10/3/2018 Data Structure & Algorithm. Quiz (30 min, closed-book) Heaps: Array-based Heap Implementation

Transcription

1 10/3/2018 Data Structure & Algorithm Quiz (30 min, closed-book) Heaps: Array-based Heap Implementation 1

2 - COSC Assignment 05 The GitHub repo for this week's assignment is at: 2

3 Typo in the assignment public E removefirst(){ /* *!!!!!!!!!!!!!!!!!!! * todo: fill the method. *!!!!!!!!!!!!!!!!!!! */ } 3

4 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. 4

5 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. 5

6 Proposition 9.2 A heap T storing n entries has height h = log n 6

7 Quiz Example Question In a heap of height h, what is the minimum number of nodes in the heap? 7

8 Heapup (Bubble up) Quiz example question: when do you need to call heapup? 1. in insert(key, value) 2. in removemin() 3. in swap(node i, node j) 8

9 Heapup (Bubble up) 9

10 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) 10

11 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) Entry min() Node insert(key, Value) Entry removemin() 11

12 Try to Implement a Heap using a Linked Structure 12

13 Implement a Heap using an ArrayList left(i) = 2*i + 1 right(i) = 2*i + 2 parent(i) = (i-1)/2 13

14 Implement a Heap using an ArrayList 14

15 Implement a Heap using an ArrayList

16 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) 16

17 Implementing a Heap A heap is a binary tree, with the following operations: void swap(int i, int j) void upheap(int i) void downheap(int i) Entry<K, V> min() Entry<K, V> insert(key, Value) Entry<K, V> removemin() 17

18 Implementing a Priority Queue with a Heap Singly Linked List (PQEntry) Key Value Heap 18

19 Priority Queue - Heap instance variables: ArrayList<PQEntry<K, V>> arrayvariable constructor: HeapPriorityQueue() public methods: public in size() Node<V> insert(int key, V value) public Node<V> min() public Node<V> removemin() 19

20 One application of Priority Queue (PQ) Sorting: Given a sequence of elements that can be compared to each other, how can we rearrange them in increasing-order/decreasing-order? (If there are ties, in non-decreasing order/non-increasing order) (One sorting algorithm we have covered: insertionsort!) 20

21 One application of Priority Queue (PQ) How can we use a priority queue sort elements? <to be filled after class> Heap Sort 21

22 Adaptable PQ 1. remove any node (not the node with the minimal key)? 2. update the key of a node? 3. update the value of a node? Quiz Example Question: What s the difference in implementation between PQ and Adaptable PQ? <to be filled after class> 22

23 We have learned: Recursion: activation trees Insertion sorting Lists: singly linked list, circularly linked lists, doubly linked lists Trees: general trees, binary trees, heaps Queues: FIFO (first-in-first-out) queues, priority queues (using three data structures) 23

24 New data structure! Map<K, V> 24

25 New data structure! Map<K, V>

26 New data structure! Map<K, V> points to an illustration 26

27 New data structure! Map<K, V> int size() boolean isempty() V get(k key) V put(k key, V value) V remove(k key) Iterable<K> keyset Iterable<V> values Iterable<Entry<K, V>> entryset() 27

28 28

29 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 29

30 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. 30

31 Assignment 02 (2 points) 31