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Chapter 24 Lists Stacks and Queues 1 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). 2 What is a Data Structure? A collection of data organized in some fashion – Stores data – Supports the operations for manipulating data in the structure array is a data structure – – – – – – – holds a collection of data in sequential order can find the size of the array store, retrieve, modify data in the array Array is simple and easy to use has two limitations: 3 Limitations of arrays Once an array is created, its size cannot be altered Array provides inadequate support for: – – – – inserting, deleting, sorting, searching operations 4 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 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 • 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. 5 Four Classic Data Structures Introduce four classic dynamic data structures: – Lists: A list is a collection of data stored sequentially It supports insertion and deletion anywhere in the list – Stacks: Can be perceived as a special type of the list Insertions and deletions take place only at the one end referred to as the top of a stack – Queues: Represents a waiting list Insertions take place at the back, also referred to as the tail of a queue Deletions take place from the front, also referred to as head of a queue – binary trees: A binary tree is a data structure to support: – searching, sorting, inserting, and deleting data efficiently 6 Lists A data – – – – – – structure to store data in sequential order list of students list of available rooms a list of cities a list of books 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 7 Two Ways to Implement Lists Use an array to store the elements – – – – array is dynamically created If the capacity of the array is exceeded create a new larger array copy all the elements from current array to new array 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 8 Design of ArrayList and LinkedList For – – – – – – – – convenience, let’s name these two classes: MyArrayList MyLinkedList These two classes have common operations, but different data fields 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 Provide both interface and abstract class in the design User can use interface or abstract class whichever is convenient Such an abstract class is known as a convenience class MyArrayList MyList MyAbstractList MyLinkedList 9 MyList Interface and MyAbstractList Class «interface» MyList<E> +add(e: E) : void Appends a new element at the end of this list. +add(index: int, e: E) : void Adds a new element at the specified index in this list. +clear(): void Removes all the elements from this list. +contains(e: E): boolean Returns true if this list contains the element. +get(index: int) : E Returns the element from this list at the specified index. +indexOf(e: E) : int Returns the index of the first matching element in this list. +isEmpty(): boolean Returns true if this list contains no elements. +lastIndexOf(e: E) : int Returns the index of the last matching element in this list. +remove(e: E): boolean Removes the element from this list. +size(): int Returns the number of elements in this list. +remove(index: int) : E Removes the element at the specified index and returns the removed element. +set(index: int, e: E) : E Sets the element at the specified index and returns the element you are replacing. MyAbstractList<E> #size: int The size of the list. #MyAbstractList() Creates a default list. #MyAbstractList(objects: E[]) Creates a list from an array of objects. +add(e: E) : void Implements the add method. +isEmpty(): boolean Implements the isEmpty method. +size(): int Implements the size method. +remove(e: E): boolean Implements the remove method. MyList MyAbstractList 10 Array Lists Array is a fixed-size data structure Once an array is created, its size cannot be changed you can use array to implement dynamic data structures 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 new array now becomes the current array 11 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 e0 e1 e After inserting e at insertion point i, list size is incremented by 1 1 … i … ei-1 ei i+1 … k-1 k … ek-1 ek ei+1 Insertion point 0 1 e0 e 1 … i … ei-1 e data.length -1 …shift… i+1 i+2 … ei e inserted here ei+1 … k k+1 ek-1 ek data.length -1 12 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 e0 e1 … i … ei-1 ei Delete this element After deleting the element, list size is decremented by 1 0 1 e0 e 1 … i … ei-1 ei+1 i+1 … k-1 k … ek-1 ek ei+1 …shift… … … data.length -1 k-2 k-1 ek-1 ek data.length -1 13 Implementing MyArrayList MyAbstractList<E> MyArrayList<E> -data: E[] +MyArrayList() Creates a default array list. +MyArrayList(objects: E[]) Creates an array list from an array of objects. -ensureCapacity(): void Doubles the current array size if needed. MyArrayList TestList Run 14 Linked Lists MyArrayList – – is implemented using an array – get (int index) accessing array elements – set (int index, Object o) modifying an element through an index – add (Object o) adding an element at the end of the list are efficient – methods add(int index, Object o) remove(int index) are inefficient 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 15 Nodes in Linked Lists A linked list consists of nodes Each node contains an element each node is linked to its next neighbor a node can be defined as a class, as follows: head Node 1 Node 2 element element next next Node n … element tail null class Node<E> { E element; Node next; public Node(E o) { element = o; 16 Adding Three Nodes variable head refers to the first node in the list variable tail refers to the last node in the list If the list is empty, both are null 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 17 Adding Three Nodes 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 18 Adding Three Nodes Step 3: – Create the second node and insert it to the list: tail tail.next = new Node<String>("Denver"); head "Chicago" "Denver" next next: null tail tail = tail.next; head "Chicago" "Denver" next next: null 19 Adding Three Nodes Step 4: – Create the third node and insert it to the list: tail tail.next = new Node<String>("Dallas"); head "Chicago" "Denver" "Dallas" next next next: null tail tail = tail.next; head "Chicago" "Denver" "Dallas" next next next: null 20 Traversing All Elements in the List Each node – – contains the element and a data field named next – next 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; } 21 MyLinkedList MyAbstractList<E> Node<E> element: E next: Node<E> m 1 MyLinkedList<E> -head: Node<E> -tail: Node<E> 1 Link +MyLinkedList() Creates a default linked list. +MyLinkedList(objects: E[]) Creates a linked list from an array of objects. +addFirst(e: E): void Adds the object to the head of the list. +addLast(e: E): void Adds the object to the tail of the list. +getFirst(): E Returns the first object in the list. +getLast(): E Returns the last object in the list. +removeFirst(): E Removes the first object from the list. +removeLast(): E Removes the last object from the list. MyLinkedList 22 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 tail … next A new node to be inserted element here next ei ei+1 next next … ek null (a) Before a new node is inserted. head tail element e0 next next New node inserted here … ei ei+1 next next … ek null (b) After a new node is inserted. 23 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 tail … next ei ei+1 next next … ek null A new node to be inserted here (a) Before a new node is inserted. o null head e0 next tail … ei ei+1 next next (b) After a new node is inserted. … ek o next null New node inserted here 24 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 temp ei ei+1 next next A new node to be inserted here e tail … ek null (a) Before a new node is inserted. null head e0 current temp ei ei+1 next next … next A new node is inserted in the list e tail … ek null (b) After a new node is inserted. next 25 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; } } tail head e0 e1 next next … Delete this node ei ei+1 next next … null (a) Before the node is deleted. head e1 next ek tail … ei ei+1 next next … ek null (b) After the first node is deleted 26 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() tail current head … e0 e1 next next ek-2 ek-1 ek next next null (a) Before the node is deleted. Delete this node tail head … e0 e1 next next ek-2 ek-1 next null (b) After the last node is deleted 27 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 current current.next element element element next next next tail … element null Node to be deleted (a) Before the node is deleted. previous current.next element element next next tail … element null (b) After the node is deleted. 28 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. head Node 1 Node 2 element element next next Node n … element tail next 29 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 head Node 1 Node 2 element element next next null null previous previous Node n … element tail 30 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 head Node 1 Node 2 element element next next next previous previous previous Node n … element tail 31 Stacks A stack – can be viewed as a special type of list – elements are accessed, inserted, and deleted only from the end, called the top, of the stack Data1 Data2 Data3 Data2 Data1 Data1 Data3 Data2 Data2 Data1 Data3 Data2 Data1 Data1 Data1 32 Queues A queue – – – – – represents a waiting list can be viewed as a special type of list elements are inserted into the end (tail) of the queue Elements are accessed/deleted from beginning of queue (head) Data1 Data2 Data3 Data2 Data1 Data1 Data3 Data2 Data1 Data3 Data3 Data2 Data1 Data2 Data3 33 Implementing Stacks and Queues Using an array list to implement Stack Use a linked list to implement Queue 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 deletions are made at the beginning of queue – it is more efficient to implement a queue using a linked list than an array list Implement: – a stack class using an array list – a queue using a linked list 34 Design of the Stack and Queue Classes There are two ways to design the stack and queue classes: – Using inheritance: MyArrayList You can declare the stack class by extending the array list class, and the queue class by extending the linked list class. 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 35 Composition is Better Both designs are fine – – using composition is better because it enables you to declare a complete new stack class and queue class without inheriting the unnecessary and inappropriate methods from the array list and linked list 36 MyStack and MyQueue MyStack MyStack -list: MyArrayList +isEmpty(): boolean Returns true if this stack is empty. +getSize(): int Returns the number of elements in this stack. +peek(): Object Returns the top element in this stack. +pop(): Object Returns and removes the top element in this stack. +push(o: Object): Object Adds a new element to the top of this stack. +search(o: Object): int Returns the position of the specified element in this stack. MyQueue<E> MyQueue -list: MyLinkedList<E> +enqueue(e: E): void Adds an element to this queue. +dequeue(): E Removes an element from this queue. +getSize(): int Returns the number of elements from this queue. 37 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 38