Exercises in Java

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Exercises
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2010 When the rehashing step is implemented, you must use O(N) probes to reinsert the N elements Give an estimate for the number of probes (ie,N o r 2N or something else) (Hint: Compute the average cost of inserting in the new table These insertions vary from load factor 0 to load factor 025) 2011 Under certain assumptions, the expected cost of an insertion in a hash table with secondary clustering is given by ll(1 - A) - A - ln(1 - A) Unfortunately, this formula is not accurate for quadratic probing However assuming that it is, a what is the expected cost of an unsuccessful search b what is the expected cost of a successful search
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A quadratic probing hash table is used to store 10,000 string objects (using the string class implemented in Section 26) Assume that the load factor is 04 and that the average string length is 8 Determine a, the hash table size objects b the amount of memory used to store the 10,000 s ~ r i n g c, the amount of memory used to store the remaining (uninitialized) string objects d, the amount of additional memory used by the hash table e the total memory used by the hash table f the space overhead
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In Practice
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2013 Implement linear probing 2014 For the probing hash table implement the rehashing code without making a recursive call to insert 2015 Experiment with the following alternative for line 9 in Figure 202:
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2016 Experiment with a hash function that examines every other character in a string Is this a better choice than the one in the text Explain 2017 Modify the HashTable class so that the isEmpty operation can be supported in constant time 2018 Modify the deletion algorithm so that if the load factor goes below 118, a rehash is performed to yield a table half as large
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Programming Problems
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2019 Implement an STL-style m a p class using a hash table The class is instantiated with the types of the objects being stored, a not-equals function object, and a hash function object 2020 Find yourself a large online dictionary Choose a table size that is twice as large as the dictionary Apply the hash function described in the text to each word, and store a count of the number of times each position is hashed to You will get a distribution: Some percentage of the positions will not be hashed to, some will be hashed to once, some twice, and so on Compare this distribution with what would occur for theoretical random numbers (discussed in Section 103) 2021 Perform simulations to compare the observed performance of hashing with the theoretical results Declare a probing hash table, insert 10,000 randomly generated integers into the table, and count the average number of probes used This number is the average cost of a successful search Repeat the test several times for a good average Run it for both linear probing and quadratic probing, and do it for final load factors 01,02, , 09 Always declare the table so that no rehashing is needed Thus the test for load factor 04 would declare a table of size approximately 25,000 (adjusted to be prime) 2022 Compare the time required to perform successful searches and insertions in a separate chaining table with load factor 1 and a quadratic probing table with load factor 05 Run it for simple integers, strings, and complex records in which the search key is a string 2023 A BASIC program consists of a series of statements, each of which is numbered in ascending order Control is passed by use of a goto or gosub and a statement number Write a program that reads a legal basic program and renumbers the statements so that the first starts at number F and each statement has a number D higher than the previous statement The statement numbers in the input might be as large as a 32-bit integer, and you may assume that the renumbered statement numbers fit in a 32-bit integer Your program must run in linear time
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