Advanced data structures slide 2 2+

ADVANCED DATA STRUCTURESSTACKS

CRISTIAN REY C. SECO, MIT

Objectives

At the end of the lesson, the student should be able to: Explain the basic concepts and operations on the ADT

stack Implement the ADT stack using sequential and linked

representation Discuss applications of stack: the pattern recognition

problem and conversion from infix to postfix Explain how multiple stacks can be stored using

one dimensional array Reallocate memory during stack overflow in multiple-

stack array using unit-shift policy and Garwick's algorithm

Introduction

Stack - linearly ordered set of elements having the last-in, first-out (LIFO) discipline

Operations are done on top of the stack only and we have no access to other elements

Basic operations: push and pop Representation: sequential or linked

Operations

Insertion of new element onto the stack (push)

Deletion of the top element from the stack (pop)

Getting the size of stack Checking for empty stack Getting the top element without deleting it

from the stack

Operations

Push

Operations

Pop

Operations

procedure SPUSH(S,n,top,x)array S(1:n)if top = n then call STACKFULLtop <- top + 1S(top) <- xend SPUSH

procedure SPOP(S,n,top,x)array S(1:n)if top = 0 then call STACKEMPTYelse [ x <- S(top);top <- top –1 ]end SPOP

Operations

public interface Stack{ public int size(); /* returns the size of the stack */ public boolean isEmpty(); /* checks if empty */ public Object top() throws StackException; public Object pop() throws StackException; public void push(Object item) throws StackException;}

class StackException extends RuntimeException{ public StackException(String err) { super(err); }}

interface

interface – reserved word in java, a class that contains only the method headings, and each method heading is terminated with a semicolon

inheritance

Inheritance means that a new class can be derived from or based on an already existing class.

The new class inherits features such as methods from the existing class, which saves a lot of time for programmers.

Example: a newly define class StackException that would extend the definition of RuntimeException.

inheritance

When you use inheritance, the class containing your application program will have more than one method.

Constructor is a special type of method of a class that is

automatically executed when an object of the class is created.

It is used to initialize object. The name of the constructor is always the same as the name of the class

Implementations

Sequential Representation Makes use of arrays Stack is empty if top=-1 and full if top=n-1 Deletion from an empty stack causes an underflow Insertion onto a full stack causes an overflow

Implementations

public class ArrayStack implements Stack{ public static final int CAPACITY = 1000; public int capacity; Object S[]; int top = -1;

public ArrayStack() { this(CAPACITY); }

public ArrayStack(int c) { capacity = c; S = new Object[capacity]; }

public int size() { return (top+1); }

public boolean isEmpty() { return (top < 0); }

Implementations

public Object top(){ if (isEmpty()) throw new StackException("Stack empty."); return S[top];}

public Object pop(){ Object item; if (isEmpty()) throw new StackException("Stack underflow."); item = S[top]; S[top--] = null; return item;}

public void push(Object item){ if (size()==capacity) throw new StackException

("Stack overflow."); S[++top]=item;}

Implementations

• Linked Representation– A linked list of stack nodes could be used to implement a stack

Implementations

public class LinkedStack implements Stack{ private Node top; private int numElements = 0; public int size() { return (numElements); }

public boolean isEmpty() { return (top == null); }

public Object top(){ if (isEmpty()) throw new StackException ("Stack empty."); return top.info;}

Implementations

public Object pop() { Node temp; if (isEmpty()) throw new StackException("Stack underflow."); temp = top; top = top.link; return temp.info; } public void push(Object item) { Node newNode = new Node(); newNode.info = item; newNode.link = top; top = newNode; }}

Application: Infix to Postfix

Expressions can be in: infix form - every subexpression is of the form operand-operator-operand

postfix form - every subexpression is of the form operand-operand-operator, form most appropriate for computers

Application: Infix to Postfix

Theorem: A postfix expression is well-formed if the rank of every proper head is greater than or equal to 1 and the rank of the expression is 1.

Operator Priority Property Example^ 3 right associative a^b^c = a^(b^c)* / 2 left associative a*b*c = (a*b)*c+ - 1 left associative a+b+c = (a+b)+c

Application: Infix to Postfix

Examples:

Infix Expression Postfix Expressiona * b + c / d a b * c d / -a ^ b ^ c - d a b c ^ ^ d -a * ( b + ( c + d ) / e ) - f a b c d + e /+* f -a * b / c + f * ( g + d ) / ( f – h ) ^ i a b * c / f g d + * f h – i ^ / +

Application: Infix to Postfix

Exercises:

Infix Expression 1) a * b + c / d a b * c d / -2) a ^ b ^ c - d a b c ^ ^ d -3) a * ( b + ( c + d ) / e ) - f a b c d + e /+* f -4) a * b / c + f * ( g + d ) / ( f – h ) ^ i a b * c / f g d + * f h – i ^ / +