding the initial element ListNode n = new ListNode(o,null); if (front == null){ //Case 2- adding subsequent elements

Data Structures 18

Dynamic Linked List

9 a4

a3a4

#

an

5 a2

a1

7 a3

a2

front

a1

3 … …get(…)…

…remove(…)…

…add(…)…

…search(…)

Data Structures 19

List Structure

List Structure:

public Interface List{

public Object get(int index) throws IndexOutOfBoundsException;

public void remove(int index) throws IndexOutOfBoundsException;

public void add(Object item, int index) throws IndexOutOfBoundsException;

public int search(Object item);

public boolean isEmpty();

public void makeEmpty();

public int size();

}

0 1 2

back

Cannot add/remove/get items beyond “back”

Can you implement this?

Data Structures 20

Dynamic Linked List

public class DList implements List{ class ListNode{ int data; ListNode next; ListNode(int o, ListNode n){ data = o; n = next; } }

private ListNode front;

public List(){ …} public void add(Object o, int pos) throws … {…} public Object get(int pos) throws… {…} public void remove(int pos) throws… {…} public int search(Object o){…} public boolean isEmpty(){…} public int size(){…} public void makeEmpty(){…}}

Observe:• Inner class

• A single instance variable, front

• Client’s view same for both dynamic and static implementations.

Data Structures 21

Dynamic Linked List

RULE: Always initialize references to null or other known valuein all dynamic structures.

public class DList implements List{ class ListNode{ int data; ListNode next; ListNode(int o, ListNode n){ data = o; n = next; } }

private ListNode front;

public List(){ front = null;}…

}

Data Structures 22

Dynamic Linked List

RULE: When making a change to any dynamic structure,

treat changing a node referenced by a named variablenamed variable as special case.

public void add(Object o, int pos) throws IndexOutOfBoundsException { 0. Check for exception case 1. Create a new ListNode with o as the data 2. if inserting at the front of the list, then //named variable, front, changing!!! 3. Insert the new ListNode in front so as not to lose the remaining elements } 4. else{ //front, named variable, does not change 5. traverse to one-before the place to add 6. Insert the new element in so as not to lose the remaining list. }}

Data Structures 23

Dynamic Linked Listpublic class DList implements List{ … /** * This method will add the data object o into position pos * in the list. * @param o the data item to be added * @param pos the position to which o should be added in the list * @exception IndexOutOfBoundsException will be thrown if (pos<0) * or (pos > size of the list) */ public void add(int o, int pos) throws IndexOutOfBoundsException{

if (pos<0)||(pos>size()) throw new IndexOutOfBoundsException();ListNode n = new ListNode(o,null); //create a new nodeif (pos == 0){ //adding to front? n.next(front); //add carefully! front = n;}else{ //adding internally ListNode temp = front; //traverse for(int i=0; i<pos-1; i++) temp = temp.next; n.next = temp.next; //insert in temp.next = n;}

}

Data Structures 24

Dynamic Linked List

RULE: When making a change to any dynamic structure, treat making a change to a node referenced by a named variable a special case.

public void remove(int pos) throws IndexOutOfBoundsException { 0. Check for exception case 1. Remove the first Node? //Named variable, front, changing!!!

2. Remove so as not to lose the rest of the list

3. else4. Traverse to one before the node to remove5. Detach the node so as not to lose the rest of the list

}

Data Structures 25

public class DList implements List{ … /** * The purpose of this method is to remove a data object from * the list at the given position * @param the item position to be removed * @exception IndexOutOfBoundsException will be thrown if (pos<0) * or (pos>=size()) */ public void remove(int pos) throws IndexOutOfBoundsException{

if (pos<0)||(pos>=size()) throw new IndexOutOfBoundsException();ListNode temp;if (pos == 0){ //remove the first node?

temp = front; //carefully - so as not to losefront = front.next; //the list!

}else{ //remove an interior node

ListNode n = front; //traversefor(int i=0; i<pos-1; i++) n = n.next;temp = n.next;n.next = temp.next; //remove

}temp.next = null;

}

Dynamic Linked List

Data Structures 26

public class DList …{ …

public int search(int target){ IntegerNode temp = front; int location = 0; while (temp!=null){ if (temp.getItem() == target) return location; location++; temp = temp.getNext(); } return -1;}public boolean isEmpty(){

return (front == null);}public int size(){

1. traverse the list counting the elements2. return the count

}public void makeEmpty(){

front = null;}

}

Dynamic Linked List