Chapter 6 Stacks
Copyright © 2004 Pearson Addison-Wesley. All rights reserved.1-2 Chapter Objectives Examine stack processing Define a stack abstract data type Demonstrate how a stack can be used to solve problems Examine various stack implementations Compare stack implementations
Copyright © 2004 Pearson Addison-Wesley. All rights reserved.1-3 Stacks A stack is a linear collection whose elements are added and removed from one end A stack is LIFO – last in, first out The last element to be put on the stack is the first element to be removed A stack is usually depicted vertically, with additions and deletions occurring at the top of the stack
Copyright © 2004 Pearson Addison-Wesley. All rights reserved.1-4 figure 6.1 A conceptual view of a stack
Copyright © 2004 Pearson Addison-Wesley. All rights reserved.1-5 figure 6.2 The operations on a stack See StackADT.java (page 148)StackADT.java
Copyright © 2004 Pearson Addison-Wesley. All rights reserved.1-6 figure 6.3 The StackADT interface in UML
Copyright © 2004 Pearson Addison-Wesley. All rights reserved.1-7 Using Stacks Stacks are particularly helpful when solving certain types of problems Consider the undo operation in an application keeps track of the most recent operations in reverse order
Copyright © 2004 Pearson Addison-Wesley. All rights reserved.1-8 Postfix Expressions Let's examine a program that uses a stack to evaluate postfix expressions In a postfix expression, the operator comes after its two operands We generally use infix notation, with parentheses to force precedence: (3 + 4) * 2 In postfix notation, this would be written *
Copyright © 2004 Pearson Addison-Wesley. All rights reserved.1-9 Postfix Expressions To evaluate a postfix expression: scan from left to right, determining if the next token is an operator or operand if it is an operand, push it on the stack if it is an operator, pop the stack twice to get the two operands, perform the operation, and push the result onto the stack At the end, there will be one value on the stack, which is the value of the expression
Copyright © 2004 Pearson Addison-Wesley. All rights reserved.1-10 figure 6.4 Using a stack to evaluate a postfix expression
Copyright © 2004 Pearson Addison-Wesley. All rights reserved.1-11 Postfix Expressions To simplify the example, let's assume the operands to the expressions are integer literals Our solution uses an ArrayStack, though any implementation of a stack would suffice See Postfix.java (page 152)Postfix.java See PostfixEvaluator.java (page 153)PostfixEvaluator.java
Copyright © 2004 Pearson Addison-Wesley. All rights reserved.1-12 figure 6.5 A UML class diagram for the postfix expression program
Copyright © 2004 Pearson Addison-Wesley. All rights reserved.1-13 The LinkedStack Class Now let's examine a linked implementation of a stack We will reuse the LinearNode class that we used in Chapter 3 to define the linked implementation of a bag collection Internally, a stack is represented as a linked list of nodes, with a reference to the top of the stack and an integer count of the number of nodes in the stack
Copyright © 2004 Pearson Addison-Wesley. All rights reserved.1-14 figure 6.6 A linked implementation of a stack
Copyright © 2004 Pearson Addison-Wesley. All rights reserved.1-15 The push Operation // // Adds the specified element to the top of the stack. // public void push (Object element) { LinearNode temp = new LinearNode (element); temp.setNext(top); top = temp; count++; }
Copyright © 2004 Pearson Addison-Wesley. All rights reserved.1-16 figure 6.7 The stack after pushing element E
Copyright © 2004 Pearson Addison-Wesley. All rights reserved.1-17 The pop Operation // // Removes the element at the top of the stack and returns a // reference to it. Throws an EmptyStackException if the stack // is empty. // public Object pop() throws EmptyStackException { if (isEmpty()) throw new EmptyStackException(); Object result = top.getElement(); top = top.getNext(); count--; return result; }
Copyright © 2004 Pearson Addison-Wesley. All rights reserved.1-18 figure 6.8 The stack after a pop operation
Copyright © 2004 Pearson Addison-Wesley. All rights reserved.1-19 The ArrayStack Class Now let's examine an array-based implementation of a stack We'll make the following 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
Copyright © 2004 Pearson Addison-Wesley. All rights reserved.1-20 figure 6.9 An array implementation of a stack
Copyright © 2004 Pearson Addison-Wesley. All rights reserved.1-21 The push Operation // // Adds the specified element to the top of the stack, expanding // the capacity of the stack array if necessary. // public void push (Object element) { if (size() == stack.length) expandCapacity(); stack[top] = element; top++; }
Copyright © 2004 Pearson Addison-Wesley. All rights reserved.1-22 figure 6.10 The stack after pushing element E
Copyright © 2004 Pearson Addison-Wesley. All rights reserved.1-23 The pop Operation // // Removes the element at the top of the stack and returns a // reference to it. Throws an EmptyStackException if the stack // is empty. // public Object pop() throws EmptyStackException { if (isEmpty()) throw new EmptyStackException(); top--; Object result = stack[top]; stack[top] = null; return result; }
Copyright © 2004 Pearson Addison-Wesley. All rights reserved.1-24 figure 6.11 The stack after popping the top element
Copyright © 2004 Pearson Addison-Wesley. All rights reserved.1-25 The java.util.Stack Class The Java Collections framework defines a Stack class with similar operations It is derived from the Vector class and therefore has some characteristics that are not appropriate for a pure stack The java.util.Stack class has been around since the original version of Java, and has been retrofitted to meld with the Collections framework
figure 6.12 A UML description of the java.util.Stack class
Copyright © 2004 Pearson Addison-Wesley. All rights reserved.1-27 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 for all implementations are O(1) We'll see that other collections (which don't have that characteristic) aren't as efficient for all operations