Chapter 7 Queues

Data Structure 2 Chapter Outline  Objectives  Follow and explain queue-based algorithms using the front, rear, entering the queue, and exiting the queue  Use a Queue class to implement stack-based algorithm such as scheduling first come, first serve  Recognize situations that require a priority queue  Contents  Introduction to Queues  Queue Applications  Implementations of the Queue ADT  Priority Queues

Data Structure 3 What is a Queue?  Logical (or ADT) level: A queue is an ordered group of homogeneous items (elements), in which new elements are added at one end (the rear), and elements are removed from the other end (the front).  A queue is a FIFO “first in, first out” structure.

Data Structure 4 The Queue ADT  Queue’s method  Enqueue : Adding an item to the queue  “Entering the queue”  Dequeue : Removing an item from the queue  “Deleting from the queue”  Queue underflow  If a program attempts to remove an item from an empty queue

Data Structure 5 Contrasting a Stack and a Queue A B C D Input : A B C D stack A B C D top front Rear Queue

Data Structure 6 Uses for Queues  Copying a word 1. Declare a queue of characters 2. While(there are more characters of the word to read) { Read a character Insert the character into the queue } 3. While(the queue is not empty) { Get the front character from the queue Write the character to the screen }  Simulation programs such as the traffic ate an intersection  Input/Output buffering

Data Structure 7 Array Implementation of a Queue  Add items at one end of the array and Remove items for other end  Access the used portion of the array at both ends, increasing the size of the used portion at one end and decreasing the size of the used portion at the other end  Need a two variables for tracking the array  front  rear

Data Structure 8 Array Implementation of a Queue  Queue items will be in the array components  data[front], data[front+1],... data[rear]  To add an item, increment rear and store the new item  To get the next item, retrieve data[front] rear is incremented but never decremented ? Reach the end of the array variable front would be incremented free up the array locations with index values less than front

Data Structure 9 Array Implementation of a Queue  Way to reuse freed locations  Maintain all the queue items so that front is equal to 0  It is very inefficient  Think of the array as being bent into a circle  When the rear index reaches the end of the array, start using the available locations at the front of the array  The successor of the last array index is the first array index

Data Structure 10 Array Implementation of a Queue [0] [1] [2] [3] [4] A B C ? ? frontrear [0] [1] [2] [3] [4] ? ? C D E frontrear data

Data Structure 11 Array Implementation of a Queue [0] [1] [2] [3] [4] F ? C D E frontrear data

Data Structure 12 Array Implementation of a Queue  Circular array ? C D E F data [0] [1] [2] [3] [4] front rear

Data Structure 13 Array Implementation of a Queue  data : Queue’s item are held in data  front, rear : private instance variable hold the indexes for the front and rear  manyItems : records the number of items that are in the queue  nextIndex : private method  Helper method  It is not part of the public specification  It is just for our own use in implementing a specific kind of queue

Data Structure 14 Array Implementation of a Queue  Helper Methods  When a class requires some small computation that is likely to be used several times  Improve the clarity of code  Is private, Does not need to be included in the documentation

Data Structure 15 Array Implementation of a Queue  Invariant of the Queue ADT  The number of items in the queue is stored in the instance variable manyItems  For a nonempty queue, the items are stored in a circular array beginning at data[front] and continuing through data[rear]  For an empty queue, manyItems is zero and data is a reference to an array, but we are not using any of the array

Data Structure 16 Array Implementation of a Queue  ensureCapacity method  If the array is already big enough, we return with no work  Otherwise, allocate a new larger array and copy the elements from original array to the new array  Three cases  If manyItems is zero  If manyItems is nonzero and front <= rear  If manyItems is nonzero and front > rear

Data Structure 17 Array Implementation of a Queue  ensureCapacity method [0] [1] [2] [3] [4] C D ? A B v v [0] [1] [2] [3] [4] A B C D ? [5] [6] [7] [8] ? ? rear front rear

Data Structure 18 Array Implementation of a Queue public void ensureCapacity(int minimumCapacity) { Object biggerArray[]; int n1, n2; if(data.length >= minimumCapacity) return; else if(manyItems == 0) data = new Object[minimumCapacity]; else if(front <= rear) { biggerArray = new Object[minimumCapacity]; System.arraycopy(data, front, biggerArray, front, manyItems); data = biggerArray; }

Data Structure 19 Array Implementation of a Queue else { biggerArray = new Object[minimumCapacity]; n1 = data.length – front; n2 = rear + 1; System.arraycopy(data, front, biggerArray, 0 n1); System.arraycopy(data, 0, biggerArray, n1, n2); front = 0; rear = manyItems - 1; data = biggerArray; }

Data Structure 20 Linked List Implementation of a Queue Front Item Second Item Third Item null front rear

Data Structure 21 Linked List Implementation of a Queue  Invariant of the Queue ADT  The numbers of items in the queue is stored in the manyNodes  The items in the queue are stored in a linked list with the front of the queue stored at the head node and the rear of the queue stored at the final node  For a nonempty queue, front is the head reference  For an empty queue, both front and rear are the null reference

Data Structure 22 Linked List Implementation of a Queue  Insert method null front 10 rear

Data Structure 23 Linked List Implementation of a Queue  Insert method  public void insert(Object item) { if(isEmpty()) { front = new Node(item, null); rear = front; } else { rear.addNodeAfter(item); rear = rear.getLink(); } manyNodes++; }

Data Structure 24 Linked List Implementation of a Queue  getFront method null front 10 rear null front rear

Data Structure 25 Linked List Implementation of a Queue  getFront method Public Object getFront() { Object answer; if(manyNodes == 0) throw new NoSuchElementException(“Queue underflow.”); answer = front.getData(); front = front.getLink(); ManyNodes--; if(manyNodes == 0) rear = null; return answer; }

Data Structure 26 Linked List Implementation of a Queue  Forgetting Which End is Which null front 10 rear null What’s the problem? Case 1) enqueue Case 2) dequeue

Data Structure 27 Priority Queues  Is a data structure that stores items along with a priority for each item.  Items are removed in order of priorities  Ginger Snap, priority 0  Natalie Attired, priority 3  Emanual Transmission, priority 2  Gene Pool, priority 3  Kay Sera, priority 2

Data Structure 28 Priority Queues  Constructor for the ObjectPriorityQueue  Public ObjectPriorityQueue(int highest)  Initialize an empty priority queue  getFront  public Object getFront()  Get the highest priority item, removing it from this priority queue  Precondition: this queue is not empty  Postcondition : return value is highest priority item of this queue and the item has been removed

Data Structure 29 Priority Queues  Insert  public void insert(Object item, int priority)  Add a new item to this priority queue  Precondition : 0<= priority and priority is no more than the highest priority  Postcondition : the item has been added to this priority queue

Data Structure 30 Priority Queues ADT  What is the best way to take advantage of the existing ordinary queue?  To provide the priority queue with an array of ordinary queues  Suppose highest is 2  Implemented using three ordinary queues  One to hold the items with priority 0  Another queue for the items of priority 1  Third queue for the items of priority 2

Data Structure 31 Priority Queues ADT  Example1)  Ginger Snap, priority 0  Natalie Attired, priority 3  Emanual Transmission, priority 2  Gene Pool, priority 3  Kay Sera, priority 2  Queues[3] : Natalie Attired, Gene Pool  Queues[2] : Emanual Transmission, Kay Sera  Queues[1] : empty  Queues[0] : Ginger Snap