代写asgn5: towers AKA

asgn5: towers AKA mm..OOMs

version 1.2

Due Wednesday, February 21

Draft Due Monday, February 19.

In this assignment, we will take our first foray into abstract datatypes (ADTs), the building blocks of large systems.  We start you off with a linked list ADT that can be compiled to support lists containing different kinds of items. Modifying the list ADT to contain key/value pairs  instead of integers provides the basic functionality of an associative  array, in which we can look up integer values by a string key.  Using this linked list of key/value pairs as a building block, we implement a hash table ADT that allows us to get (or look up) an integer value given its string key, or to put  (or insert / update) the integer value associated with a key. We ultimately use this hash table to solve a common practical problem: processing a large text file an assigning unique integer identifiers to words that reappear.

Along the way, you will need to implement two performance optimizations, each of which will improve the performance of your ADTs by over a factor of 100.  These performance improvements make software that would otherwise be unusable practical, and require careful reasoning about how we traverse our data structures.

1    Introduction

In this assignment, we are going to de-mystify what is probably the most  “magical” data structure in all of computer science:  the  hash  table.  The hash table goes by a variety of other names that you may have enountered in other languages or in other classes,  including  maps,  hashmaps,  dictionaries   (or  dicts  in Python), and associative  arrays.  This last name is probably the most descriptive of how hash tables work in practice: they allow us to look up data not by its position in some ordered array, but by providing some meaningful  “key,” such as a human-readable string.  For example, in Python we might record the favorite songs of a few users in this way:

favs  =  {}

favs[’Alice’]  =  ’Rhymes  like  dimes’

favs[’Bob’]  =  ’Flava  in  ya  ear’

favs[’Carol’]  =  ’Scarlet  Begonias’

print("Bob’s  favoriate  song  is  %s"  %  favs[’Bob’])

Here, favs was a python dict (or hash table) that allowed us to look up songs by peoples’ names. Hash tables are special for two main reasons:

.  They are convenient, allowing us fetch data based on keys.

.  They are fast. With a good hash table implementation, looking up a key can be almost as efficient as looking up an item in an array using its index. Performance matters—if it didn’t, we probably would be programming in an easier language than C!

But how do hash tables achieve both of these miraculous properties? Recall that looking up items in an array via their index is fast because 1) it is fast to read memory at a particular location (this is why it is called “random-access memory“ or RAM), and it is fast to do math. If given an index into an array, all we need to do is some math and then read some memory, so we can do it very quickly.  If, on the other hand, we want to find items based not on where they are in memory but on what they are (e.g., whether a string has a particular value), our best strategy if the data is stored in an array is to scan the whole array. The bigger the array, the longer we can expect a lookup to take—not a great property when we are dealing with big data. On the surface, ifour data is stored in an array, it seems like we are faced with a tradeoff:  convenience or performance.

Recall the linked list data structure we studied in lecture. Linked lists make a number of different tradeoffs than arrays. They are (arguably) a little better suited to implementing big associative arrays, because they grow dynamically.  But looking for a particular item still requires traversing the list from one end to the other.  In Part II of this assignment, you will implement a simple associative array as a linked list of (key, value) pairs. You will see that while tuning the data structure can give huge performance improvements (> 100X!), traversing a linked list remains an unacceptably slow way to perform lookups.

1.1    Hashes and Cubbies

Wouldn’t it be great if we didn’t need to trade off between convenience and performance? What if there was a data structure that (like array indexing) allowed us to use math to figure out how to get most of the way to where a particular piece of data is or belongs, while still supporting lookups based on key?  It turns out that such a hybrid data structure does exist: the hash table.

It is useful to think of a hash table as a collection of lockers or cubbies.  Within each cubbie is a bunch of items; books, pens and pencils, sweaters and so on. Looking inside a cubbie requires traversing (i.e., picking up and looking at) all of the items until you find what you are looking for. If the cubbie is cluttered this could take awhile but if there are just a few items it should be quick!  Looking in a cubbie is a lot like traversing a list.  But what about finding your cubbie?  This is typically very fast, since the cubbies are numbered. Perhaps on the first day of school you need to hunt around a bit, but in general you can 1) go straight to a cubbie using math, and then 2) begin a traversal of a small list.  This is  way  better than removing the cubbies and placing everyone’s belongings in one giant closet—then, to find your sweater, you would need to look at all the items in the entire school.

When you think about it, libraries work in a similar way. First, you take the book that you are looking for (typically a string) and convert it into some weird number in the Dewey decimal system.  Using that number, I can very quickly find the shelf where the book belongs, if the library has a copy.  But once I am there, I still need to scan the shelf.  The shelf is like a linked list that I traverse; the whole library was like an array that I indexed into to find my shelf.

The Dewey decimal numbering system made it easy to find the shelf where my book belongs—even though those numbers are completely meaningless to me!  It did what is called hashing:  converting from a space of key (typically strings, but keys could be anything) to a (much smaller) space of numbers.  A good hash function should minimize collisions, where different items map to the same number.  After all, if the Dewey decimal system said all books belonged on the same shelf, or just three shelves, those shelves would be cluttered and hard to search.  Good hash functions are outside the scope of this class.  We will provide you with a poor hash function, which should illustrate that these techniques are very powerful no matter what.

The basic recipe for hashing (called “chained hash tables”) is:

1.  Create an array of lists (e.g., linked lists).

2.  For each item to be inserted or looked up, take the key (e.g., a string such as  “Alice”) and hash  it into a number (e.g., 12353453).

3.  Take the modulus of this (typically large) number and the number of elements in your list.  This (e.g., 15) is called the “hash bucket.”

4. Insert (or search) the list at that bucket.

That’s it!  When the number of buckets is 1, this devolves into list search; when the number of buckets is large enough there are no collisions (one book per shelf).

2    Part I: A linked list of ints

In the starter code, we share a basic linked list implementation much like the one we went over in class.  This linked list is intended to be polymorphic in the sense that the same code (which describes how to create a list, add elements, lookup elements, etc) should compile and run no matter how the item  type is defined. That is to say, a list is a list, whether it is a list of ints, or char arrays, or pointers, or structs, or whatever. To change what kind of a list it is, we need only to redefine item, and recompile.

Making the linked list polymorphic was mostly pretty easy, since the implementation passes around items without caring what is inside them.  The one exception is the list find function, which is supposed to take an item and, if the list contains a matching item, to return a pointer to that item.  But what does it mean to “match” an item? This will depend on the type of item. Two integers match if they are identical under equality (==), whereas two strings match if strcmp returns 0 when called with both.  As we will see, two key/value pairs should match if their keys are the same.

To handle this special behavior of matching while remaining type-agnostic, list find requires a pointer to  a  function  as one of its inputs.   The job of this function,  cmp, is to report whether two items match. Hence, for each way of interpreting an item we need a different implementation of cmp.  We have provided one that works when items are defined as ints.

The toy target in the Makefile will create (once you have implemented a few missing functions) a simple program that you can use to test the starter code implementation of the linked list.  Read what toy.c is doing.

2.1    Step 1:  Complete the linked list implementation

Did you read what toy.c was doing? It tests a linked list by inserting a bunch of data into it, removing an element from the middle, and making sure that traversals of the list still work.  To do this, it calls a function (list remove) that we have not provided .   list remove, like list find, traverses a list until it finds a node matching its item argument.  Then, instead of returning that node, it removes it from the list—after list remove, the list should be unchanged except that it has one element less. Implement list   remove.

‘toy‘ also allocates a bunch of heap memory and, at the end, attempts to give it up.  You will also need to implement list destroy . Implement list destroy, prototyped in ll.h . Note that list destroy takes a LL  **—that is, a pointer to  a pointer to  a linked list.  This is because it is list destroy’s job not only to free the memory pointed to by the linked list pointer, but to set that pointer to NULL.

When list destroy is called, all of the heap memory allocated by the list should be given back to the OS. You can check this yourself:

$  valgrind  ./toy

Test your code. Make sure that you are cleaning up all the heap memory.

3    Part II: A naive associative array

The linked list code that we shared with you managed linked lists of ints.  Change it to operate over key-value pairs, by redefining item as shown below.  You will need to change cmp as well, to implement matching in the following way:  two key/value pairs match if their keys  are identical  (under string  comparison) .

typedef  struct  item  item;

struct  item  {

char  key[255];

int  id;

};

bool  cmp(item  *,  item*);

3.1    Some simple benchmarking

We provide a testing function called getwords that  “kicks the tires” on your implementation by reading through a list of dictionary words (about 104K words) and inserting each word (along with an ID number) into your linked list. Build the Makefile target bench1. Run it.

$  time  ./bench1

Good heavens, that is slow.  What is going on?  Just inserting every word in the dictionary takes forever!!

On my laptop, this runs for almost a minute. Fix this. A minor but important change to the linked list implementation can improve the performance by several orders of magnitude!!  After this fix, the function runs on my laptop in about 40 milliseconds.

3.2    Creating a Hashtable API

Using a linked list to store key/value pairs is a way to implement a hash table, but it’s unwieldy.  I just want something that I can give a string to and get back an int!

Implement the Hashtable API by ”wrapping” the linked list of key/value pairs.

typedef  struct  Hashtable  Hashtable;

struct  Hashtable  {

//  your  data  structure  here

};

Hashtable  *  hash_create(void);

bool  hash_put(Hashtable  *,  char  *key,  int  val);

int  *  hash_get(Hashtable  *,  char  *key);

void  hash_destroy(Hashtable  *);

It is your job to provide an implementation of the Hashtable API, shown above.  hash   create allocates memory for an initializes a hash table.  Given a key (in this case a string that is 255 characters or less), hash get returns a pointer to the int that is the value for that key.  Given a key and an int value, hash put stores the key and value; if there is already a value associated with that key, it should be replaced with the new one. hash destroy frees all the memory associated with a hash table .

Note that we are building a tower.  Just as the linked list uses the item datatype and its helper function, your hash table can (and should) use the linked list.  It is up to you to figure out how—most of the work has already been done!

4    Part III: More performance tuning

Now, let’s use this thing for a real task:  assigning unique integer IDs to a HUGE list of strings containing duplicates. Build the Makefile target bench2. Run it.

Did you read it first? bench2 is simulating a real-world workload.  It is scanning a file full of strings again and again. For each string, it checks the hash table to see if it has already assigned this string an integer id. If it has not, it picks a new  id and assigns it to the string in the hash table. Note that unlike the workload in bench1, which stressed how quickly we could add items to the tail of a linked list, this workload is much harder, stressing probes of the items.

I bet the performance—even after your optimization to the linked list—is poor, huh?  I bet it scales poorly, too. You can experiment with its scaling behavior by providing arguments. For example:

$  ./bench2  5

Will scan the input file 5 times instead of just once. Try running it for a few small numbers. How long do you think it would take to scan the input file 100 times? What about 1000?

5    Part V: A hash table

The time has come to actually implement a hash table. You can do this!

You do not need to worry about the hash function.  We have provided you with a really crummy one, called hash. The basic idea is that you can turn a string into a number by looking at the first few bytes of that string and interpreting them as numbers.  A little later in the course when we discuss bitwise operations we can talk about how you could write a crummy hash function yourselves.  In practice, we typically borrow one rather than reinventing the wheel. Please feel free to swap this out with something better.

Reimplement the functions in hash.h to use the magic of hashing.

5.1    Does it matter?

It does. The plot below shows my reference implementation on bench2:

1.  In red, before the first optimization to the linked list,

2.  In blue, after that optimization but before implementing hashing,

3.  In yellow, hashing, with just 2 buckets,

4.  In green, 10 buckets, etc.

With 1000 buckets, my laptop can run 100 iterations in just over 10 seconds. Back of the envelope, since the file contains roughly 100K words, that is...   (100 , 000 × 100)/10 =∼ 1M records per second, I think, which is respectable.

6    The coup de grace

Congratulations: you are now not just a simple programmer, but a library writer. You have written a piece of code that, instead of being run once, can be used over and over again to support a myriad of applications. Of course, what is the fun of creating a library without using it to do something real?

For the final phase of tower building, you must build a simple application that uses your hash table implementation.  The job of your program, called  uniqq, is to read a file from stdin and output only the number of unique lines in that file (followed by a newline).

Create a file called uniqq.c and a Makefile target for uniqq. You may feel free to reuse code from xd for reading inputs from stdin.

Make sure to test your code! We recommend that you use the UNIX utilities uniq and wc for testing.

7    Taking stock AKA tl;dr

Building towers means managing a big bunch of files, and this can get confusing.  Below is a key to help you get organized:

7.1    Deliverables

For full credit on this assignment, you must:

1. Implement list remove and list destroy .   When you have done this, toy should build and run without error, and valgrind should report that there are no memory leaks.

2.  Adapt the linked list to operate over key/value pairs by changing the definition of item and replacing the implementation of cmp. When you have done this, bench1 should build and run without error, but will run very slowly!

3.  Fix this performance issue by changing the implementation of the linked list.  You should be able to achieve this in negative lines of code. After your fix, bench1 should run (without error) in one second or less.

4. Implement the Hashtable API by providing implementations of hash create , hash put , hash destroy , and hash get .  When you have done this, bench2 should build and run without error, but will run very slowly!

5.  Fix this performance issue by implementing the magic that is hashing.   You  may be  surprised to improve the performance of your system by a few more orders of magnitude. Your program should go from running about one minute per scan of the file to fractions of a second.  Confirm that bench2 runs fast as hell, free from errors, and without memory leaks.

6.  Finally, use your library to implement a unique word counting application, uniqq.  Test your imple- mentation.

7.2    In your design doc...

Make sure to discuss:

1. In Part I, you implemented garbage collection—routines that clean up dynamically-allocated memory. How did you make sure the memory was all cleaned up? How did you check?

2. In Part II, you made a major optimization to the linked list optimization.  What was it, and why do you think it changed the performance of bench1 so much?

3. In Part III, you implemented hash tables.  What happens to the performance of bench2 as you vary the number of buckets in your hash table? How many buckets did you ultimately choose to use?

4.  How did you make sure that your code was free from bugs? What did you test, and how did you test it? In particular, how did you create inputs and check the output of uniqq?

8    In Conclusion

By building a tower—an application, atop a hash table, atop a linked list, atop a key/value pair datatype— you were able to efficiently implement a complex task via a sophisticated data structure and algorithm. You may find yourself wondering (as many have before you why a powerful language like C does not have hash tables built-in, as (for example) arrays are.  We hope this assignment has shown that, if you ever need a hash table, it should be quite straightforward to whip one up, in just a few dozen lines of code.  A few dozen lines of code for a few orders of magnitude speedup is a great trade!