1. Fall 2007CS 2251 Stacks Chapter 5

2. Fall 2007CS 2252 Chapter Objectives To learn about the stack data type and how to use its four methods: push, pop, peek, and empty To understand how Java implements a stack To learn how to implement a stack using an underlying array or a linked list To see how to use a stack in several applications

3. Fall 2007CS 2253 Stack Abstract Data Type A stack is a data structure with the property that only the top element of the stack is accessible The stack’s storage policy is Last-In, First-Out A stack can be compared to a Pez dispenser –Only the top item can be accessed –Can only extract one item at a time

4. Fall 2007CS 2254 Stack Abstract Data Type Only the top element of a stack is visible, therefore the number of operations performed by a stack are few –Inspect (peek) the top element –Retrieve (pop) the top element –Push a new element on the stack –Test for an empty stack

5. Fall 2007CS 2255 Stack ADT Operations Puts the item on the top of the stack and returns a reference to it. E push( E obj) Removes and returns the object at the top of the stack. E pop() Returns the object at the top of the stack without removing it. E peek() Returns true if the stack is empty and false otherwise. boolean empty() BehaviorMethods

6. Fall 2007CS 2256 Stack Applications Stacks are used for –method calls while a program is running Two Example programs using stacks –Palindrome finder –Parentheses matcher

7. Fall 2007CS 2257 Palindrome Finder A palindrome is a string that reads the same in either direction –"kayak" –“Able was I ere I saw Elba” – “Madam I'm Adam”

8. Fall 2007CS 2258 PalindromeFinder Fields The stack which stores the characters from the string private Stack charStack The string to be checkedprivate String inputString PurposeData Field

9. Fall 2007CS 2259 PalindromeFinder Methods Returns true if the original and reverse strings have the same characters (ignoring case) public boolean isPalindrome Returns the reverse stringprivate String buildReverse() Fill the stack with characters from the string private void fillStack() Initialize a PalindromeFinderpublic PalindromeFinder( String str) BehaviorMethod

10. Fall 2007CS 22510 Parentheses Matching 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 –Parsing a Java program for example Solution is to use stacks!

11. Fall 2007CS 22511 ParenChecker Methods Returns true if ch is a closed parenthesis. private static boolean isClose( char ch) Returns true if ch is an open parenthesis. private static boolean isOpen( char ch) Returns true if the expression is balanced with respect to parentheses. public static boolean isBalanced( String expr) BehaviorMethod

12. Fall 2007CS 22512 Algorithm for isBalanced Create an empty stack of Characters Set balanced to true. Set index to 0. while balanced is true and index< length Get the next character if character is '(' push character onto stack else if character is ')' pop the top character from the stack if stack was empty set balanced to false return true if balanced is true and stack is empty

13. Fall 2007CS 22513 Implementing a Stack Extending Vector (java.util.Stack) Adapting a List Using an array Creating a linked structure

14. Fall 2007CS 22514 Stack as an Extension of Vector The Java API includes a Stack class as part of the package java.util The vector class implements a growable array of objects Elements of a vector can be accessed using an integer index and the size can grow or shrink as needed to accommodate the adding and removing of elements

15. Fall 2007CS 22515 Stack Extends Vector public class Stack extends Vector Stack inherits all the methods and data of Vector methods like get( int index) are not appropriate for a Stack

16. Fall 2007CS 22516 Stack with a List Component 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

17. Fall 2007CS 22517 Implementing a Stack Using an Array 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 See ArrayStack.java

18. Fall 2007CS 22518 ArrayStack

19. Fall 2007CS 22519 Linked Data Structure for Stack We can implement a stack using a linked list of nodes see LinkedStack.java

20. Fall 2007CS 22520 Comparing Stack Implementations Extending a Vector (as is done by Java) is a 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

21. Fall 2007CS 22521 Expressions and Stacks Consider two case studies that relate to evaluating arithmetic expressions –Postfix and infix notation Expressions normally written in infix form –Binary operators 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

22. Fall 2007CS 22522 Expressions

23. Fall 2007CS 22523 Postfix expressions Advantage of postfix form is that there is no need to group subexpressions in parentheses No need to consider operator precedence

24. Fall 2007CS 22524 PostfixEvaluator Returns true if ch is an operator private boolean isOperator( char ch) Pops two operands, applies the operator and returns the result. private int evalOp( char op) Returns the value of the expression public int eval( String expr) Stack of operandsStack operandStack Attribute/BehaviorField or method

25. Fall 2007CS 22525 Evaluating Postfix Expressions

26. Fall 2007CS 22526 Postfix Evaluation Algorithm Create an empty stack of Integers while there are more tokens get the next token if the first character is a digit push the integer onto the stack else pop right operand pop left operand evaluate the operation push result onto stack Pop the result and return

27. Fall 2007CS 22527 Infix to Postfix Conversion The postfix expressionprivate stringBuilder postfix Stack of operatorsprivate Stack operatorStack AttributeData Field

28. Fall 2007CS 22528 Infix to Postfix Conversion Returns true if ch is an operator private boolean isOperator( char ch) Returns the precedence of op private int precedence( char op) Updates the operator stackprivate void processOperator( char op) Returns postfix string equivalent it infix public String convert (String infix) BehaviorMethod

29. Fall 2007CS 22529 Infix to Postfix Conversion

30. Fall 2007CS 22530 Infix to Postfix Conversion

31. Fall 2007CS 22531 Conversion Algorithm Initialize postfix to empty StringBuilder create empty operator stack while there are tokens in infix string get the next token if token is operand append to postfix else if token is operator call processOperator else indicate syntax error pop remaining operators and append to postfix

32. Fall 2007CS 22532 Algorithm for ProcessOperator if operator stack is empty push operator onto stack else topOp -> peek operator stack if current operator has higher precedence push current operator onto stack else while stack not empty and precedence <= current precedence pop top operator and append to postfix if operator stack not empty topOp -> peek operator stack push current operator on the stack

33. Fall 2007CS 22533 Chapter Review A stack is a last-in, first-out (LIFO) data structure A stack is a simple but powerful data structure; its four operations include empty, peek, pop, and push Stacks are useful to process information in the reverse of the order that it is encountered Java.util.Stack is implemented as an extension of the Vector class

34. Fall 2007CS 22534 Chapter Review (continued) Three ways to implement a stack: –Using an object of a class that implements the List interface as a container –Using an array as a container –Using a linked list as a container Stacks can be applied in programs for evaluating arithmetic expressions

35. Fall 2007CS 22535 ProcessOperator with Parens if operator stack is empty or current operator = '(' push operator onto stack else topOp -> peek operator stack if current operator has higher precedence push current operator onto stack else while stack not empty and precedence <= precedence(topOp) pop top operator if topOp = ')' break append to postfix if operator stack not empty topOp -> peek operator stack if current operator != ')' push current operator on the stack