Queues. Virtuelle Fachhochschule. Prof. Dr. Debora Weber-Wulff

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1 Queues Virtuelle Fachhochschule Prof. Dr. Debora Weber-Wulff!1

2 Queues First In, First Out Well-known in socialist society Operations enqueue join the back of the line dequeue remove from the front of the line getfront access the item first in line Cliparts!2 21 Prof. Dr. Debora Weber-Wulff

3 ADT for Stack sorts: <Element>, BOOLEAN operations: isempty: STACK à BOOLEAN pop: STACK à STACK push: STACK x <Element> à STACK top: STACK à <Element> Not necessary in "real" OO this is this!!3 21 Prof. Dr. Debora Weber-Wulff

4 ADT for Queue sorts: elem, BOOLEAN operations: empty: à QUEUE isempty: QUEUE à BOOLEAN dequeue: QUEUE à QUEUE enqueue: QUEUE x elem à QUEUE getfront: QUEUE à elem But this is the same as a stack? What gives?!4 21 Prof. Dr. Debora Weber-Wulff

5 ADT for Stack SORT elem, BOOLEAN empty: -> Stack isempty: Stack -> BOOLEAN push: Stack x elem -> Stack pop: Stack -> Stack top: Stack -> elem!5 21 Prof. Dr. Debora Weber-Wulff

6 ADT for SOMETHING? SORT thing, BOOLEAN empty: -> FOO isempty: FOO -> BOOLEAN huey: FOO x thing -> FOO dewy: FOO -> FOO louie: FOO -> thing!6 21 Prof. Dr. Debora Weber-Wulff

7 ADT Stack = ADT Queue? STACK and QUEUE are two very different data types... STACK is LIFO, and QUEUE is FIFO, for example. This behavioral difference is captured not in the syntax, but in the semantic component of an algebraic specification.!7 21 Prof. Dr. Debora Weber-Wulff

8 The Axioms are important! isempty(new Stack()) = true isempty(push(s, x)) = false pop (new Stack()) = error top (new Stack()) = error pop (push (s, x)) = s top (push (s, x)) = x isempty(new Queue()) = true isempty(enqueue(q,x)) = false dequeue(new Queue()) = error getfront(new Queue()) = error dequeue(enqueue(q,x)) = if isempty(q) then q else enqueue(dequeue(q),x) getfront(enqueue(q,x)) = if isempty(q) then x else getfront(q)!8 21 Prof. Dr. Debora Weber-Wulff

9 Queue Implementation Array? q u e u e last q.enqueue(e): q[++last] = e q.getfront(): q[0] O(1) q.dequeue(): O(1) for(int i = 1; i < last; i++) { q[i-1] = q[i]; last--; Shifting all elements is O(n)!9 21 Prof. Dr. Debora Weber-Wulff

10 Queue Implementation Array with wrap around last first q.enqueue(e): wrap around if(last == q.length-1) { last = 0; else { last++; ; q[last] = e; q.getfront(): q[first] q.dequeue(): "first++" with wraparound But only fixed number of places! O(1) O(1) O(1)!10 21 Prof. Dr. Debora Weber-Wulff

11 Queue Interface public interface Queue { void enqueue(object x); Object getfront() throws Underflow; void dequeue() throws Underflow; boolean isempty(); void makeempty(); void printall();!11 21 Prof. Dr. Debora Weber-Wulff

12 public class ArrayQueue implements Queue { protected Object[] objects; protected int front = 0; protected int back = 0; protected int capacity = 16; // Invariants: // objects[i]== null for 0 < = i < front; // objects[i]!= null for front < = i < back; // objects[i]== null for back < = i < capacity;!12 21 Prof. Dr. Debora Weber-Wulff

13 public void enqueue (Object x) { if(back > = capacity){ Object[]temp = objects; // make a new one, twice as big capacity = capacity * 2; objects = new Object[capacity]; // copy everything to the front for(int i = 0; i<back-front; i++){ objects[i] = temp[i+front]; back = back-front; front = 0; objects[back++] = x;!13 21 Prof. Dr. Debora Weber-Wulff

14 public void dequeue() throws Underflow{ if(isempty()) throw new Underflow(); objects[first] = null; first = first + 1; // shift left if past midpoint if(2 * front > = capacity) { for(int i=0; i < back-front; i++) { objects[i] = objects[i+front]; back = back-front; front = 0;!14 21 Prof. Dr. Debora Weber-Wulff

15 The rest is simple public Object getfront() throws Underflow{ if (isempty ()) throw new Underflow ("getfront"); return objects[front]; public boolean isempty(){ return front == back; public void makeempty(){ front = back = 0;!15 21

16 Queue as Linked List Much easier to implement (as long as you check for null) Variable amount of objects front back obj next!16 21 Prof. Dr. Debora Weber-Wulff

17 Queue as Linked List public class LinkedQueue implements Queue { private class Node { Object obj; Node next; Node(Object obj) { this.obj = obj; this.next = null; private Node front; private Node back; // Internal Class!17 21 Prof. Dr. Debora Weber-Wulff

18 public LinkedQueue() { makeempty(); public void makeempty() { front = back = null; public boolean isempty() { return front = = null; public Object getfront() throws Underflow{ if(isempty()) throw new Underflow("get Front"); return front.obj;!18 21 Prof. Dr. Debora Weber-Wulff

19 public void enqueue(object x) { if(isempty()) // make a queue of one element {back = front = new Node(x); else {back = back.next = new Node(x); public void dequeue() throws Underflow { if(isempty()) throw new Underflow("dequeue"); front = front.next;!19 21 Prof. Dr. Debora Weber-Wulff

20 Priority Queues Some jobs are more equal than others Each entry has a priority. The "next" element is the first one with the highest (=minimal) priority. void insert(comparable x); Comparable deletemin() throws Underflow; Comparable findmin(); void makeempty(); boolean isempty();!20 21 Prof. Dr. Debora Weber-Wulff

21 What are queues used for? Situations in which demand > supply cashiers cars at a toll booth print jobs mouse actions Cliparts Simulations of such situations How do we determine when the next customer / car / print job / comes? Random Gauß Poisson!21 21 Prof. Dr. Debora Weber-Wulff

CMSC 132: Object-Oriented Programming II. Stack and Queue

CMSC 132: Object-Oriented Programming II Stack and Queue 1 Stack Allows access to only the last item inserted. An item is inserted or removed from the stack from one end called the top of the stack. This