1. 1 Chapter 13 Priority Queues

2. 2 Chap.13 Contents 13.1 Introduction 13.2 The PurePriorityQueue Interface 13.3 Implementations of the PurePriorityQueue Interface 13.3.2 The Heap Implementation of the PurePriorityQueue Interface 13.4 Application: Huffman Codes

3. 3 13.1 Introduction A priority queue (PQ) is an interface (property) in which access or deletion is of: the highest-priority element, according to some method of assigning priorities to elements.

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7. 7 13.2 The PurePriorityQueue Interface public interface PriorityQueue { /** * size 回傳 PurePriorityQueue 中元素的個數 */ int size ( )

8. 8 /* isEmpty 看 PurePriorityQueue * 是否沒有元素. * * return true – if PurePriorityQueue * 沒有元素 ; * otherwise, return false ; */ boolean isEmpty ( )

9. 9 /** * add 加元素到 PurePriorityQueue. * * The worstTime(n) is O(n). * * @param element – 要插入 PurePriorityQueue 的元素 */ void add (E element)

10. 10 /* getMin * 回傳 PurePriorityQueue 中的最高優先權元素 * * The worstTime(n) is O (1). * * @return PurePriorityQueue 的最高優先權元素 * * @throws NoSuchElementException – * if PurePriorityQueue 是空的 */ E getMin ( )

11. 11 /* removeMin * 從 PurePriorityQueue 移除具有最高優先權的元素 * * The worstTime(n) is O (log n). * * @return 被移除的元素 * *@throws NoSuchElementException – * if PurePriorityQueue 是空的 */ E removeMin ( )

12. 12 13.3 Implementations of The PurePriorityQueue Interface 有三種 data structures 可實 作之，分別是 : 1) linked list 2) tree set 3) heap

13. 1. Use Linked List 13

14. 14 public class LinkedPQ impelments PurePriorityQueue { LinkedList list ; Comparator comparator ;

15. 15 public LinkedPQ() {list = new LinkedList ( ) ; comparator = null ; } public LinkedPQ (Comparator comp) {this() ; comparator = comp ;} public int size() { return list.size() ; } public E getMin() { return list.getFirst() ; } public E removeMin(){ return list.removeFirst() ;}

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17. 17 public void add (E element){ if /* 空或 element 優先權比最後的大 */ (list.isEmpty( ) || compare (element, list.get (list.size( ) – 1)) >= 0) /* 直接 add 此 element */ list.add (element) ; else {/* 找適當位置 add 使優先權由小到大 */ ListIterator itr = list.listIterator( ); while (itr.hasNext() && compare (element, itr.next( )) >= 0) ; /* 倒退一位, 再 add*/ itr.previous( ) ; itr.add (element) ; }} //end of add WorstTime (n) is linear in n.

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19. 19 2. Use Tree Set

20. 20 public class TreeSetPQ implements PriorityQueue { TreeSet set; Comparator comparator; // the 2 constructors, size, isEmpty and compare // methods 與 LinkedPQ class 的類似 public TreeSetPQ (Comparator c) { comparator = c ; set = new TreeSet (c); } // one-parameter constructor

21. 21 public void add (E element) {set.add (element);} public E getMin ( ) {return set.first( );} public E removeMin ( ) {E temp = set.first( ); set.remove (set.first( )); return temp;} } // end of class TreeSetPQ For these three methods, worst time (n) is logarithmic in n.

22. 3. Use Heap 22

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24. 24 Heap [Collins English Dictionary] A collection of articles or mass of material gathered together in one place. 這定義用於 compiler, OS. Ex: Heap storage ( 堆 ) vs. stack storage ( 疊 ) in main memory.

25. 25 但是， Data Structure 中的 Heap ， 有不同的定義 : Heap 是一棵 tree ， 且任何一個節點比 所有 descendants ( 後代 ) 都小

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29. 29 heap 不是 binary search tree! 因為對 root 而言 binary search tree 是 左小右大 heap 則是上 (root) 小 下 ( 左右 ) 大 這叫 min heap (minimal element at root) 另有 max heap (maximal element at root) 則是下 ( 左右 ) 小 上 (root) 大

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32. 32 下列的學生分數程式，創出 Heap 結構 ， 並執行 Heap 動作 : add 和 removeMin 請輸入學生姓名及 GPA 或 ***( 結束 )”; Mary 4.0 (red indicates user input) John 3.5 *** 系統輸出如下 John 3.5 Mary 4.0

33. 33 public static void main(String[] args){ final String PROMPT= “ 請輸入學生姓名及 GPA 或 ***( 結束 )”; final String RESULTS =“\n 學生姓名及 GPA 如下 ” ; String line ; Heap heap = new Heap ( ) ; BufferedReader keyboardReader = new BufferedReader (new InputStreamReader(System.in) ) ; try{ while(true) {System.out.print (PROMPT) ; line = keyboardReader.readLine() ; if (line.equals(“***”)) break ; heap.add (new Student(line) );} //while system.out.println (RESULTS); while(!heap.isEmpty()) System.out.println (heap.removeMin() ) ; }//try catch(Exception e){ System.out.println(e) ;} } // end of main

34. 34 import java.util.* ; public class Student implements Comparable { protected String name ; protected double gpa ; /** Student 從特定的 String s 初始化 Student object. * * @param s – String 初始化 Student object. *@throws NullPointerException, NoSuchElementException, * NumberFormatException */ public Student (String s){ StringTokenizer tokens = new StringTokenizer(s) ; name = tokens.nextToken() ; gpa = Double.parseDouble( tokens.nextToken() ) ; } // constructor public String toString() {return name+“ “+ gpa;} } // end of class Student

35. 35 13.3.2 The Heap Implementation of the PurePriorityQueue Interface

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44. 44 Protected void percolateUp(){ // 設定 child 為 最後一個 node (size -1) int child = size -1; int parent; Object temp ; while(child > 0){ parent = (child-1)/2; // 如果 parent <= child 不用做了 if(compare(heap[parent],heap[child] <= 0) break; // 否則 swap parent 與 child temp=heap[parent];heap[parent]=heap[child];heap[child]=temp; /*child 向上走一步 */ child = parent; }//end while } //end of percolateUp

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50. 50 Protected void percolateDown(int start){ // parent 為 tree 的 root (index 0 ) // child 為 root 的左子樹 int parent = start, child = 2*parent + 1; Object temp ; while(child < size){ // 如 child 有右兄弟 且 右兄弟較小 則設定 child 為右兄弟 if(child < size – 1 && compare(heap[child],heap[child+1])> 0) child ++; // 如 parent <= child 不用再比了 if(compare(heap[parent],heap[child] <= 0) break; // 否則 swap parent 與 child temp = heap[child]; heap[child] = heap[parent];heap[parent] = temp; // child 向下走一步 parent = child; child = 2 * parent +1; }//while } // end of percolateDown

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52. 52 40 60 50 實際儲存於 array: 40 60 50 index: 0 1 2

53. 53 13.4 Application: Huffman Codes

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94. 94 13.4.3 The Huffman Encoding Project

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