Queue Deque and Priority Queue Implementations Chapter 11

Queue, Deque, and Priority Queue Implementations Chapter 11 1 Adapted from Pearson Education, Inc.

Contents �A Linked Implementation of a Queue � An Array-Based Implementation of a Queue �A Circular Array � A Circular Array with One Unused Location �A Vector-Based Implementation of a Queue � Circular Linked Implementations of a Queue �A Two-Part Circular Linked Chain � Java Class Library: The Class Abstract. Queue �A Doubly Linked Implementation of a Deque � Possible Implementations of a Priority Queue 2 Adapted from Pearson Education, Inc.

Objectives � Implement ADT queue by using chain of linked nodes, an array, or vector � Add or delete nodes at either end of chain of doubly linked nodes � Implement ADT deque by using chain of doubly linked nodes � Implement ADT priority queue by using array or chain of linked nodes 3 Adapted from Pearson Education, Inc.

Consider Queue Operations � Ask � Operations � Is � enqueue(new. Entry) � dequeue() � get. Front() yourself: Two operations Operating at front Of the queue the head reference sufficient? � What would the Big Oh of B enqueuing be? � Answer: � Better to have tail as well so that enqueueing can be O(1) A 4 X G Adapted from Pearson Education, Inc.

A Linked Implementation of the ADT Queue public class Linked. Queue <T> implements Queue. Interface <T> { private Node first. Node; // references front of queue private Node last. Node; // references back of queue public Linked. Queue () { first. Node = null; last. Node = null; } // end default constructor … ADT Queue methods go here … private class Node // private inner class { private T data; // entry in bag private Node next; // link to next node … } // end Node }// end Linked. Queue 5 Adapted from Pearson Education, Inc.

Adding first item to an empty queue �Figure (a) 6 11 -2 Before adding a new node to an empty chain (b) after adding it BOTH first. Node AND last. Node Adapted from Pearson Education, Inc. need adjustment

Adding an item to a non-empty queue public void enqueue (T new. Entry) { Node new. Node = new Node (new. Entry, null); if ( is. Empty()) first. Node = new. Node; else last. Node. set. Next. Node(new. Node); 7 Adapted from Pearson Education, Inc.

Adding an item to a non-empty queue public void enqueue (T new. Entry) { Node new. Node = new Node (new. Entry, null); if ( is. Empty()) first. Node = new. Node; else last. Node. set. Next. Node(new. Node); last. Node = new. Node; } // end enqueue 8 ONLY last. Node needs adjustment Adapted from Pearson Education, Inc.

Removing an item from a queue with more than one item 9 ONLY first. Node needs adjustment Adapted from Pearson Education, Inc.

Removing last item from a queue public T dequeue () { T front = null; if (!is. Empty ()) { front = first. Node. data; first. Node = first. Node. next; if (first. Node == null) last. Node = null; } // end if return front; 10 } // end dequeue BOTH first. Node AND last. Node Adapted from Pearson Education, Inc. need adjustment

An Array Implementation of the ADT Queue public class Array. Queue < T > implements Queue. Interface < T > { private T [] queue; private int front. Index; private int back. Index; private static final int DEFAULT_INITIAL_CAPACITY = 50; public Array. Queue () { this (DEFAULT_INITIAL_CAPACITY); } // end default constructor public Array. Queue (int initial. Capacity) { T [] temp. Queue = (T []) new Object [initial. Capacity + 1]; queue = temp. Queue; front. Index = 0; back. Index = initial. Capacity; } // end constructor …… ADT Queue methods go here … }// end Array. Queue 11 Adapted from Pearson Education, Inc.

Figure 11 -6 An array that represents a queue without moving any entries: (a) initially; (b) after removing the entry at the front twice; Copyright © 2012 by Pearson Education, Inc. All rights reserved

Figure 11 -6 An array that represents a queue without moving any entries: (c) after several more additions and removals; (d) after two additions that wrap around to the beginning of the array; Copyright © 2012 by Pearson Education, Inc. All rights reserved

� Solution: “Circular” array � First location follows last � Increment pointers with modulo operator back. Index = (back. Index + 1) % queue. length; front. Index = (front. Index + 1) % queue. length; Copyright © 2012 by Pearson Education, Inc. All rights reserved

An empty Queue [0] [4] [1] Front 0 Back 4 Enqueue at back incr back then store item [3] [2] The queue is EMPTY ( Back + 1 ) % size = ( 4 +1)% 5 = 0 == Front = 0 15 Adapted from Pearson Education, Inc.

en. Queue A [0] A [4] [1] [3] [2] Front 0 Back 0 The queue is not EMPTY ( Back + 1 ) % size = ( 0 +1)% 5 = 1 =/= Front = 0 16 Adapted from Pearson Education, Inc.

en. Queue X [0] A [4] [1] X [3] [2] Front 0 Back 1 The queue is not EMPTY ( Back + 1 ) % size = ( 1 +1)% 5 = 2 =/= Front = 0 17 Adapted from Pearson Education, Inc.

en. Queue G, B, and Z – it’s full now [0] A [4] Z [1] X Same As When Queue Was empty Front 0 Back 4 Dequeue from Front Serve front then incr front [3] B 18 [2] G The queue is FULL BUT ( Back + 1 ) % size = ( 4 +1)% 5 = 0 == Front = 0 Adapted from Pearson Education, Inc.

de. Queue [0] [4] Z [1] X [3] B 19 [2] G Front 1 Back 4 The queue is not Empty And not full ( Back + 1 ) % size = ( 4 +1)% 5 = 0 =/= Front = 1 Adapted from Pearson Education, Inc.

de. Queue [0] [4] Z [1] Front 2 Back 4 Let’s enqueue 2 more: W and K [3] B 20 [2] G The queue is not Empty ( Back + 1 ) % size = ( 4 +1)% 5 = 0 =/= Front = 2 Adapted from Pearson Education, Inc.

en. Queue W [0] W [4] Z [1] [3] B 21 [2] G Front 2 Back 0 The queue is not Empty ( Back + 1 ) % size = ( 0 +1)% 5 = 1 =/= Front = 2 Adapted from Pearson Education, Inc.

en. Queue K – it’s full again [0] W [4] Z [1] K [3] B 22 [2] G Front 2 Back 1 How can we avoid the condition for empty and full being the same? The queue is FULL BUT ( Back + 1 ) % size = ( 1 +1)% 5 = 2 == Front = 2 Adapted from Pearson Education, Inc.

Start with an empty Queue again [0] [4] [1] One Location remains unused [3] [2] Front 0 Back 4 The queue is EMPTY ( Back + 1 ) % size = ( 4 +1)% 5 = 0 == Front = 0 23 Adapted from Pearson Education, Inc.

en. Queue A [0] A [4] [1] One Location remains unused [3] [2] Front 0 Back 0 The queue is not EMPTY ( Back + 1 ) % size = ( 0 +1)% 5 = 1 =/= Front = 0 24 Adapted from Pearson Education, Inc.

en. Queue X [0] A [4] [1] X One Location remains unused [3] [2] Front 0 Back 1 The queue is not EMPTY ( Back + 1 ) % size = ( 1 +1)% 5 = 2 =/= Front = 1 25 Adapted from Pearson Education, Inc.

en. Queue G, and B – it’s full now [0] A [4] [3] B 26 [1] X One Location remains unused [2] G Different From When Queue Was empty Front 0 Back 3 The queue is FULL ( Back + 2 ) % size = ( 3 +2)% 5 = 0 == Front = 0 Adapted from Pearson Education, Inc.

de. Queue [0] [4] [3] B 27 [1] X One Location remains unused [2] G Front 1 Back 3 The queue is not Empty And not full ( Back + 2 ) % size = ( 3 +2)% 5 = 0 =/= Front = 1 Adapted from Pearson Education, Inc.

de. Queue [0] [4] [3] B 28 [1] One Location remains unused Front 2 Back 3 Let’s enqueue 2 more: W and K [2] G The queue is not Empty ( Back + 1 ) % size = ( 3 +1)% 5 = 4 =/= Front = 2 Adapted from Pearson Education, Inc.

en. Queue W [0] [4] W [3] B 29 [1] One Location remains unused [2] G Front 2 Back 4 The queue is not Empty ( Back + 1 ) % size = ( 4 +1)% 5 = 0 =/= Front = 2 Adapted from Pearson Education, Inc.

en. Queue K [0] K [4] W [3] B 30 [1] One Location remains unused Front 2 Back 0 Let’s enqueue 1 more: Z [2] G The queue is not Empty ( Back + 1 ) % size = ( 0 +1)% 5 = 1 =/= Front = 2 Adapted from Pearson Education, Inc.

en. Queue Z – can’t do it… already full [0] K [4] W [3] B 31 [1] One Location remains unused [2] G Front 2 Back 0 The queue is FULL ( Back + 2 ) % size = ( 0 +2)% 5 = 2 == Front = 2 Adapted from Pearson Education, Inc.

Methods enqueue and dequeue public void enqueue (T new. Entry) { ensure. Capacity (); back. Index = (back. Index + 1) % queue. length; queue [back. Index] = new. Entry; } // end enqueue public T dequeue () { T front = null; if (!is. Empty ()) { front = queue [front. Index]; queue [front. Index] = null; front. Index = (front. Index + 1) % queue. length; } // end if return front; } // end dequeue 32 Adapted from Pearson Education, Inc.

Java Class Library: The Class Abstract. Queue � Methods provided � public boolean add(T new. Entry) � public boolean offer(T new. Entry) � public T remove() � public T poll() � public T element() � public T peek() � public boolean is. Empty() � public void clear() � public int size() 33 Adapted from Pearson Education, Inc.

Doubly Linked Implementation of a Deque public class Linked. Deque <T> implements Deque. Interface <T> { private DLNode first. Node; // references front of deque private DLNode last. Node; // references back of deque public Linked. Deque () { first. Node = null; last. Node = null; } // end default constructor … ADT Queue methods go here … private class DLNode { private T data; private DLNode next; private DLNode previous; … } // end DLNode // deque entry // link to next node // link to previous node } // end Linked. Deque 34 Adapted from Pearson Education, Inc.

Adding to the back of a non-empty deque (a) after the new node is allocated; (b) after the addition is complete 35 Adapted from Pearson Education, Inc.

Removing the first node from a deque containing at least two entries 36 Adapted from Pearson Education, Inc.

Possible Implementations of a Priority Queue Figure 11 -20 Two possible implementations of a priority queue using (a) an array; (b) a chain of linked nodes 37 Adapted from Pearson Education, Inc.

End Chapter 11 38 Adapted from Pearson Education, Inc.