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HEAPS AND PRIORITY QUEUES
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Figure 13.6 Deleting 88 from a heap
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out first. That means that each element is assigned a priority number, and the element with the highest priority comes out first. Priority queues are widely used in computer systems. For example, if a printer is shared by several computers on a local area network, the print jobs that are queued to it would normally be held temporarily in a priority queue wherein smaller jobs are given higher priority over larger jobs. Priority queues are usually implemented as heaps since the heap data structure always keeps the element with the largest key at the root and its insertion and removal operations are so efficient. According to Theorem 13.1, those operations are guaranteed to run in in O(lgn) time. THE JCF PriorityQueue CLASS The Java Collections Framework includes a PriorityQueue class. As Figure 4.1 on page 70 shows, that class extends the AbstractQueue and AbstractList classes, implementing the Queue and List interfaces. EXAMPLE 13.6 The java.util.PriorityQueue Class
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public class TestingPriorityQueues { public static void main(String[] args) { PriorityQueue<String> pq = new PriorityQueue<String>(); pq.add("FR"); pq.add("DE"); pq.add("GB");
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HEAPS AND PRIORITY QUEUES
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pq.add("IT"); pq.add("ES"); while (!pq.isEmpty()) { System.out.printf("%s }
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", pq.remove());
The output is:
DE ES FR GB IT
The collection pq is a priority queue, so its elements are removed according to their priorities. The element type for this queue is String, which has its own natural ordering: alphabetical order. So regardless of the order in which they are inserted, they are removed in alphabetical order.
If the element type has no natural ordering, then PriorityQueue instances will apply the compareTo() method to determine priorities among the elements. EXAMPLE 13.7 Using Elements that Explicitly Implement the Comparable Interface
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public class TestingPriorityQueues { public static void main(String[] args) { PriorityQueue<Student> pq = new PriorityQueue<Student>(); pq.add(new Student("Ann",44)); pq.add(new Student("Bob",99)); pq.add(new Student("Cal",33)); pq.add(new Student("Don",66)); while (!pq.isEmpty()) { System.out.printf("%s ", pq.remove()); } } } class Student implements Comparable{ private String name; private int credits; public Student(String name, int credits) { this.name = name; this.credits = credits; } public int compareTo(Object object) { if (object == this) { return 0; } else if (!(object instanceof Student)) { throw new IllegalArgumentException("comparing apples and oranges!"); } Student that = (Student)object; return this.credits - that.credits; } public String toString() { return String.format("%s(%d)", name, credits); } }
The output is:
Cal(33) Ann(44) Don(66) Bob(99)
HEAPS AND PRIORITY QUEUES
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The priority queue pq defined at line 3 stores instances of the Student class that is defined at line 14. That class is declared to implement the Comparable interface, which obliges it to define a compareTo() method. That method, defined at line 23, uses the credits field of the Student objects to compare them. Students with more credits have higher priority. The print loop at line 8 is the same as the one in Example 13.6: It applies the priority queue s remove() method to remove and print the elements according to their ascending priority levels, independently of their insertion order (except for equal priorities).
Review Questions
13.1 13.2 13.3 13.4 13.5 13.6 13.7 What are the two main applications of heaps How efficient are insertions into and removals from a heap Why is a priority queue called a BIFO container What is the difference between a queue and a priority queue Why are heaps used to implement priority queues In the natural mapping of a binary tree into an array a[], why do we start at a[1] instead of at a[0] If it takes an average of 3ms to remove an element from a priority queue with 1,000 elements, how long would you expect it to take to remove an element from a priority queue with 1,000,000 elements Suppose a method is devised to sort an array by storing its element in a priority queue and then removing them back into the array. What is the run time for such an algorithm
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