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Lecture 8 CS203 Implementation of Data Structures 2 In the last couple of weeks, we have covered various data structures that are implemented in the Java Collections Framework. As a working programmer, you may often use these, and most of the rest of the time, you will use various libraries that supply alternatives. You will not often have to implement the data structures yourself. However, in order to understand how these structures work at a lower level, we will cover implementation this week. Lists 3 A list stores 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. Two Ways to Implement Lists 4 There are two common ways to implement a list in Java. Using arrays. 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. Using a linked list. 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. Two Ways to Implement Lists 5 Sample Code is linked from course page ArrayList and LinkedList 6 For convenience, let’s 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 MyList Interface and MyAbstractList Class «interface» MyList<E> 7 +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 Array List 8 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 twice the size of the current one. Copy the elements from the current array to the new array. The new array now becomes the current array. Insertion 9 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 e 1 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 e1 … 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 Deletion 10 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 e 1 … i … ei-1 ei Delete this element After deleting the element, list size is decremented by 1 0 1 e0 e1 … 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 Implementing MyArrayList 11 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. Linked Lists 12 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. 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: 13 head Node 1 Node 2 element element next next class Node<E> { E element; Node next; public Node(E o) { element = o; } } Node n … element null tail Adding Three Nodes 14 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 Adding Three Nodes, cont. 15 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 Adding Three Nodes, cont. 16 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 Adding Three Nodes, cont. 17 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 Traversing All Elements in the List 18 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; } MyLinkedList 19 MyAbstractList<E> Node<E> m 1 element: E next: Node<E> MyLinkedList<E> -head: Node<E> -tail: Node<E> 1 Link MyLinkedList +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. TestMyLinkedList Run 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; } 20 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 (b) After a new node is inserted. … ek null 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++; } … 21 tail e0 ei ei+1 next 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 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 { head Node<E> current = head; for (int i = 1; i < index; i++) e0 current = current.next; next Node<E> temp = current.next; current.next = new Node<E>(o); (current.next).next = temp; size++; } } head e0 22 … 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 current temp ei ei+1 next next … next A new node is inserted in the list e next tail … ek null (b) After a new node is inserted. 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; } } 23 tail head e0 e1 next next … Delete this node ei ei+1 next next … null (a) Before the node is deleted. head e1 next tail … ei ei+1 next next … ek ek null (b) After the first node is deleted 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() 24 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 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; head for (int i = 1; i < index; i++) { element previous = previous.next; next } Node<E> current = previous.next; previous.next = current.next; size--; head return current.element; } element } next 25 … previous current current.next element element element next next next tai … elem null Node to be deleted (a) Before the node is deleted. … previous current.next element element next next (b) After the node is deleted. tai … elem null Time Complexity for ArrayList and LinkedList Methods MyArrayList/ArrayList 26 MyLinkedList/LinkedList add(index: int, e: E) O (1) O (n ) O (1) O (n ) clear() O (1) O (1) contains(e: E) O (n ) O (n ) get(index: int) O(1) O (n ) indexOf(e: E) O (n ) O (n ) isEmpty() O (1) O (1) lastIndexOf(e: E) O (n ) O (n ) remove(e: E) O (n ) O (n ) size() O (1) O (1) remove(index: int) O(n) O (n ) set(index: int, e: E) O(n) O (n ) addFirst(e: E) O(n) O (1) removeFirst() O(n) O (1) add(e: E) Circular Linked Lists 27 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. Example uses: playing video/audio files repeatedly ALT + TAB in Windows. head Node 1 Node 2 element element next next Node n … element next tail Doubly Linked Lists 28 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 Circular Doubly Linked Lists 29 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 Stacks 30 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 Data2 Data1 Data1 Data3 Data2 Data2 Data1 Data1 Data1 Data3 Data2 Data1 Queues 31 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 Data2 Data1 Data1 Data3 Data2 Data1 Data3 Data3 Data2 Data1 Data2 Data3 Implementing Stacks and Queues 32 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. Design of the Stack and Queue Classes 33 There are two ways to design the stack and queue classes: Using inheritance: You can define the stack class by extending the array list class, and the queue class by extending the linked list class. ArrayList GenericStack LinkedList GenericQueue – Using composition: You can define an array list as a data field in the stack class, and a linked list as a data field in the queue class. GenericStack ArrayList GenericQueue LinkedList Composition is Better 34 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. MyStack and MyQueue 35 GenericStack<E> GenericStack -list: java.util.ArrayList<E> An array list to store elements. +GenericStack() Creates an empty stack. +getSize(): int Returns the number of elements in this stack. +peek(): E Returns the top element in this stack. +pop(): E Returns and removes the top element in this stack. +push(o: E): void Adds a new element to the top of this stack. +isEmpty(): boolean Returns true if the stack is empty. GenericQueue<E> GenericQueue -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. Priority Queue A regular queue is a first-in and first-out data36 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 Adds an element to this queue. +dequeue(): E Removes an element from this queue. +getSize(): int Returns the number of elements from this queue. Heap 37 The term "Heap" is used in several different ways. The Priority Queue example code uses a heap that adheres to this definition: A heap is a binary tree (one in which each node has at most two children) that with these two properties: Order property: If A is a parent node of B then the key of node A is ordered with respect to the key of node B with the same ordering applying across the heap. Either the keys of parent nodes are always greater than or equal to those of the children and the highest key is in the root node (max heap) or the keys of parent nodes are less than or equal to those of the children and the lowest key is in the root node (min heap). Shape property: 1- All leaves are either at depth d or d-1 (for some value d). 2- All of the leaves at depth d-1 are to the right of the leaves at depth d. 3- (a) There is at most 1 node with just 1 child. (b) Any such child is the left child of its parent, and (c) it is the rightmost leaf at depth d. Heap 38 Representing a Heap 39 The tree is represented by values in a list or array. For a node at position i, its left child is at position 2i+1 and its right child is at position 2i+2, and its parent is (i-1)/2. For example, the node for element 39 is at position 4, so its left child (element 14) is at 9 (2*4+1), its right child (element 33) is at 10 (2*4+2), and its parent (element 42) is at 1 ((4-1)/2). [0] [1] [2] [3] [4] [5] [6] [7] [8] [9] [10][11][12][13] 62 [10][11] 62 42 59 32 39 44 13 22 29 14 33 30 17 9 42 32 22 59 39 29 14 44 33 30 17 parent 13 9 left right Adding Elements to the Heap 40 Adding 3, 5, 1, 19, 11, and 22 to a heap, initially empty 3 5 5 3 3 (a) After adding 3 (b) After adding 5 19 5 1 (c) After adding 1 19 1 11 22 1 3 3 (d) After adding 19 (e) After adding 11 5 11 3 19 5 1 (f) After adding 22 Rebuild the heap after adding a new node 41 Adding 88 to the heap 22 22 11 3 19 5 1 88 (a) Add 88 to a heap 88 11 3 88 5 1 19 (b) After swapping 88 with 19 11 3 22 5 1 19 (b) After swapping 88 with 22 Removing the Root and Rebuild the Tree 42 Removing root 62 from the heap 62 42 32 22 59 39 29 14 44 33 30 13 17 9 Removing the Root and Rebuild the Tree 43 Move 9 to root 9 42 32 22 59 39 29 14 44 33 30 13 17 Removing the Root and Rebuild the Tree 44 Swap 9 with 59 59 42 32 22 9 39 29 14 44 33 30 13 17 Removing the Root and Rebuild the Tree 45 Swap 9 with 44 59 42 32 22 44 39 29 14 9 33 30 13 17 Removing the Root and Rebuild the Tree 46 Swap 9 with 30 59 42 32 22 44 39 29 14 30 33 9 13 17