CHAPTER 6 Stacks Array Implementation

2 Stacks A stack is a linear collection whose elements are added and removed from one end The last element to be put on the stack is the first element to be removed A stack is LIFO – last in, first out

3 A conceptual view of a stack

4 Basic operations Push: store a data item at the top of the stack Pop: retrieve a data item from the top of the stack

5 Example Push Item 1 Push Item 2 Push Item 3 Pop Push Item 4 Pop Item 1 Item 2 Item 1 Item 3 Item 2 Item 1 Item 2 Item 1 Item 4 Item 2 Item 1

6 More operations on a stack

7 Example A procedure to replace the elements of a nonempty stack, assuming they are of type integers, with their sum Pre: A nonempty stack with elements of type integers. Post: s contains only one element - the sum of previously stored elements.

8 Algorithm 1. element1  S.pop() 2. while stack is not empty repeat 2.1. element2  S.pop() 2.2. S.push(element1+element2) 2.3. element1  S.pop() 3. push(S,element1)

9 Stack applications Undo operations in editors Evaluating an arithmetic expression using postfix notation Converting infix expression into postfix expression Depth-first search in a tree/graph

10 Stack implementation The interface class Array implementation Linked implementation

11 Generic Types Java enables us to define a class based upon a generic type This means that we can define a class so that it stores, operates on, and manages objects whose type is not specified until the class is instantiated The type supplied at the time of instantiation replaces the type T wherever it is used in the declaration of the class

12 Example of Generic Types class Box { // declaration and code that manage objects // of type T } Box box1 = new Box ();

13 The Stack interface class public interface StackADT { // Adds one element to the top of this stack public void push (T element); // Removes and returns the top element from this stack public T pop(); // Returns without removing the top element of this stack public T peek(); // Returns true if this stack contains no elements public boolean isEmpty(); // Returns the number of elements in this stack public int size(); // Returns a string representation of this stack public String toString(); }

14 Array implementation Design decisions: maintain an array of Object references the bottom of the stack is at index 0 the elements of the stack are in order and contiguous an integer variable top stores the index of the next available slot in the array This approach allows the stack to grow and shrink at the higher indexes

15 Array implementation

16 Private variables private final int DEFAULT_CAPACITY = 100; private int top; // indicates the next open slot private T[ ] stack;

17 Constructor public ArrayStack() { top = 0; stack = (T [ ])(new Object[DEFAULT_CAPACITY]); } public ArrayStack (int initialCapacity) { top = 0; stack = (T [ ])(new Object[initialCapacity]); }

18 Push If the array is full, expand its capacity Store the element to be pushed at position ‘top’ Increment ‘top’ public void push (T element) { if (size() == stack.length) expandCapacity(); stack[top] = element; top++; }

19 Pop If empty throw exception Decrement ‘top’ Get the contents at position ‘top’ into ‘result’ Return result public T pop() throws EmptyCollectionException { if (isEmpty()) throw new EmptyCollectionException(“stack”); top--; T result = stack[top]; return result; }

20 Peek If empty throw exception Return the contents of the top node public T peek() throws EmptyCollectionException { if (isEmpty()) throw new EmptyCollectionException(“stack”); return stack[top-1]; }

21 isEmpty if size is zero return true else return false public boolean isEmpty() { if (top == 0) return true else return false; }

22 Size return the size public int size() { return top; }

23 Managing Capacity Declare a new array with twice the size of the current array Copy the elements of the current array into the new array Update the reference variable stack to point to the new array

24 Managing Capacity public void expandCapacity() { T[ ] larger = (T[ ])(new Object[stack.length *2]); for(int index=0; index < stack.length; index++) larger[index] = stack[index]; stack = larger; }

25 Handling Exceptions An exception is an object that defines an unusual or erroneous situation A program can be designed to process an exception in one of three ways: - Not handle the exception at all - Handle the exception where it occurs - Handle the exception at another point in the program If an exception is not handled at all by the program, the program will produce an exception message and terminate

26 Handling Exceptions public class EmptyCollectionException extends RuntimeException { // // Sets up this exception with an appropriate message. // public EmptyCollectionException (String collection) { super ("The " + collection + " is empty."); }

27 Handling Exceptions – Try and Catch To handle an exception when it is thrown, we use a try statement A try statement consists of a try block followed by one or more catch clauses try { // statements in the try block } catch (IOException exception) { // statements that handle the I/O problem }

28 Analysis of Stack Operations Because stack operations all work on one end of the collection, they are generally efficient The push and pop operations, for both linked and array implementations, are O(1) Likewise, the other operations are O(1) The expandArray method has complexity O(n), where n is the number of elements in the stack