Stack A stack is a linear, homogeneous, container that stores and dispenses its content in a LIFO manner. LIFO - The last (most recent) item inserted, and not yet removed, will be the first (next) item dispensed. Real World Examples a spring-loaded cafeteria tray dispenser.  a driveway wide that is one-car wide The Object of Data Abstraction and Structure, David D. Riley © Addison Wesley pub.

Stack Stack Operations An Abstract Picture push insert a new item into the stack pop remove one item from the container top inspect one item from the container, but don’t remove it An Abstract Picture The Object of Data Abstraction and Structure, David D. Riley © Addison Wesley pub.

Stack - a Better Abstraction (i.e. the class specification) Domain sequence of ItemType Constructor public Stack() post: this == sequence{} Query methods public boolean isEmpty() post: result == (this->size() == 0) public ItemType top() pre: ! isEmpty() post: result == this->first() Update methods public void push(ItemType z) post: this == this@pre->prepend(z) public void pop() pre: ! isEmpty() (throws java.util.EmptyStackException) post: this == this@pre->subSequence( 2, this@pre->size() ) Stack<ItemType> The Object of Data Abstraction and Structure, David D. Riley © Addison Wesley pub.

Stack<ItemType> Example Stack<ItemType> + Stack() + boolean isEmpty() + void push(ItemType z) + void pop() + ItemType top() Stack<String> s1, s2; String str; s1 = new Stack<String>(); s1.push( “humble” ); s1.push( “bumble” ); s1.push( “mumble” ); s1.pop(); s1.push( “tumble” ); str = (String) s1.top(); s1.push( “rumble” ); s1.push( “crumble” ); s1.push( s1.top() ); s2 = new Stack(); while ( !s1.isEmpty() ) { s2.push( s1.top() ); } The Object of Data Abstraction and Structure, David D. Riley © Addison Wesley pub.

Stack Implementations How would you represent ... ... a bounded stack? ... an unbounded stack? Would you use inheritance or aggregation? The Object of Data Abstraction and Structure, David D. Riley © Addison Wesley pub.

public class Stack<ItemType> /** Class Invariant * theArray.length > 0 and 0 <= topNdx <= theArray.length * informally: theArray stores the items of the stack and topNdx-1 is the index * of the top of the stack while 0 is the index of the stack’s bottom */ public class Stack<ItemType> private Object[] theArray; private int topNdx; /** pre: s > 0 * post: theArray.length == s * and topNdx == 0*/ public Stack(int s) { theArray = new Object[s]; topNdx = 0; } /** post: result == (topNdx==0) */ public boolean isEmpty() { return topNdx == 0; //continued … The Object of Data Abstraction and Structure, David D. Riley © Addison Wesley pub.

public void pop() { public Object top() { topNdx--; /** pre: topNdx < theArray.length * post: topNdx == topNdx@pre + 1 * and theArray[topNdx-1] == z */ public void push(ItemType z) { theArray[topNdx] = z; topNdx++; } /** pre: topNdx > 0 * post: topNdx == topNdx@pre - 1 */ public void pop() { topNdx--; * post: result == theArray[topNdx-1] */ public Object top() { return theArray[topNdx-1]; The Object of Data Abstraction and Structure, David D. Riley © Addison Wesley pub.

Stack Applications Each method call causes an activation record (local variables & parameters) to be pushed upon the run-time stack. When a method returns its activation record is popped off the run-time stack. Each time the compiler encounters a { it is pushed upon the parse stack. Each time the compiler encounters a } it is pops the matching } from the parse stack. The finite state machine can be augmented by adding a stack. Such a device is called a push-down automaton. The Object of Data Abstraction and Structure, David D. Riley © Addison Wesley pub.

Evaluating RPN Expressions Stacks are useful for evaluating many kinds of expressions. Reverse Polish notation In Reverse Polish Notation (RPN) operands occur before their associated operator, and operators occur as soon as possible. (Also called _____________.) Rules: 1) Operands occur left-to-right in the same order as infix expression 2) Operation follows immediately after its operand/subexpression Examples Infix RPN 7 - 3 7, 3, - 8 * 4 + 5 1 + (2*3) - 4 ((9+8)*7)-(6*(5+(4/3))) The Object of Data Abstraction and Structure, David D. Riley © Addison Wesley pub.

RPN Evaluation Algorithm Scan expression left to right, and… For each operand - push For each operator - replace two top operands by their subexpression value (Note: top of stack is right operand, second in stack is left.) Example 9, 8, +, 7, *, 6, 5, 4, 3, /, +, *, - OperandStack The Object of Data Abstraction and Structure, David D. Riley © Addison Wesley pub.