Stacks. Stacks (and Queues) Stacks. q Stack: what is it? q ADT. q Applications. q Implementation(s) CSCU9A3 1

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1 Stacks (and Queues) 1 Stacks Stack: what is it? ADT Applications Implementation(s) 2 CSCU9A3 1

2 Stacks and ueues A stack is a very important data structure in computing science. A stack is a seuence of elements to which new elements are added (pushed), and from which elements are removed (popped), at the same end. Stack sometimes referred to as a last in, first out structure (LIFO). In a ueue, elements are removed from the opposite end to which they are added. Queue sometimes referred to as a first in, first out structure (FIFO). 3 Stacks and ueues The difference is the remove operation. add remove add remove 4 CSCU9A3 2

3 Last In First Out A top B A top C B A top D C B A top E D C B A top D C B A 5 Abstract Data Types (ADTs) An abstract data type (ADT) is an abstraction of a data structure An ADT specifies: n Data stored n Operations on the data n Error conditions associated with operations Example: ADT modeling a simple stock trading system n The data stored are buy/sell orders n The operations supported are w order buy(stock, shares, price) w order sell(stock, shares, price) w void cancel(order) n Error conditions: w Buy/sell a nonexistent stock w Cancel a nonexistent order 6 CSCU9A3 3

4 The Stack ADT The Stack ADT stores arbitrary objects Insertions and deletions follow the last-in first-out scheme Think of a spring-loaded plate dispenser. (Pez?) 7 The Stack ADT Main stack operations: n push(object): inserts an element n Object pop(): removes and returns the last inserted element Auxiliary stack operations: n Object peek(): returns the last inserted element without removing it. (Sometimes appears as Object top()) n integer size(): returns the number of elements stored n boolean isempty(): indicates whether no elements are stored 8 CSCU9A3 4

5 Stack Operations Assume a simple stack for integers. Stack s = new Stack(); s.push(12); s.push(4); s.push( s.top() + 2 ); s.pop() s.push( s.top() ); //what are contents of stack? 9 Stack usage and limitations Write an algorithm to Reverse the contents of an array. How about using a stack? Write a method to print out contents of stack in reverse order. 10 CSCU9A3 5

6 Stack Interface in Java Java interface corresponding to our Stack ADT Reuires the definition of class EmptyStackException Different from the built-in Java class java.util.stack public interface Stack<E> { public int size(); public boolean isempty(); public Object top() throws EmptyStackException; public void push(e element); public Object pop() throws EmptyStackException; 11 Exceptions Attempting the execution of an operation of ADT may sometimes cause an error condition, called an exception Exceptions are said to be thrown by an operation that cannot be executed In the Stack ADT, operations pop and top cannot be performed if the stack is empty Attempting the execution of pop or top on an empty stack throws an EmptyStackException 12 CSCU9A3 6

7 Applications of Stacks Direct applications n Page-visited history in a Web browser n Undo seuence in a text editor n Chain of method calls in the Java Virtual Machine Indirect applications n Auxiliary data structure for algorithms n Component of other data structures 13 Method Stack in the JVM The Java Virtual Machine (JVM) keeps track of the chain of active methods with a stack When a method is called, the JVM pushes on the stack a frame containing n Local variables and return value n Program counter, keeping track of the statement being executed When a method ends, its frame is popped from the stack and control is passed to the method on top of the stack main() { int i = 5; foo(i); foo(int j) { int k; k = j+1; bar(k); bar(int m) { bar PC = 1 m = 6 foo PC = 3 j = 5 k = 6 main PC = 2 i = 5 14 CSCU9A3 7

8 Array-based Stack Allocate an array of some size (pre-defined) n Maximum N elements in stack Bottom stack element stored at element 0 last index in the array is the top n What is index when stack is empty? Increment top when one element is pushed, decrement after pop 15 Array-based Stack Algorithm size() return top + 1 Algorithm pop() if isempty() then throw EmptyStackException else top top - 1 return S[top + 1] S t 16 CSCU9A3 8

9 Array-based Stack (cont.) The array storing the stack elements may become full A push operation will then throw a FullStackException n Limitation of the arraybased implementation n Not intrinsic to the Stack ADT Algorithm push(o) if t = S.length - 1 then throw FullStackException else t t + 1 S[t] o S t 17 Performance and Limitations Performance n Let n be the number of elements in the stack n The space used is O(n) n Each operation runs in time O(1) Limitations n The maximum size of the stack must be defined a priori and cannot be changed n Trying to push a new element into a full stack causes an implementation-specific exception 18 CSCU9A3 9

10 Common Stack Error Stack s = new Stack(); // put stuff in stack for(int i = 0; i < 7; i++) s.push( i ); // print out contents of stack // while emptying it for(int i = 0; i < s.size(); i++) System.out.println( s.pop() ); // Output? Why? 19 Corrected Version Stack s = new Stack(); // put stuff in stack for(int i = 0; i < 7; i++) s.push( i ); // print out contents of stack // while emptying it int limit = s.size(); for(int i = 0; i < limit; i++) System.out.println( s.pop() ); //or // while(!s.isempty() ) // System.out.println( s.pop() ); 20 CSCU9A3 10

11 Array-based Stack in Java public class ArrayStack<E> implements Stack<E> { // holds the stack elements private E S[ ]; // index to top element private int top = -1; // constructor public ArrayStack(int capacity) { S = (E[]) new Object[capacity]); public E pop() throws EmptyStackException { if isempty() { throw new EmptyStackException ( Empty stack: cannot pop ); E temp = S[top]; // facilitate garbage collection: S[top] = null; top = top 1; return temp; (other methods of Stack interface) 21 Example use in Java public class Tester { // other methods public void intreverse(integer a[]) { Stack<Integer> s; s = new ArrayStack<Integer>(); public void floatreverse(float f[]) { Stack<Float> s; s = new ArrayStack<Float>(); (code to reverse array f) for(int i = 0; i < a.length; a++) s.push(a[i]); for(int i = 0; i < a.length; a++) a[i] = s.pop(); 22 CSCU9A3 11

12 Parentheses Matching Each (, {, or [ must be paired with a matching ),, or [ n correct: ( )(( )){([( )]) n correct: ((( )(( )){([( )]) n incorrect: )(( )){([( )]) n incorrect: ({[ ]) n incorrect: ( 23 Parentheses Matching Algorithm Algorithm ParenMatch(X,n): Input: An array X of n tokens, each of which is either a grouping symbol, a variable, an arithmetic operator, or a number Output: true if and only if all the grouping symbols in X match Let S be an empty stack for i=0 to n-1 do if X[i] is an opening grouping symbol then S.push(X[i]) else if X[i] is a closing grouping symbol then if S.isEmpty() then return false {nothing to match with if S.pop() does not match the type of X[i] then return false {wrong type if S.isEmpty() then return true {every symbol matched else return false {some symbols were never matched 24 CSCU9A3 12

13 HTML Tag Matching For fully-correct HTML, each <name> should pair with a matching </name> <body> <center> <h1> The Little Boat </h1> </center> <p> The storm tossed the little boat like a cheap sneaker in an old washing machine. The three drunken fishermen were used to such treatment, of course, but not the tree salesman, who even as a stowaway now felt that he had overpaid for the voyage. </p> <ol> <li> Will the salesman die? </li> <li> What color is the boat? </li> <li> And what about Naomi? </li> </ol> </body> The Little Boat The storm tossed the little boat like a cheap sneaker in an old washing machine. The three drunken fishermen were used to such treatment, of course, but not the tree salesman, who even as a stowaway now felt that he had overpaid for the voyage. 1. Will the salesman die? 2. What color is the boat? 3. And what about Naomi? 25 Infix notation Consider the aithmetic expression: * (5-2) Binary operators reuires two operands. To evaluate the expression, we use the following rules: * and / have higher precedence than + and -, when operators have the same precedence, we apply them from left to right, brackets change the order of precedence. Hence the following example gives a different answer: * (3-1) Consider a system of arithmetic with different rules 26 CSCU9A3 13

14 Reverse Polish With reverse Polish (postfix) notation, no precedence rules or parentheses reuired! In postfix notation, we put the operator after its operands instead of between them. Hence, instead of 5 + 4, we have Postfix Notation The first expression above, would be re-written as: * (5-2) * while the second would be written as: * (3-1) * The operands are written in the same order while the operators are now written in the order in which they are to be applied. 28 CSCU9A3 14

15 Evaluating Postfix Expressions (continued) 29 Examples Let us first apply it to our simple example: Next Token : Answer is 9! With the expression: * Next - * CSCU9A3 15