FIT1008 Introduction to Computer Science (FIT2085: for Engineers) Interview Prac 3 – Weeks 11 and 12
Semester 1, 2019
Objectives of this practical session
To be able to implement and use hash tables in Python.
Important requirements
For this prac, you are required to:
• Create a new file/module for each task named task[num].
• Provide documentation for each basic piece of functionality in your code (see below)
• The documentation needs to include:
– pre and post conditions
– Big O best and worst time complexity – information on any parameters used
• Provide testing for those functions/methods explicitly specified in the questions. The testing needs to include:
– a function to test it
– at least two test cases per test function. These cases need to show that your
functions/methods can handle both valid and invalid inputs (if it takes inputs).
– assertions for testing the cases, rather than just printing out messages
• VERY IMPORTANT: As before the code cannot use any of the Python functionality that would make the job trivial (like dictionaries, slicing, etc). You need to implement the functions yourself by going through the array, as we did in the lectures.
Important: Checkpoint for Week 11
To reach the check point you must complete Tasks 1, 2 and 3 by the end of your lab in Week 11, and submit all python files corresponding to these tasks. Remember: reaching the checkpoint is a hurdle.
Task 1 6 marks
Define a class HashTable implementing a hash table, using Linear Probing to resolve collisions. As in Prac 2, you should use a list to represent the underlying array. Include implementations for the following methods:
•
• •
• •
__init__(self, table_capacity, hash_base): Creates a new hash table, with initial table ca- pacity table_capacity, and with using base hash_base for the hash function (see hash below). If table_capacity or hash_base are not specified, the hash table should use appropriate default values.
getitem (self, key): Returns the value corresponding to key in the hash table. Raises a KeyError if key does not exist in the hash table. Remember that this can be called from Python code as table[key]
setitem (self, key, value): Sets the value corresponding to key in the hash table to be value. If the hash table is full and the key does not exist in the table yet, it first calls the rehash method (see below) and then reinserts the key and value. Called as table[key] = value
contains (self, key): Returns True if key is in the table and False otherwise.
hash(self, key): Calculates the hash value for the given key, using the universal hash function specified in lecture 27 (page 35) with the base hash_base given on table creation.
• rehash(self): It first creates a new array using as size the smallest prime number in the Primes list below that is larger than twice the current size. It then updates the size of the hash table and reinserts all key-value pairs in the old array into the new array using the new size. Raises a ValueError if there is no such prime in the list. For now, this method is only called when the table is full and we want to insert an element.
Primes = [ 3, 7, 11, 17, 23, 29, 37, 47, 59, 71, 89, 107, 131, 163, 197, 239, 293, 353, 431, 521, 631, 761, 919, 1103, 1327, 1597, 1931, 2333, 2801, 3371, 4049, 4861, 5839, 7013, 8419, 10103, 12143, 14591, 17519, 21023, 25229, 30293, 36353, 43627, 52361, 62851, 75431, 90523, 108631, 130363, 156437, 187751, 225307, 270371, 324449, 389357, 467237, 560689, 672827, 807403, 968897, 1162687, 1395263, 1674319, 2009191, 2411033, 2893249, 3471899, 4166287, 4999559, 5999471, 7199369]
We have provided a file TestHashTable.py which defines tests for some of the HashTable methods. But be warned: these tests are not comprehensive, and it is in your interest to think about what kinds of inputs we have not covered.
Important: you must define your own tests for the __setitem__ and rehash methods.
Task 2 5 marks
• Write a function load_dictionary(hash_table, filename) which reads a file filename containing one word per line, and adds each word to hash_table with integer 1 as the associated data. Important: you must define tests for the load_dictionary method. You should use one or more small dictionary files to do so.
• Download from Moodle the dictionary files english small.txt, english large.txt and french.txt. For each of these dictionaries, use a methodology similar to that studied in the Workshop of week 5 to time how long it takes for load_dictionary to run. Do this for each combination of the values specified below for TABLESIZE and b in the universal hash function (giving a total of 3*3=9 com- binations per file – nested for loops would be a good way to implement this – you can use ”in” for this).
b TABLESIZE
1 250727 27183 402221
250726 1000081
Present the times recorded in a table. Write a short analysis regarding what values work best
and which work poorly. Explain why these might be the case. Be sure to include your table and explanation in task_2.py (as a multi-line string).
Note: You can use Ctrl+c to stop execution of your program if some combination of values takes too long. If a single combination of values takes more than 3 minutes to complete, you may report it as TIMEOUT (but think about the reasons why!).
Task 3 4 marks
When discussing open addressing, we introduced several concepts:
• A collision occurs when we attempt to insert a key, but the location for that key is already occupied by a different key.
• A probe chain is the sequence of positions we inspect before finding an empty space.
Consider inserting keys s1, s2 and s3 (which all hash to location 10) into an empty table with linear probing:
• When we insert s1, location 10 is empty, so there is no conflict.
• If we then insert s2, location 10 is full, but 11 is empty. This is a conflict, with probe chain length 1. • When we insert s3, 10 and 11 are full, but 12 is free. This is one conflict, with probe chain length 2.
Extend your HashTable class with a method statistics(self) which returns a tuple (collision count, probe total, probe max, rehash count), consisting of: (a) the total number of collisions, (b) the total length of the probe chains, (c) the length of the longest probe chain, and (d) the number of times rehash
has been called.
Important: you must define appropriate tests for your statistics method.
Once the hash table has been modified, repeat Task 2 printing not only the run times but also the four counters above, and comment on the relationship between these counters and the runtime. Also, comment on the length of the longest probe chain and the promise of O(1) time complexity. rehash_count should be 0 in all runs – explain why. Again, remember to include your table and explanations in your submission.
Task 4 3 marks
CHECKPOINT
(You should reach this point during week 11)
Modify your hash table from the previous task to use Quadratic Probing to resolve collisions. Compare the running time, and the value of the four counters obtained when loading each dictionary with Quadratic Probing against those found when using Linear Probing.
Task 5 4 marks
Implement a hash table that uses Separate Chaining to resolve collisions, where the linked data structure used is a Binary Search Tree (we will see this data type in Week 11, and you will be provided with an implementation of the Binary Search Tree, so do not worry about this just yet).
Note that the content of the array cells should initially be None (if you want to store the number of elements per chain – up to you – then you should use instead something like a tuple that starts as (None,0), where 0 is the initial number of elements). Once you need to add a (key,data) pair in that cell, you should create an empty binary search tree (say my_tree = BinarySearchTree()), then insert the (key,data) into my_tree, and then put my_tree in the cell (or in the tuple as (my_tree,1).
Once this is done, compare again the runtime and value of the counters obtained for Separate Chaining against those obtained for Quadratic and for Linear Probing.
Background
In most large collections of written language, the frequency of a given word in that collection is inversely proportional to its rank in the words. That is to say: the second most common word appears about half as often as the most common word, the third most common word appears about a third as often as the most common word and so on1.
If we count the number of occurrences of each word in such a collection, we can use just the number of occurrences to determine the approximate rank of each word. Taking the number of occurrences of the most common word to be max and the relationship described earlier, we can give a rarity score to each word:
• Any word that appears at least max/100 times is considered to be common (score 0).
• Any word that appears less than max/1000 times is considered to be rare (score 2).
• Any word in between (less than max/100 and greater or equal to max/1000) is considered to be
uncommon (score 1).
• Any word which has never been observed is a misspelling (score 3).
In the following we will use a hash table to facilitate a frequency analysis on a given text file.
Task 6 4 marks
Create a new class Freq that uses the Linear Probing hash table to perform a frequency analysis of a set of files as follows. First, implement the method add_file(self,filename), which reads each word from the file into the hash table, in such a way that the data associated to the word is its “occurrence count”, i.e., the number of times the word has been “added” to the hash table (which is the same as the number
1This is known as Zipf’s law. You can read more at https://en.wikipedia.org/wiki/Zipf%27s_law
of times it has already appeared in the file). The class (and its methods) must keep track of the number of occurrences max for the most common word read.
Then, implement a method rarity(self, word) that given a word, returns its rarity score.
Download some ebooks as text files from https://www.gutenberg.org/ and use Freq to read these files into your hash table. At the end of this process the table will store the number of times each word appears in the texts. We will consider the resulting hash table as a reasonably accurate representation of the frequency of words in the English language. Make sure you use the data you collected in the previous tasks to select an appropriate table size for the selected text files. Also, modify __setitem__ to call rehash when the load of the hash table is above 0.5, rather than when full (this will not be used if you choose an appropriate table size, but is more realistic for cases where you do not know the number or size of the books being read).
Important: You must define tests for the add_file and rarity methods. Task 7 2 marks
Download another ebook from https://www.gutenberg.org/ and using the frequencies of the files read by Freq in Task 6, print the percentage of common, uncommon, rare and misspelled words for the given ebook.
Task 8 2 marks
Add a delete method to your Linear Probing hash table. This function is to take key as input and then delete the entry corresponding to that key, reinserting all elements from the position where the key appears, until the first empty position. Raise a KeyError if key is not in the hash table. And please reuse (do not copy and paste) as much functionality of the rehash method as possible
Important: You must define appropriate tests for the delete method.
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