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15.6 – Queues

15.6 – Queues. A queue is a linear collection whose elements are added on one end and removed from the other Queue elements are processed in a first in, first out (FIFO) manner Elements are removed from the queue in the same order in which they are placed on the queue

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15.6 – Queues

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  1. 15.6 – Queues • A queue is a linear collection whose elements are added on one end and removed from the other • Queue elements are processed in a first in, first out (FIFO) manner • Elements are removed from the queue in the same order in which they are placed on the queue • A queue is consistent with the general concept of • a waiting line to buy movie tickets • a request to print a document • crawling the web to retrieve documents

  2. 15.6 – Queues Adding an element Removingan element rear of queue front of queue

  3. 15.6 – javafoundations.Queue //******************************************************************** // Queue.java Java Foundations // // Defines the interface to a queue collection. //******************************************************************** package javafoundations; public interface Queue<T> { // Adds the specified element to the rear of the queue. public void enqueue (T element); // Removes and returns the element at the front of the queue. public T dequeue(); // Returns a reference to the element at the front of the queue // without removing it. public T first(); // Returns true if the queue contains no elements and false // otherwise. public boolean isEmpty(); // Returns the number of elements in the queue. public int size(); // Returns a string representation of the queue. public String toString(); }

  4. 15.7 – Radix Sort • A radix sort is unusual because it does not involve comparisons between elements! • The technique used in the radix sort is based on the structure of the sort key • Separate queues are created for each possible value of each digit or character of the sort key • The number of queues, or the number of possible values, is called the radix • if we were sorting strings made up of lowercase alphabetic characters, the radix would be 26, one for each possible character • if we were sorting decimal numbers, then the radix would be 10, one for each digit 0 to 9 • The radix sort makes a pass through the values for each position in the sort key

  5. 15.7 – Radix Sort (1st pass) front of queue  442 503 312 145 250 341 325 102 420 143 Original list

  6. 15.7 – Radix Sort (2nd pass results) front of queue  503 102 312 325 420 145 143 442 341 250

  7. 15.7 – Radix Sort (3rd pass results) front of queue  145 143 102 250 341 325 312 442 420 503

  8. 15.6 – RadixSort.java for (int digitVal = 0; digitVal <= 9; digitVal++) digitQueues[digitVal] = new ArrayQueue<Integer>(); // sort the list for (int position=0; position <= 3; position++) { for (int scan = 0; scan < list.length; scan++) { temp = String.valueOf (list[scan]); digit = Character.digit (temp.charAt(3-position), 10); digitQueues[digit].enqueue (list[scan]); } // gather numbers back into list num = 0; for (int digitVal = 0; digitVal <= 9; digitVal++) { while (!(digitQueues[digitVal].isEmpty())) { list[num] = digitQueues[digitVal].dequeue().intValue(); num++; } } } (more…)

  9. 15.8 – Implementing Queues with Arrays • Adds a new element to the rear of the queue, which is stored at the high end of the array Dequeue ‘A’ Left-shift tocorrectqueue A B C D E Enqueue ‘E’

  10. 15.8 – javafoundations.ArrayQueue //******************************************************************** // ArrayQueue.java Java Foundations // // Represents an array implementation of a queue. The front of // the queue is kept at array index 0. //******************************************************************** package javafoundations; import javafoundations.exceptions.*; public class ArrayQueue<T> implements Queue<T> { private final int DEFAULT_CAPACITY = 10; private int count; private T[] queue; //----------------------------------------------------------------- // Creates an empty queue using the default capacity. //----------------------------------------------------------------- public ArrayQueue() { } (more…)

  11. //----------------------------------------------------------------- // Removes the element at the front of this queue and returns a // reference to it. Throws an EmptyCollectionException if the // queue is empty. //----------------------------------------------------------------- public T dequeue() throws EmptyCollectionException { if (count == 0) throw new EmptyCollectionException ("Dequeue operation failed. " + "The queue is empty."); T result = count--; // shift the elements to keep the front element at index 0 for (int index=0; index < count; index++) queue[count] = null; return result; } // The following methods are left as Programming Projects. // public void enqueue (T element) { } // public T first () throws EmptyCollectionException { } // public boolean isEmpty() { } // public int size() { } // public String toString() { } } 15.8 – javafoundations.ArrayQueue

  12. 15.9 – Implementing Queues with Circular Arrays • As elements are dequeued, the front of the queue will move further into the array • As elements are enqueued, the rear of the queue will also move further into the array • The challenge comes when the rear of the queue reaches the end of the array • When this occurs, it “wraps around” to the front of the array • Use two variables, front and rear, to represent the location where the first element is stored, and where the next available slot in the array is located (respectively)

  13. n 0 n-1 1 2 3 4 … 5 … 6 7 8 15.9 – Implementing Queues with Circular Arrays A B front 3 4 C rear 7 6 count 4 3 D

  14. 15.9 – The Changing State of a Circular Array Q D A E B C A D E B C D E A B C 3 0 7 8 2 5 5 front rear count

  15. 15.9 – javafoundations.CircularArrayQueue //******************************************************************** // CircularArrayQueue.java Java Foundations // // Represents an array implementation of a queue in which neither // end of the queue is fixed in the array. The variables storing the // indexes of the front and rear of the queue continually increment // as elements are removed and added, cycling back to 0 when they // reach the end of the array. //******************************************************************** package javafoundations; import javafoundations.exceptions.*; public class CircularArrayQueue<T> implements Queue<T> { private final int DEFAULT_CAPACITY = 10; private int front, rear, count; private T[] queue; (more…)

  16. 15.9 – javafoundations.CircularArrayQueue //----------------------------------------------------------------- // Creates an empty queue using the default capacity. //----------------------------------------------------------------- public CircularArrayQueue() { } //----------------------------------------------------------------- // Adds the specified element to the rear of this queue, expanding // the capacity of the queue array if necessary. //----------------------------------------------------------------- public void enqueue (T element) { if (count == queue.length) expandCapacity(); queue[rear] = element; rear = count++; } (more…)

  17. 15.9 – javafoundations.CircularArrayQueue //----------------------------------------------------------------- // Creates a new array to store the contents of this queue with // twice the capacity of the old one. //----------------------------------------------------------------- public void expandCapacity() { T[] larger = (T[])(new Object[queue.length*2]); for (int index=0; index < count; index++) larger[index] = front = 0; rear = count; queue = larger; } //----------------------------------------------------------------- // The following methods are left as Programming Projects. //----------------------------------------------------------------- // public T dequeue () throws EmptyCollectionException { } // public T first () throws EmptyCollectionException { } // public int size() { } // public boolean isEmpty() { } // public String toString() { } }

  18. rear front A B C D 4 count 15.10 – Implementing Queues with Links

  19. 15.10 – javafoundations.LinkedQueue //******************************************************************** // LinkedQueue.java Java Foundations // // Represents a linked implementation of a queue. //******************************************************************** package javafoundations; import javafoundations.exceptions.*; public class LinkedQueue<T> implements Queue<T> { private int count; private LinearNode<T> front, rear; //----------------------------------------------------------------- // Creates an empty queue. //----------------------------------------------------------------- public LinkedQueue() { } (more…)

  20. 15.10 – javafoundations.LinkedQueue //----------------------------------------------------------------- // Adds the specified element to the rear of this queue. //----------------------------------------------------------------- public void enqueue (T element) { LinearNode<T> node = new LinearNode<T>(element); if (count == 0) front = node; else rear.setNext(node); rear = node; count++; } //----------------------------------------------------------------- // The following methods are left as Programming Projects. //----------------------------------------------------------------- // public T dequeue () throws EmptyCollectionException { } // public T first () throws EmptyCollectionException { } // public boolean isEmpty() { } // public int size() { } // public String toString() { } }

  21. Josephus Flavius Problem • Given n people, numbered 1 to n, sitting on a circle • Starting with person #1, a hot potato is passed around the circle. • After m passes, the person holding the potato is eliminated • The circle closes ranks, and the game continues with the person who is sitting next to the eliminated person. • The last remaining person, wins. Simulation at http://www.cut-the-knot.org/recurrence/flavius.shtml

  22. Josephus Flavius Game publicstatic void playJosephus (int n, int m) { // simulates the Josephus problem for n people and m passes, using a Queue Queue Q = new Queue(); int i, remove; for (i = 1; i <= n; i++) // create a queue of n integers Q.enq(new Integer(i)); while (Q.size() > 1) { // until 1 integer is left for (i = 0; i < m; i++) // pass over m integers ____________________________ // remove next integer System.out.println("Player " + Q.deq() + " removed"); } // last integer that remains is the "winner" System.out.println("Player " + Q.front() + " wins"); }

  23. 15.11 – Analysis of Stack Implementations • Both stacks and queues can be implemented very efficiently • In almost all cases, the operations are not affected by the number of elements in the collection • All operations for a stack (push, pop, peek, etc.) are O(1) • Almost all operations for a queue are O(1) • The only exception is the dequeue operation for the ArrayQueue implementation – the shifting of elements makes it O(n) • The dequeue operation for the CircularArrayQueue is O(1) because of the ability to eliminate the shifting of elements

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