10/1/2018 Data Structure & Algorithm. Circularly Linked List Doubly Linked List Priority queues Heaps

Transcription

1 10/1/2018 Data Structure & Algorithm Circularly Linked List Doubly Linked List Priority queues Heaps 1

2 Linked list: Head and Tail NULL Element Next 1. Head 2. Tail 3. Size 2

3 Make SinglyLinkedList implements Iterable Example code: 3

4 Circularly Linked List Doubly Linked List Priority queues Heaps 4

5 Round-Robin Scheduling CPU Waiting Process 5

6 Round-Robin Scheduling Multiple processes share a CPU. Each process uses CPU for a certain amount of time, a time slice. If the time slice ends before the process finishes its job, the process is interrupted, and is added back to the waiting process. 6

7 Round-Robin Scheduling // suppose Waitlist is a Singly Linked list 1. process p = WaitList.removeFirst() 2. p uses the CPU for a time slice 3. WaitList.addLast(p) 7

8 Circularly Linked List 8

9 Circularly Linked List instance variable: head, tail, size constructor: CircularlyLinkedList() public methods: int size() boolean isempty() E first() E last() public void rotate() void addfrist() void addlast() E removefirst() Quiz question example: implement a method of Circularly Linked List 9

10 Circularly Linked List Doubly Linked List Priority queues Heaps 10

11 Doubly Linked List Node of Single Linked List Node of Double Linked List Prev Next Element Next Element 11

12 Doubly Linked List Header Prev Element Next Trailer 12

13 Doubly Linked List Node Implementation Instance variables: element, prev, next Constructor: Node(E e, Node<e> p, Node<E> n) Public methods: E getelement() Node<E> getprev() Node<E> getnext() void setprev(node<e> p) void setnext(node<e> n) 13

14 Doubly Linked List List Implementation Instance variables: header, trailer, size Constructor: DoublyLinkedList() Public methods: int size() boolean isempty() E first() E last() void addfrist() void addlast() E removefirst() E removelast() void addbetween(e e, Node<E> p, Node<E> n) void E remove(node<e> n) 14

15 Break 15

16 Circularly Linked List Doubly Linked List Priority queues Heaps 16

17 How do we implement a queue using a Singly Linked List? Queue is exactly like a pipe. First come, first serve. First in, first out. 17

18 Queue Public methods: int size() boolean isempty() void enqueue(e e) E first() E dequeuer() 18

19 Priority Queue 19

20 Priority Queue PQEntry instance variables: key, value constructor: PQEntry(K key, V value) public methods: K getkey() V getvalue() void setkey(k key) void setvalue(k key) 20

21 Quiz question example: Priority Queue Behavior Given the following sequence of invocations, write down the priority queue s list and the return of the invocation after each invocation. priorityqueue.insert(1, A ) priorityqueue.insert(2, B ) removemin() priorityqueue.insert(3, C ) priorityqueue.insert(4, D ) priorityqueue.insert(3, Q ) priorityqueue.insert(2, E ) removemin(); removemin(); removemin(); removemin(); removemin(); 21

22 Priority Queue Queue (unsorted) instance variables: SinglyLinkedList list constructor: UnsortedPriorityQueue() public methods: public in size() Node<V> insert(int key, V value) public Node<V> min() public Node<V> removemin() Private methods: Node<V> findmin() 22

23 Analysis of Priority Queue Methods (Unsorted) public methods: public in size() Node<V> insert(int key, V value) public Node<V> min() public Node<V> removemin() O(1) O(1) O(n) O(n) Private methods: Node<V> findmin() 23

24 Priority Queue Queue (sorted) instance variables: DoublyLinkedList list constructor: SortedPriorityQueue() public methods: public in size() Node<V> insert(int key, V value) public Node<V> min() public Node<V> removemin() Private methods: Node<V> findmin() 24

25 Analysis of Priority Queue Methods (sorted) instance variables: DoublyLinkedList list constructor: SortedPriorityQueue() public methods: public in size() Node<V> insert(int key, V value) public Node<V> min() public Node<V> removemin() Private methods: Node<V> findmin() O(1) O(n) O(1) O(1) 25

26 Circularly Linked List Doubly Linked List Priority queues Heaps 26

27 Break 27

28 Heap A binary tree T that stores entries at its positions, such that, 1. a relational property defined in terms of the way keys are stored 2. a structural property defined in terms of the shape of T itself 28

29 Heap (cont.) A binary tree T that stores entries at its positions, such that, 1. a relational property defined in terms of the way keys are stored Heap-order property: for every position p other than the root, the key stored at p is greater than or equal to the key stored at p s parent. 29

30 Heap (cont.) 30

31 Heap (cont.) 2. a structural property defined in terms of the shape of T itself Complete binary tree property: A heap T with height h is a complete binary tree if levels 0, 1, 2,..., h- 1 of T have the maximal number of nodes possible, and the remaining nodes at level h reside in the leftmost possible positions at the level. 31

32 Heap (cont.) 32

33 Proposition 9.2 A heap T storing n entries has height h = log n 33

34 Inserting a node to a Heap - Upheap How to insert a node, 8?

35 Inserting a node to a Heap - Upheap How to insert a node, 8?

36 Inserting a node to a Heap - Upheap How to insert a node, 8?

37 Inserting a node to a Heap - Downheap How to remove the min node, root? 37

38 Inserting a node to a Heap - Downheap How to remove the min node, root? 38

39 Inserting a node to a Heap - Downheap How to remove the min node, root? 39

40 Inserting a node to a Heap - Downheap How to remove the min node, root? 40

41 Inserting a node to a Heap - Downheap How to remove the min node, root? 41

42 Inserting a node to a Heap - Downheap How to remove the min node, root? 42

43 Inserting a node to a Heap - Downheap How to remove the min node, root? 43

44 Implementing a Heap A heap is a binary tree, with the following operations: void swap(node i, Node j) void upheap(node i) void downheap(node i) PQEntry min() Node insert(key, Value) PQEntry removemin() 44

45 Try to Implement a Heap using a Linked Structure 45

46 Implement a Heap using an ArrayList left(i) = 2*i + 1 right(i) = 2*i + 2 parent(i) = (i-1)/2 46

47 Implement a Heap using an ArrayList

48 Implement a Heap using an ArrayList (i is an index of the array) parent(i) = (i-1)/2 parent(5) = (5-1)/2 = 2 swap(5, 2) 48

49 Implementing a Priority Queue with a Heap Singly Linked List (PQEntry) Key Value Heap 49

50 Assignment 01 (3 points) due Monday Oct. 8, noon Implement Doubly Linked List, and make it implement Iterable<E> public class DoublyLinkedList<E> implements Iterable<E> Example code for Singly Linked List: p 50

51 Assignment 02 (2 points) due Monday Oct. 8, noon R-9.21 Illustrate all the steps of the adaptable priority queue (will be discussed on Wednesday) call remove(e) for entry e storing (16, X) in the heap of Figure 9.1. (submit a word doc or a pdf) R-9.22 Illustrate all the steps of the adaptable priority queue call replacekey(e, 18) for entry e storing (5, A) in the heap of Figure 9.1. (submit a word doc or a pdf) Figure is on the next slide. 51

52 Assignment 02 (2 points) 52