stack and queue

Stack and Queue

Stack

Definition• Stack is an ordered collection of data

items in which access is possible only at one end (called the top of the stack).

• Stacks are known as LIFO (Last In, First Out) lists. The last element inserted will be the first to be retrieved

Stack as an AbstractData Type

Basic operations:1. Construct a stack (usually empty)2. Check if stack is empty3. Push: Add an element at the top of the stack4. Pop: Remove the top element of the stack5. Peek: Retrieve the top element of the stack

Adding a plate pushes those below it down in the stack

Removing a plate pops those below it up one position.

Push and Pop Primary operations: Push and Pop Push

◦ Add an element to the top of the stack Pop

◦ Remove the element at the top of the stack

A

top

empty stack

top

top

top

push an element push another

A

B

pop

A

Implementation of Stacks Any list implementation could be used to

implement a stack◦ Arrays (static: the size of stack is given initially)◦ Linked lists (dynamic: never become full)

We will explore implementations based on array and linked list

Array Implementation Need to declare an array size ahead of time Associated with each stack is TopOfStack

◦ for an empty stack, set TopOfStack to -1 Push

◦ (1)   Increment TopOfStack by 1.◦ (2)   Set Stack[TopOfStack] = X

Pop◦ (1)   Set return value to Stack[TopOfStack]◦ (2)   Decrement TopOfStack by 1

These operations are performed in very fast constant time

Stack classclass Stack {public:

Stack(int size = 10); // constructorbool IsEmpty() { return top == -1; }bool IsFull() { return top == maxSize; }double Peek();void push(const double x);double pop();void displayStack();

private:int maxSize // max stack size = size - 1int top; // current top of stackdouble[] values; // element array

};

Stack class Attributes of Stack

◦ maxTop: the max size of stack◦ top: the index of the top element of stack◦ values: point to an array which stores elements of stack

Operations of Stack◦ IsEmpty: return true if stack is empty, return false

otherwise◦ IsFull: return true if stack is full, return false otherwise◦ Peek: return the element at the top of stack◦ Push: add an element to the top of stack◦ Pop: delete the element at the top of stack◦ DisplayStack: print all the data in the stack

Create Stack The constructor of Stack

◦ Allocate a stack array of size. By default, size = 10.

◦ When the stack is full, top will have its maximum value, i.e. size – 1.

◦ Initially top is set to -1. It means the stack is empty.Stack(int size) {

maxTop= size - 1;values = new double[size];top = -1;

}

Although the constructor dynamically allocates the stack array, the stack is still static. The size is fixed after the initialization.

Push Stack void Push(const double x);

◦ Push an element onto the stack◦ If the stack is full, print the error information.◦ Note top always represents the index of the

top element. After pushing an element, increment top.

void push(double x) {if (IsFull())

System.out.println("Error: the stack is full.“); else

values[++top] = x;}

Pop Stack double Pop()

◦ Pop and return the element at the top of the stack

◦ If the stack is empty, print the error information. (In this case, the return value is useless.)

◦ Don’t forgot to decrement top

double pop() throw EmptyStackException{if (IsEmpty()) {

System.out.println("Error: the stack is empty.“);throw EmptyStackException;

}else {

return values[top--];}

}

Stack Top double Peek()

◦ Return the top element of the stack◦ Unlike Pop, this function does not remove

the top element

double Peek() throws EmptyStackException{if (IsEmpty()) {

System.out.println("Error: the stack is empty." ); throw EmptyStackException;

}else

return values[top];}

Printing all the elements

void DisplayStack()◦ Print all the elements

void DisplayStack() {System.out.print("top -->“);for (int i = top; i >= 0; i--)

System.out.print( "\t|\t" +values[i] + "\t|\n“); System.out.println("\t|---------------|“);}

}

Using Stack

Initialize stack with 5 items

push(5.0);push(6.5);push(-3.0);push(-8.0);

DisplayStack();

pop(); then print top();pop(); then print top();

result

Stack: Linked List Implementation Push and pop at the head of the list

◦ New nodes should be inserted at the front of the list, so that they become the top of the stack

◦ Nodes are removed from the front (top) of the list Straight-forward linked list implementation

◦ push and pop can be implemented fairly easily, e.g. assuming that head is a reference to the node at the front of the list

List Stack ExampleJava Code

Stack st = new Stack();st.push(6);

top

6

List Stack ExampleJava Code

Stack st = new Stack();st.push(6); st.push(1);

top

6

1

List Stack ExampleJava Code

Stack st = new Stack();st.push(6); st.push(1); st.push(7);top

6

1

7

List Stack ExampleStack st = new Stack();st.push(6); st.push(1); st.push(7); st.push(8); top

6

1

7

8

List Stack ExampleJava Code

Stack st = new Stack();st.push(6); st.push(1); st.push(7); st.push(8); st.pop();

top

6

1

7

8

List Stack ExampleJava Code

Stack st = new Stack();st.push(6); st.push(1); st.push(7); st.push(8); st.pop();

top

6

1

7

Stack: ADT List Implementation Push() and pop() either at the beginning or at

the end of ADT List◦ at the beginning:

public void push(Object newItem) { list.insertAtHead(item); } // end pushpublic Object pop() {

return list.removeFromHead();} // end pop

Chapter 5: Stacks 24

Java implementation of StackSpecification of the Stack Abstract Data Type (continued)

Chapter 5: Stacks 25

Text studies two client programs using stacks◦ Palindrome finder◦ Parentheses matcher

A Palindrome is a string that reads the same in either direction◦ Examples: “Able was I ere I saw Elba”

Stack Applications

Chapter 5: Stacks 26

Stack Applications (continued)

Chapter 5: Stacks 27

When analyzing arithmetic expressions, it is important to determine whether an expression is balanced with respect to parentheses◦ (a+b*(c/(d-e)))+(d/e)

Problem is further complicated if braces or brackets are used in conjunction with parenthesis

Solution is to use stacks!

Stack Applications (continued)

Chapter 5: Stacks 28

Stack Applications (continued)

Chapter 5: Stacks 29

Stack Applications (continued)

Chapter 5: Stacks 30

Can use either the ArrayList, Vector, or the LinkedList classes as all implement the List interface

Name of class illustrated in text is ListStack◦ ListStack is an adapter class as it adapts the

methods available in another class to the interface its clients expect by giving different names to essentially the same operations

Implementing a Stack with a List Component

Chapter 5: Stacks 31

Need to allocate storage for an array with an initial default capacity when creating a new stack object

Need to keep track of the top of the stack No size method

Implementing a Stack Using an Array

Chapter 5: Stacks 32

Implementing a Stack Using an Array (continued)

Chapter 5: Stacks 33

We can implement a stack using a linked list of nodes

Implementing a Stack as a Linked Data Structure

Chapter 5: Stacks 34

Vector is poor choice for stack implementation as all Vector methods are accessible

Easiest implementation would be to use an ArrayList component for storing data

All insertions and deletions are constant time regardless of the type of implementation discussed◦ All insertions and deletions occur at one end

Comparison of Stack Implementations

Chapter 5: Stacks 35

Consider two case studies that relate to evaluating arithmetic expressions◦ Postfix and infix notation

Expressions normally written in infix form◦ Binary operations inserted between their

operands A computer normally scans an expression

string in the order that it is input; easier to evaluate an expression in postfix form

Additional Stack Applications

Chapter 5: Stacks 36

Additional Stack Applications (continued)

37

Advantage of postfix form is that there is no need to group subexpressions in parentheses

No need to consider operator precedence

Additional Stack Applications (continued)

38

Evaluating Postfix Expressions

39

Evaluating Postfix Expressions (continued)

Chapter 5: Stacks 40

Evaluating Postfix Expressions (continued)

Chapter 5: Stacks 41

Evaluating Postfix Expressions (continued)

Chapter 5: Stacks 42

Converting from Infix to Postfix

43

Additional Stack Applications (continued)

44

Evaluating Postfix Expressions (continued)

45

Evaluating Postfix Expressions (continued)

46

Queue

Queue Overview Queue ADT Basic operations of queue

◦ Enqueuing, dequeuing. Implementation of queue

◦ Array◦ Linked list

Queue ADT Like a stack, a queue is also a list.

However, with a queue, insertion is done at one end, while deletion is performed at the other end.

Accessing the elements of queues follows a First In, First Out (FIFO) order.◦ Like customers standing in a check-out line in a

store, the first customer in is the first customer served.

The Queue ADT Another form of restricted list

◦ Insertion is done at one end, whereas deletion is performed at the other end

Basic operations:◦ enqueue: insert an element at the rear of the list◦ dequeue: delete the element at the front of the list

First-in First-out (FIFO) list

Enqueue and Dequeue Primary queue operations: Enqueue and

Dequeue Like check-out lines in a store, a queue has a

front and a rear. Enqueue

◦ Insert an element at the rear of the queue Dequeue

◦ Remove an element from the front of the queue

Insert (Enqueue)

Remove(Dequeue) rearfront

Implementation of Queue Just as stacks can be implemented as arrays

or linked lists, so with queues. Dynamic queues have the same advantages

over static queues as dynamic stacks have over static stacks

Queue Implementation of Array

There are several different algorithms to implement Enqueue and Dequeue

Naïve way◦ When enqueuing, the front index is always

fixed and the rear index moves forward in the array.

front

rear

Enqueue(3)

3

front

rear

Enqueue(6)

3 6

front

rear

Enqueue(9)

3 6 9

Queue Implementation of Array

Naïve way◦ When enqueuing, the front index is always

fixed and the rear index moves forward in the array.

◦ When dequeuing, the element at the front the queue is removed. Move all the elements after it by one position. (Inefficient!!!)

Dequeue()

front

rear

6 9

Dequeue() Dequeue()

front

rear

9

rear = -1

front

Queue Implementation of Array

Better way◦ When an item is enqueued, make the rear index

move forward.◦ When an item is dequeued, the front index

moves by one element towards the back of the queue (thus removing the front item, so no copying to neighboring elements is needed).XXXXOOOOO (rear) OXXXXOOOO (after 1 dequeue, and 1 enqueue)OOXXXXXOO (after another dequeue, and 2 enqueues)OOOOXXXXX (after 2 more dequeues, and 2 enqueues)

(front)

The problem here is that the rear index cannot move beyond the last element in the array.

Implementation using Circular Array

Using a circular array When an element moves past the end of a

circular array, it wraps around to the beginning, e.g.◦ OOOOO7963 4OOOO7963 (after Enqueue(4))◦ After Enqueue(4), the rear index moves from 3 to 4.

Empty or Full? Empty queue

◦ back = front - 1 Full queue?

◦ the same!◦ Reason: n values to represent n+1 states

Solutions◦ Use a boolean variable to say explicitly whether the

queue is empty or not◦ Make the array of size n+1 and only allow n elements

to be stored◦ Use a counter of the number of elements in the queue

Queue Implementation of Linked List

class Queue {public:

Queue(int size = 10); // constructorbool IsEmpty(void);bool IsFull(void);bool Enqueue(double x);bool Dequeue(double & x);void DisplayQueue(void);

private:int front; // front indexint rear; // rear indexint counter; // number of elementsint maxSize; // size of array queuedouble[] values; // element array

};

Queue Class Attributes of Queue

◦ front/rear: front/rear index◦ counter: number of elements in the queue◦ maxSize: capacity of the queue◦ values: point to an array which stores elements of the queue

Operations of Queue◦IsEmpty: return true if queue is empty, return false

otherwise◦ IsFull: return true if queue is full, return false otherwise◦ Enqueue: add an element to the rear of queue◦ Dequeue: delete the element at the front of queue◦ DisplayQueue: print all the data

Create Queue Queue(int size = 10)

◦ Allocate a queue array of size. By default, size = 10.

◦ front is set to 0, pointing to the first element of the array

◦ rear is set to -1. The queue is empty initially.Queue(int size ) {

values = new double[size];maxSize = size;front = 0;rear = -1;

counter = 0;}

IsEmpty & IsFull Since we keep track of the number of elements

that are actually in the queue: counter, it is easy to check if the queue is empty or full.

Boolean IsEmpty() {if (counter != 0) return false;else return true;

}Boolean IsFull() {

if (counter < maxSize) return false;else return true;

}

Enqueue

boolean Enqueue(double x) {if (IsFull()) {

System.out.println("Error: the queue is full.“);return false;

}else {

// calculate the new rear position (circular)rear = (rear + 1) % maxSize; // insert new itemvalues[rear] = x;// update countercounter++;return true;

}}

Dequeue

double Dequeue() throws EmptyQueueException {if (IsEmpty()) {

System.out.println("Error: the queue is empty.“);throw EmptyQueueException;

}else {

// retrieve the front itemx = values[front];// move front front = (front + 1) % maxSize;// update countercounter--;return x;;

}}

Printing the elements

void DisplayQueue() {System.out.print("front -->“);for (int i = 0; i < counter; i++) {

if (i == 0) System.out.print( "\t”);else System.out.print("\t\t“); System.out.print(values[(front + i) % maxSize]);if (i != counter - 1)

System.out.println();else

System.out.println( "\t<-- rear“);}

}

Using QueueCreate a queue with 5 itemsEnqueue 0,1,2,3,and 4

DisplayQueue();

DequeueDisplayQueue();Enqueue 7;DisplayQueue();

Queue Implementation based on Linked Listclass Queue {

// Data membersNode front; // pointer to front nodeNode rear; // pointer to last nodeint counter; // number of elements

// ConstructorQueue() { // constructor

front = rear = null;counter = 0;

}boolean IsEmpty() {

if (counter != 0) return false;else return true;

}void Enqueue(double x);double Dequeue();void DisplayQueue();

};

Enqueue

void Enqueue(double x) {Node newNode = new Node(x);if (IsEmpty()) {

front = newNode;rear = newNode;

}else {

rear.setNextNode(newNode);rear = newNode;

}counter++;

}

8

rear

rear

newNode

5

58

Dequeuedouble Dequeue() throws EmptyQueueException {

if (IsEmpty()) {System.out.println("Error: the queue is empty.“);throw EmptyQueueException;

}else {

x = front.getData;Node nextNode = front.getNextNode();front = nextNode;counter--;

}}

8

front

5

583

front

Printing all the elements

void DisplayQueue() {System.out.println("front -->“);Node currNode = front;for (int i = 0; i < counter; i++) {

if (i == 0) System.out.print("\t“);else System.out.print("\t\t“); System.out.print(currNode.getData);if (i != counter - 1)

System.out.println();else

System.out.println("\t<-- rear“);currNode = currNode.getNextNode();

}}

Result Queue implemented using linked list will

be never full

based on array based on linked list

Chapter 6: Queues

Specification for a Queue Interface in Java

Chapter 6: Queues

Implementing a Queue Using Java’s LinkedList Can be implemented as an adapter of any

class that implements the List interface◦ ArrayList◦ Vector◦ LinkedList

Removal is O(n) with a linked list◦ O(n) when using ArrayList or Vector

Chapter 6: Queues

Implementing a Queue Using a Circular Array Time efficiency of using a single- or double-

linked list to implement a queue is acceptable◦ However there are some space inefficiencies

Storage space is increased when using a linked list due to references stored at each list node

Array Implementation◦ Insertion at rear of array is constant time◦ Removal from the front is linear time◦ Removal from rear of array is constant time◦ Insertion at the front is linear time

Chapter 6: Queues

Comparing the Three Implementations All three implementations are comparable in

terms of computation time Linked-list implementations require more storage

because of the extra space required for the links◦ Each node for a single-linked list would store a total of

two references◦ Each node for a double-linked list would store a total of

three references A circular array that is filled to capacity would

require half the storage of a single-linked list to store the same number of elements

Chapter 6: Queues

Simulating Waiting Lines Using Queues Simulation is used to study the performance of a

physical system by using a physical, mathematical, or computer model of the system

Simulation allows designers of a new system to estimate the expected performance before building it

Simulation can lead to changes in the design that will improve the expected performance of the new system

Useful when the real system would be too expensive to build or too dangerous to experiment with after its construction

Chapter 6: Queues

Simulating Waiting Lines Using Queues (continued) System designers often use computer

models to simulate physical systems◦ Airline check-in counter for example◦ A special branch of mathematics called queuing

theory has been developed to study such problems

Chapter 6: Queues

Simulate a Strategy for Serving Airline Passengers

Chapter 6: Queues

Simulate a Strategy for Serving Airline Passengers (continued)

Chapter 6: Queues

Simulate a Strategy for Serving Airline Passengers (continued)

Chapter 6: Queues

Simulating Waiting Lines Using Queues (continued)

Chapter 6: Queues

Simulating Waiting Lines Using Queues (continued)

Chapter 6: Queues

Simulating Waiting Lines Using Queues (continued)

Chapter 6: Queues

Simulating Waiting Lines Using Queues (continued)