1. © 2006 Pearson Addison-Wesley. All rights reserved7A-1 Chapter 7 Stacks (and a bit of generics for flavor)

2. © 2006 Pearson Addison-Wesley. All rights reserved7A-2 Developing an ADT During the Design of a Solution A stack –Last-in, first-out (LIFO) property The last item placed on the stack will be the first item removed –Analogy A stack of dishes in a cafeteria Figure 7-1 Stack of cafeteria dishes

3. © 2006 Pearson Addison-Wesley. All rights reserved7A-3 Developing an ADT During the Design of a Solution ADT stack operations –Create an empty stack –Determine whether a stack is empty –Add a new item to the stack --- push(item) –Remove from the stack the item that was added most recently -- item = pop() –Remove all the items from the stack –Retrieve from the stack the item that was added most recently -- item = peek()

4. © 2006 Pearson Addison-Wesley. All rights reserved7A-4 Refining the Definition of the ADT Stack Pseudocode for the ADT stack operations createStack() // Creates an empty stack. isEmpty() // Determines whether a stack is empty. push(newItem) throws StackException // Adds newItem to the top of the stack. // Throws StackException if the insertion is // not successful.

5. © 2006 Pearson Addison-Wesley. All rights reserved7A-5 Refining the Definition of the ADT Stack Pseudocode for the ADT stack operations (Continued) pop() throws StackException // Retrieves and then removes the top of the stack. // Throws StackException if the deletion is not // successful. popAll() // Removes all items from the stack. peek() throws StackException // Retrieves the top of the stack. Throws // StackException if the retrieval is not successful

6. © 2006 Pearson Addison-Wesley. All rights reserved7A-6 Using the ADT Stack in a Solution displayBackward and readAndCorrect algorithms can be refined by using stack operations A program can use a stack independently of the stack’s implementation

7. © 2006 Pearson Addison-Wesley. All rights reserved7A-7 Simple Applications of the ADT Stack: Checking for Balanced Braces A stack can be used to verify whether a program contains balanced braces –An example of balanced braces abc{defg{ijk}{l{mn}}op}qr –An example of unbalanced braces abc{def}}{ghij{kl}m

8. © 2006 Pearson Addison-Wesley. All rights reserved7A-8 Checking for Balanced Braces Requirements for balanced braces –Each time you encounter a “}”, it matches an already encountered “{” –When you reach the end of the string, you have matched each “{”

9. © 2006 Pearson Addison-Wesley. All rights reserved7A-9 Checking for Balanced Braces Figure 7-3 Traces of the algorithm that checks for balanced braces

10. © 2006 Pearson Addison-Wesley. All rights reserved7A-10 Implementations of the ADT Stack Figure 7-4 Implementation of the ADT stack that use a) an array; b) a linked list; c) an ADT list java.util.Stack

11. © 2006 Pearson Addison-Wesley. All rights reserved7A-11 An Array-Based Implementation of the ADT Stack StackArrayBased class –Implements StackInterface –Instances Stacks –Private data fields An array of Objects called items The index top Figure 7-5 An array-based implementation

12. © 2006 Pearson Addison-Wesley. All rights reserved7A-12 To the javadocs! A Reference-Based Implementation of the ADT Stack A reference-based implementation –Required when the stack needs to grow and shrink dynamically java.util.Stack inherits from Vector a List. – How do we implement: pop, peek, push ?

13. © 2006 Pearson Addison-Wesley. All rights reserved7A-13 An Implementation That Uses the ADT List The ADT list can be used to represent the items in a stack If the item in position 1 of a list represents the top of the stack –push(newItem) operation is implemented as add(1, newItem) –pop() operation is implemented as get(1) remove(1) –peek() operation is implemented as get(1)

14. © 2006 Pearson Addison-Wesley. All rights reserved7A-14 Application: Algebraic Expressions When the ADT stack is used to solve a problem, the use of the ADT’s operations should not depend on its implementation To evaluate an infix expressions –Convert the infix expression to postfix form –Evaluate the postfix expression

15. © 2006 Pearson Addison-Wesley. All rights reserved7A-15 Evaluating Postfix Expressions A postfix calculator –Requires you to enter postfix expressions Example: 2, 3, 4, +, * –When an operand is entered, the calculator Pushes it onto a stack –When an operator is entered, the calculator Applies it to the top two operands of the stack Pops the operands from the stack Pushes the result of the operation on the stack

16. © 2006 Pearson Addison-Wesley. All rights reserved7A-16 Evaluating Postfix Expressions Figure 7-8 The action of a postfix calculator when evaluating the expression 2 * (3 + 4)

17. © 2006 Pearson Addison-Wesley. All rights reserved7A-17 Evaluating Postfix Expressions To evaluate a postfix expression which is entered as a string of characters –Simplifying assumptions The string is a syntactically correct postfix expression No unary operators are present No exponentiation operators are present Operands are single lowercase letters that represent integer values

18. © 2006 Pearson Addison-Wesley. All rights reserved7A-18 Converting Infix Expressions to Equivalent Postfix Expressions An infix expression can be evaluated by first being converted into an equivalent postfix expression Facts about converting from infix to postfix –Operands always stay in the same order with respect to one another –An operator will move only “to the right” with respect to the operands –All parentheses are removed Whenever you hit an close parenthesis add the operators onto the Stack until you get to the open parenthesis

19. © 2006 Pearson Addison-Wesley. All rights reserved7A-19 Converting Infix Expressions to Equivalent Postfix Expressions Figure 7-9 A trace of the algorithm that converts the infix expression a - (b + c * d)/e to postfix form

20. © 2006 Pearson Addison-Wesley. All rights reserved7A-20 Application: A Search Problem High Planes Airline Company (HPAir) –Problem For each customer request, indicate whether a sequence of HPAir flights exists from the origin city to the destination city

21. © 2006 Pearson Addison-Wesley. All rights reserved7A-21 Representing the Flight Data The flight map for HPAir is a graph –Adjacent vertices Two vertices that are joined by an edge –Directed path A sequence of directed edges Figure 7-10 Flight map for HPAir

22. © 2006 Pearson Addison-Wesley. All rights reserved7A-22 A Nonrecursive Solution that Uses a Stack The solution performs an exhaustive search –Beginning at the origin city, the solution will try every possible sequence of flights until either It finds a sequence that gets to the destination city It determines that no such sequence exists The ADT stack is useful in organizing an exhaustive search Backtracking can be used to recover from a wrong choice of a city

23. © 2006 Pearson Addison-Wesley. All rights reserved7A-23 A Nonrecursive Solution that Uses a Stack Figure 7-11 The stack of cities as you travel a) from P; b) to R; c) to X; d) back to R; e) back to P; f) to W

24. © 2006 Pearson Addison-Wesley. All rights reserved7A-24 A Nonrecursive Solution that Uses a Stack Figure 7-13 A trace of the search algorithm, given the flight map in Figure 6-9

25. © 2006 Pearson Addison-Wesley. All rights reserved7A-25 And now for something completely different - Java Generics Java uses a concept called Generics throughout the java Collections Framework (JCF). The Collections framework is the overall parent of all the data types we’ve been talking about: Collection<-List<-LinkedList, Collection<-List<-Vector<-Stack Generics –Develop classes and interfaces and defer certain data-type information Until you are actually ready to use the class or interface Definition of the class or interface is followed by –E represents the data type that client code will specify Stack myS = new Stack ();

26. © 2006 Pearson Addison-Wesley. All rights reserved7A-26 Java Generics A Stack without Generics: Stack st = new Stack(); st.push(“Java”); st.push(“is”); // public void push(Object obj); To get things out: Object o = st.pop(); // public Object pop(); String temp = (String)o; // casting to a String ** DANGEROUS -- COMPILER CANNOT PROTECT YOU! (You can protect yourself, by adding more code.. But why do that? Generics to the rescue!)**

27. © 2006 Pearson Addison-Wesley. All rights reserved7A-27 Java Generics A Stack without Generics: Stack st = new Stack(); st.push(“Java”); // public void push(Object o); st.push(“is”); st.push(new Integer(34)); To get things out: Object o = st.pop(); String temp = (String)o; // casting to a String ** Program crashes with RuntimeException when you get to the Integer on the Stack though!!! **

28. © 2006 Pearson Addison-Wesley. All rights reserved7A-28 Java Generics come to save the day! A Stack with Generics: Stack st = new Stack (); st.push(“Java”); st.push(“is”); st.push(new Integer(34)); // COMPILER ERROR! To get things out: String temp = st.pop(); // We know it’s a String.. No casting!

29. © 2006 Pearson Addison-Wesley. All rights reserved7A-29 The Java VM Stack From: Javaworld ( http://www.javaworld.com/javaworld/jw-06-1997/jw-06- hood.html) Pushing and popping the stack frame –Your program invokes a method –the Java virtual machine creates a new stack frame for the method. Stack Frame Contains: –space for the method's local variables, –its operand stack, –any other information required by a particular virtual machine implementation. –When the JVM invokes a method, it creates a stack frame of the proper size for that method. –Adding a new frame onto the Java stack when a method is invoked is called "pushing" a stack frame; –Removing a frame when a method returns is called "popping" a stack frame.

30. © 2006 Pearson Addison-Wesley. All rights reserved7A-30 The Java VM Stack Method A Local vars Parameters Other Method B Local vars Parameters Other Method C Local vars Parameters Other Top Which method was called first? Second? Third? Method D Local vars “va” Other Method D Local vars “ava” Other Method D Local vars “Java” Other What is this an example of? Actual parameter shown instead of word “Parameters”

31. © 2006 Pearson Addison-Wesley. All rights reserved7A-31 Summary Can you write a Stack based method that takes a String and writes it backwards?

32. © 2006 Pearson Addison-Wesley. All rights reserved7A-32 Summary ADT stack operations have a last-in, first-out (LIFO) behavior Algorithms that operate on algebraic expressions are an important application of stacks A stack can be used to determine whether a sequence of flights exists between two cities A strong relationship exists between recursion and stacks