A Practical Introduction to Data Structures and Algorithm Analysis

204 Chap. 5 Binary Trees5.5 Implement a priority queue class based on the max-heap class implementationof Figure 5.19. The following methods should be supported for manipulatingthe priority queue:void enqueue(int ObjectID, int priority);int dequeue();void changeweight(int ObjectID, int newPriority);Method enqueue inserts a new object into the priority queue with ID numberObjectID and priority priority. Method dequeue removes theobject with highest priority from the priority queue and returns its object ID.Method changeweight changes the priority of the object with ID numberObjectID to be newPriority. The type for E should be a class thatstores the object ID and the priority for that object. You will need a mechanismfor finding the position of the desired object within the heap. Use anarray, storing the object with ObjectID i in position i. (Be sure in yourtesting to keep the ObjectIDs within the array bounds.) You must alsomodify the heap implementation to store the object’s position in the auxiliaryarray so that updates to objects in the heap can be updated as well in thearray.5.6 The Huffman coding tree function buildHuff of Figure 5.29 manipulatesa sorted list. This could result in a Θ(n 2 ) algorithm, because placing an intermediateHuffman tree on the list could take Θ(n) time. Revise this algorithmto use a priority queue based on a min-heap instead of a list.5.7 Complete the implementation of the Huffman coding tree, building on thecode presented in Section 5.6. Include a function to compute and store in atable the codes for each letter, and functions to encode and decode messages.This project can be further extended to support file compression. To do sorequires adding two steps: (1) Read through the input file to generate actualfrequencies for all letters in the file; and (2) store a representation for theHuffman tree at the beginning of the encoded output file to be used by thedecoding function. If you have trouble with devising such a representation,see Section 6.5.