Chapter 25 Lists, Stacks, Queues, and Priority Queues
Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807
Objectives
To design list with interface and abstract class (24.2). To design and implement a dynamic list using an array (24.3). To design and implement a dynamic list using a linked structure (24.4). To design and implement a stack using an array list (24.5). To design and implement a queue using a linked list (24.6). To evaluate expressions using stacks (24.7).
Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807
What is a Data Structure?
A data structure is a collection of data organized in some fashion. A data structure not only stores data, but also supports the operations for manipulating data in the structure. For example, an array is a data structure that holds a collection of data in sequential order. You can find the size of the array, store, retrieve, and modify data in the array. Array is simple and easy to use, but it has two limitations:
Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807
Limitations of arrays
Once an array is created, its size cannot be altered. Array provides inadequate support for inserting, deleting, sorting, and searching operations.
Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807
Object-Oriented Data Structure
In object-oriented thinking, a data structure is an object that stores other objects, referred to as data or elements. So some people refer a data structure as a container object or a collection object. To define a data structure is essentially to declare a class. The class for a data structure should use data fields to store data and provide methods to support operations such as insertion and deletion. To create a data structure is therefore to create an instance from the class. You can then apply the methods on the instance to manipulate the data structure such as inserting an element to the data structure or deleting an element from the data structure.
Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807
Four Classic Data Structures
Four classic dynamic data structures to be introduced in this chapter are lists, stacks, queues, and binary trees. A list is a collection of data stored sequentially. It supports insertion and deletion anywhere in the list. A stack can be perceived as a special type of the list where insertions and deletions take place only at the one end, referred to as the top of a stack. A queue represents a waiting list, where insertions take place at the back (also referred to as the tail of) of a queue and deletions take place from the front (also referred to as the head of) of a queue. A binary tree is a data structure to support searching, sorting, inserting, and deleting data efficiently.
Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807
Lists
A list is a popular data structure to store data in sequential order. For example, a list of students, a list of available rooms, a list of cities, and a list of books, etc. can be stored using lists. The common operations on a list are usually the following: Retrieve an element from this list. Insert a new element to this list. Delete an element from this list. Find how many elements are in this list. Find if an element is in this list. Find if this list is empty.
Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807
Two Ways to Implement Lists
There are two ways to implement a list. One is to use an array to store the elements. The array is dynamically created. If the capacity of the array is exceeded, create a new larger array and copy all the elements from the current array to the new array. The other approach is to use a linked structure. A linked structure consists of nodes. Each node is dynamically created to hold an element. All the nodes are linked together to form a list.
Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807
Design of ArrayList and LinkedList
For convenience, lets name these two classes: MyArrayList and MyLinkedList. These two classes have common operations, but different data fields. The common operations can be generalized in an interface or an abstract class. A good strategy is to combine the virtues of interfaces and abstract classes by providing both interface and abstract class in the design so the user can use either the interface or the abstract class whichever is convenient. Such an abstract class is known as a convenience class.
MyArrayList MyList MyAbstractList MyLinkedList
Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807
MyList Interface and MyAbstractList Class
interface MyList<E>
+add(e: E) : void +add(index: int, e: E) : void +clear(): void +contains(e: E): boolean +get(index: int) : E +indexOf(e: E) : int +isEmpty(): boolean +lastIndexOf(e: E) : int +remove(e: E): boolean +size(): int +remove(index: int) : E +set(index: int, e: E) : E Appends a new element at the end of this list. Adds a new element at the specified index in this list. Removes all the elements from this list. Returns true if this list contains the element. Returns the element from this list at the specified index. Returns the index of the first matching element in this list. Returns true if this list contains no elements. Returns the index of the last matching element in this list. Removes the element from this list. Returns the number of elements in this list. Removes the element at the specified index and returns the removed element. Sets the element at the specified index and returns the element you are replacing.
MyAbstractList<E>
#size: int #MyAbstractList() #MyAbstractList(objects: E[]) +add(e: E) : void +isEmpty(): boolean +size(): int +remove(e: E): boolean The size of the list. Creates a default list. Creates a list from an array of objects. Implements the add method. Implements the isEmpty method. Implements the size method. Implements the remove method.
Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807
MyList MyAbstractList
10
Array Lists
Array is a fixed-size data structure. Once an array is created, its size cannot be changed. Nevertheless, you can still use array to implement dynamic data structures. The trick is to create a new larger array to replace the current array if the current array cannot hold new elements in the list. Initially, an array, say data of Object[] type, is created with a default size. When inserting a new element into the array, first ensure there is enough room in the array. If not, create a new array with the size as twice as the current one. Copy the elements from the current array to the new array. The new array now becomes the current array.
Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807
11
Array List Animation www.cs.armstrong.edu/liang/animation/Array ListAnimation.html
Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807
12
Insertion
Before inserting a new element at a specified index, shift all the elements after the index to the right and increase the list size by 1.
Before inserting e at insertion point i 0 1 i ei-1 ei i+1 ei+1 k-1 k ek-1 ek data.length -1 e0 e1
e After inserting e at insertion point i, list size is incremented by 1 0
Insertion point 1 i ei-1 e i+1 i+2 ei ei+1
shift
k+1
e0 e1
ek-1 ek data.length -1
13
e inserted here
Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807
Deletion
To remove an element at a specified index, shift all the elements after the index to the left by one position and decrease the list size by 1.
Before deleting the element at index i 0 1 i ei-1 ei i+1 ei+1 k-1 k ek-1 ek data.length -1
e0 e1
Delete this element
shift
After deleting the element, list size is decremented by 1
i ei-1 ei+1
k-2 k-1 ek-1 ek data.length -1
e0 e1
Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807
14
Implementing MyArrayList
MyAbstractList<E> MyArrayList<E>
-data: E[] +MyArrayList() +MyArrayList(objects: E[]) -ensureCapacity(): void Creates a default array list. Creates an array list from an array of objects. Doubles the current array size if needed.
MyArrayList
TestList
Run
Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807
15
Linked Lists
Since MyArrayList is implemented using an array, the methods get(int index) and set(int index, Object o) for accessing and modifying an element through an index and the add(Object o) for adding an element at the end of the list are efficient. However, the methods add(int index, Object o) and remove(int index) are inefficient because it requires shifting potentially a large number of elements. You can use a linked structure to implement a list to improve efficiency for adding and removing an element anywhere in a list.
Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807
16
Linked List Animation
www.cs.armstrong.edu/liang/animation/LinkedList Animation.html
Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807
17
Nodes in Linked Lists
A linked list consists of nodes. Each node contains an element, and each node is linked to its next neighbor. Thus a node can be defined as a class, as follows:
Node 1 head element next Node 2 element next Node n element null tail
class Node<E> { E element; Node next; public Node(E o) { element = o; } }
Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807
18
Adding Three Nodes
The variable head refers to the first node in the list, and the variable tail refers to the last node in the list. If the list is empty, both are null. For example, you can create three nodes to store three strings in a list, as follows: Step 1: Declare head and tail:
Node<String> head = null; Node<String> tail = null; The list is empty now
Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807
19
Adding Three Nodes, cont.
Step 2: Create the first node and insert it to the list:
head = new Node<String>("Chicago"); tail = head; After the first node is inserted inserted "Chicago" head tail next: null
Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807
20
Adding Three Nodes, cont.
Step 3: Create the second node and insert it to the list:
tail head tail.next = new Node<String>("Denver"); next next: null tail tail = tail.next; head "Chicago" next "Denver" next: null "Chicago" "Denver"
Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807
21
Adding Three Nodes, cont.
Step 4: Create the third node and insert it to the list:
tail tail.next = new Node<String>("Dallas"); head "Chicago" next "Denver" next "Dallas" next: null
tail tail = tail.next; head "Chicago" next "Denver" next "Dallas" next: null
Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807
22
Traversing All Elements in the List
Each node contains the element and a data field named next that points to the next element. If the node is the last in the list, its pointer data field next contains the value null. You can use this property to detect the last node. For example, you may write the following loop to traverse all the nodes in the list.
Node<E> current = head; while (current != null) { System.out.println(current.element); current = current.next; }
Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807
23
MyLinkedList
MyAbstractList<E>
Node<E>
element: E next: Node<E>
1 Link m 1
MyLinkedList<E>
-head: Node<E> -tail: Node<E> +MyLinkedList() +MyLinkedList(objects: E[]) +addFirst(e: E): void +addLast(e: E): void +getFirst(): E +getLast(): E +removeFirst(): E +removeLast(): E Creates a default linked list. Creates a linked list from an array of objects. Adds the object to the head of the list. Adds the object to the tail of the list. Returns the first object in the list. Returns the last object in the list. Removes the first object from the list. Removes the last object from the list.
MyLinkedList
Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807
24
Implementing addFirst(E o)
public void addFirst(E o) { Node<E> newNode = new Node<E>(o); newNode.next = head; head = newNode; size++; if (tail == null) tail = head; head }
e0 next A new node to be inserted element here next head element next e0 next ei next ei+1 next ek null ei next ei+1 next ek null
tail
(a) Before a new node is inserted. tail
New node inserted here
(b) After a new node is inserted.
Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807
25
Implementing addLast(E o)
public void addLast(E o) { if (tail == null) { head = tail = new Node<E>(element); } else { tail.next = new Node(element); tail = tail.next; } head size++; }
e0 next
tail ei next ei+1 next ek null A new node to be inserted here o null tail ei next ei+1 next ek next o null
(a) Before a new node is inserted. head e0 next
(b) After a new node is inserted.
Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807
New node inserted here
26
Implementing add(int index, E o)
public void add(int index, E o) { if (index == 0) addFirst(o); else if (index >= size) addLast(o); else { Node<E> current = head; for (int i = 1; i < index; i++) current = current.next; Node<E> temp = current.next; current.next = new Node<E>(o); (current.next).next = temp; size++; } }
head e0 next
current ei next A new node to be inserted here
temp ei+1 next
tail ek null
e null
(a) Before a new node is inserted.
head e0 next
current ei next A new node is inserted in the list
temp ei+1 next
tail ek null
e next
(b) After a new node is inserted.
Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807
27
Implementing removeFirst()
public E removeFirst() { if (size == 0) return null; else { Node<E> temp = head; head = head.next; size--; if (head == null) tail = null; return temp.element; } }
head e0 next e1 next ei next ei+1 next ek
tail
null
Delete this node head e1 next ei
(a) Before the node is deleted. tail ei+1 next ek null
next
(b) After the first node is deleted
Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807
28
public E removeLast() { if (size == 0) return null; else if (size == 1) { Node<E> temp = head; head = tail = null; size = 0; return temp.element; } else { Node<E> current = head; for (int i = 0; i < size - 2; i++) current = current.next; Node temp = tail; tail = current; tail.next = null; size--; return temp.element; } }
Implementing removeLast()
head e0 next e1 next ek-2 next current ek-1 next ek null tail
(a) Before the node is deleted. head e0 next e1 next ek-2 next tail ek-1 null
Delete this node
(b) After the last node is deleted
Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807
29
Implementing remove(int index)
public E remove(int index) { if (index < 0 || index >= size) return null; else if (index == 0) return removeFirst(); else if (index == size - 1) return removeLast(); else { Node<E> previous = head; for (int i = 1; i < index; i++) { head previous = previous.next; element } Node<E> current = previous.next;next previous.next = current.next; size--; return current.element; head } } element
next
previous element next
current element next
current.next element next
tail element null
Node to be deleted (a) Before the node is deleted. previous element next current.next element next tail element null
(b) After the node is deleted.
Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807
30
Circular Linked Lists
A circular, singly linked list is like a singly linked list, except that the pointer of the last node points back to the first node.
Node 1 head element next
Node 2 element next
Node n element next tail
Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807
31
Doubly Linked Lists
A doubly linked list contains the nodes with two pointers. One points to the next node and the other points to the previous node. These two pointers are conveniently called a forward pointer and a backward pointer. So, a doubly linked list can be traversed forward and backward.
Node 1 head element next null Node 2 element next previous Node n element null previous tail
Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807
32
Circular Doubly Linked Lists
A circular, doubly linked list is doubly linked list, except that the forward pointer of the last node points to the first node and the backward pointer of the first pointer points to the last node.
Node 1 head element next previous Node 2 element next previous Node n element next previous tail
Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807
33
Stacks
A stack can be viewed as a special type of list, where the elements are accessed, inserted, and deleted only from the end, called the top, of the stack.
Data1 Data2 Data3 Data3 Data2 Data1
Data1
Data2 Data1
Data3 Data2 Data1
Data2
Data1
Data1
34
Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807
Queues
A queue represents a waiting list. A queue can be viewed as a special type of list, where the elements are inserted into the end (tail) of the queue, and are accessed and deleted from the beginning (head) of the queue.
Data1 Data2 Data3 Data3 Data2 Data1
Data1
Data2 Data1
Data3 Data2
Data3
Data1
Data2
Data3
35
Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807
Stack Animation
www.cs.armstrong.edu/liang/animation/StackAnima tion.html
Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807
36
Queue Animation
www.cs.armstrong.edu/liang/animation/QueueAnim ation.html
Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807
37
Implementing Stacks and Queues
Using an array list to implement Stack Use a linked list to implement Queue Since the insertion and deletion operations on a stack are made only at the end of the stack, using an array list to implement a stack is more efficient than a linked list. Since deletions are made at the beginning of the list, it is more efficient to implement a queue using a linked list than an array list. This section implements a stack class using an array list and a queue using a linked list.
Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807
38
Design of the Stack and Queue Classes
There are two ways to design the stack and queue classes:
Using inheritance: You can declare the stack class by extending the array list class, and the queue class by extending the linked list class.
MyArrayList MyStack MyLinkedList MyQueue
Using composition: You can declare an array list as a data field in the stack class, and a linked list as a data field in the queue class.
MyStack MyArrayList MyQueue MyLinkedList
Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807
39
Composition is Better
Both designs are fine, but using composition is better because it enables you to define a complete new stack class and queue class without inheriting the unnecessary and inappropriate methods from the array list and linked list.
Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807
40
MyStack and MyQueue
MyStack
-list: MyArrayList +isEmpty(): boolean +getSize(): int +peek(): Object +pop(): Object +push(o: Object): Object +search(o: Object): int Returns true if this stack is empty. Returns the number of elements in this stack. Returns the top element in this stack. Returns and removes the top element in this stack. Adds a new element to the top of this stack. Returns the position of the specified element in this stack.
MyStack
MyQueue<E>
-list: MyLinkedList<E> +enqueue(e: E): void +dequeue(): E +getSize(): int
MyQueue
Adds an element to this queue. Removes an element from this queue. Returns the number of elements from this queue.
Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807
41
Example: Using Stacks and Queues
Write a program that creates a stack using MyStack and a queue using MyQueue. It then uses the push (enqueu) method to add strings to the stack (queue) and the pop (dequeue) method to remove strings from the stack (queue).
TestStackQueue
Run
Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807
42
Priority Queue
A regular queue is a first-in and first-out data structure. Elements are appended to the end of the queue and are removed from the beginning of the queue. In a priority queue, elements are assigned with priorities. When accessing elements, the element with the highest priority is removed first. A priority queue has a largest-in, first-out behavior. For example, the emergency room in a hospital assigns patients with priority numbers; the patient with the highest priority is treated first.
MyPriorityQueue<E>
-heap: Heap<E> +enqueue(element: E): void +dequeue(): E +getSize(): int Adds an element to this queue. Removes an element from this queue. Returns the number of elements from this queue.
MyPriorityQueue
TestPriorityQueue
Run
43
Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved. 0132130807
