A Practical Introduction to Data Structures and Algorithm Analysis

Sec. 9.7 Projects 355Be sure to indicate how you are using H1 and H2 to do the hashing. FunctionRev(k) reverses the decimal digits of k, for example, Rev(37) = 73;Rev(7) = 7.H1(k) = k mod 13.H2(k) = (Rev(k + 1) mod 11).Keys: 2, 8, 31, 20, 19, 18, 53, 27.9.19 Write an algorithm for a deletion function for hash tables that replaces therecord with a special value indicating a tombstone. Modify the functionshashInsert and hashSearch to work correctly with tombstones.9.20 Consider the following permutation for the numbers 1 to 6:2, 4, 6, 1, 3, 5.Analyze what will happen if this permutation is used by an implementation ofpseudo-random probing on a hash table of size seven. Will this permutationsolve the problem of primary clustering? What does this say about selectinga permutation for use when implementing pseudo-random probing?9.7 Projects9.1 Implement a binary search and the quadratic binary search of Section 9.1.Run your implementations over a large range of problem sizes, timing theresults for each algorithm. Graph and compare these timing results.9.2 Implement the three self-organizing list heuristics count, move-to-front, andtranspose. Compare the cost for running the three heuristics on various inputdata. The cost metric should be the total number of comparisons requiredwhen searching the list. It is important to compare the heuristics using inputdata for which self-organizing lists are reasonable, that is, on frequency distributionsthat are uneven. One good approach is to read text files. The listshould store individual words in the text file. Begin with an empty list, aswas done for the text compression example of Section 9.2. Each time a wordis encountered in the text file, search for it in the self-organizing list. If theword is found, reorder the list as appropriate. If the word is not in the list,add it to the end of the list and then reorder as appropriate.9.3 Implement the text compression system described in Section 9.2.9.4 Implement a system for managing document retrieval. Your system shouldhave the ability to insert (abstract references to) documents into the system,associate keywords with a given document, and to search for documents withspecified keywords.