Project 4: Dynamic allocation, bit vectors, etc

The goal of this project is to exercise several things we have learned in C recently, particularly dynamic allocation of memory and bit operations (especially as would be used in bit vectors). This project consists in three distinct parts; the third part is dependent on the second part, but the first is completely independent of the other two.

(In case you're curious, this project happens to be stitched together from exercizes that I usually use in labs. This semester I'm making this a project.)

Set up

After making a directory for this project, copy the code for this project from the course directory.

cp ~tvandrun/Public/cs245/proj4/* .

Part A. String operations in C

1. Introduction

This semester we have used strings in C (of course, they're actually char arrays), but we've never learned them systematically. The one important thing to know is that C strings are terminated by a special "end-of-string" character, which you can make using \0. (Note this is similar to how you make a new line character with \n and a tab character with \t.)

Note that if you have a string with, say, 10 characters, it's important that you allocate an array of at least size 11 to hold that string---the extra array position is for the end-of-line character. Why at least size 11? Because there's no problem with the array that holds the string being larger than the string that it holds (apart from wasting a little bit of memory). You may remember way back in the Chatter lab that your structs had character arrays of length 141 because the maximum message length was 140. Many messages were shorter.

C has a string library called string.h. However, in this project you will write some functions for a "homemade string" library. See hmstring.h and hmstring.c.

2. Inspecting the code

Consider the two functions that are written for you.

3. Implementing the remaining operations.

hmstrlen().

"Homemade string length." Write an imitation of the standard string function strlen() that takes a pointer to the beginning of the string and computes its length---the number of characters before the end-of-string marker.

hmstrcat().

"Homemade string concatenation." Unlike the string concatenation operation in Java, C's strlen() does not make a new string. Notice the return type here is void. Instead it modifies the area of memory pointed to by the first parameter. Specifically, it finds the end of the string that starts at that first address and then copies the contents of the string pointed to by the second paremeter at the end of the first string. Write an equivalent implementation for hmstrcat()

hmstrcat2().

Now, just for fun, write a second version of "hommade string concatenation" that works more like string concatenation in Java. Do not modify either of the strings given, but instead, allocate a new dynamic charater array, big enough to handle all the characters in both strings total, and then copy all the characters from the old strings to the new. Finally, return the pointer to this newly allocated character array.

4. Testing your code

I have provided a makefile (for the whole project) and a driver program hmstrexample.c (for this part).

make hmstrexample
./hmstrexample

Use this to verify that your functions in hmstring are working.

Part B. Bit vectors

1. Introduction

A dynamic set is a way of containing data similar to a mathematical set except that it can change, that is, be updated. The most familiar implementation is Java's HashSet. Specifically, a dynamic set is an unordered collection of uniform-typed items with the operations

(It is worth pointing out what's dynamic about a dynamic set. In the mathematical concept of set, a set cannot change. If you have a set, say A = { 1, 4, 5}, and union to it, say B = {2, 4, 6}, you produce a new set, call it C = {1, 2, 4, 5, 6}; you do no make any change to the set A, just as adding 7 to 5 makes 12--- it doesn't change "5". A dynamic set, on the other hand, is a mutable data structure.)

Some applications of dynamic sets require a few other additional operations like the operations on mathematical sets:

Our specific task is to implement sets of numbers, subsets of the set { 0, 1, ... n}. Here's the interface if we were writing in Java:

public interface NSet {

    boolean contains(int i);
    void insert(int i);
    void remove(int i);
    NSet complement();
    NSet union(NSet other);
    NSet intersection(NSet other);
    NSet difference(NSet other);

}

and an implementation using an array of booleans:

public class InefficientSet implements NSet {

    private boolean[] array;

    public InefficientSet(int size) { array = new boolean[size]; }

    public boolean contains(int i ) { return array[i]; }
    public void insert(int i) { array[i] = true; }
    public void remove(int i) { array[i] = false; }

    public NSet complement() {
        InefficientSet toReturn = new InefficientSet(array.length);
        for (int i = 0; i < array.length; i++)
            toReturn.array[i] = !array[i];
        return toReturn;
    }

    public NSet union(NSet other) {
        InefficientSet toReturn = new InefficientSet(array.length);
        for (int i = 0; i < array.length; i++)
            toReturn.array[i] = array[i] || other.contains(i);
        return toReturn;
    }

    public NSet intersection(NSet other) {
        InefficientSet toReturn = new InefficientSet(array.length);
        for (int i = 0; i < array.length; i++)
            toReturn.array[i] = array[i] && other.contains(i);
        return toReturn;
    }

    public NSet difference(NSet other) {
        InefficientSet toReturn = new InefficientSet(array.length);
        for (int i = 0; i < array.length; i++)
            toReturn.array[i] = array[i] &&  ! other.contains(i);
        return toReturn;
    }

}

We, however, are going to use bit operations to make a very fast and space-efficient implementation of a dynamic set. This works only under specific circumstances:

The main idea is simple. For each dynamic set we keep a sequence of bits numbered from 0 to n. If the ith bit is set to true or 1, that indicates that i is in the set; false or 0 indicates that it is not.

Conceptually we want an array of bits, or as it is traditionally called, a bit vector. We can't literally use a traditional array because we don't have addresses for a single bit. We could make an array of, say, chars and use only one bit from each array location, but that would use 8 times as much memory as we really need. Instead, we will employ the bit manipulation operations we learned in class to implement a bit vector, which will then be used to implement a dynamic set.

2. The given code

For this part, you are given the library files bitvector.h and bitvector.c and the driver vectest.c. The file bitvector.h contains the definition of the bit-vector type and the prototype for the functions you have to write. bitvector.c contains stubs, and vectest.c runs a driver program. To compile your code and the driver and to run the driver, do

make vectest
./vectest

Note that vectest.c has code commented out which you need to un-comment as you go along, as it tests different parts.

3. Basic operations

Open bitvector.h and look at the struct type BitVector_t. Since we don't know how many bits we'll need, we have a pointer called vector that refers to the first byte of the memory area we'll use. size keeps track of the actual number of bits (not bytes) we're using. If we need to store 10 bits, we will allocate 2 bytes; all eight bits of the first byte will be used (for bits 0-7), and the first two bits of the second will be used (for bits 8 and 9); the other bits of the second byte will simply be left unused.

The type of the vector pointer is unsigned char *. It will be easier to think of this as an array.

a. Creating a new bit vector

In bitvector.c, implement the function createBitVector(). You'll need to allocate the struct object, as well as allocating the vector (array) itself. Think about how to determine the number of bytes you'll need given the desired number of bits. Also, make sure the set is initially empty.

b. Destroying a bit vector

At the same time, implement the destroy() function. Just make sure you free everything that was allocated.

Compile bitvector.c and vectest.c and test. Right now vectest.c does not do very much, but test that everything compiles and does not crash.

c. Testing for containment

Now write contains(). This requires you to pick out the right byte offset from the vector pointer (ie, get the right unsigned char from the array), and then isolate the correct bit from from that byte. Uncomment the relevant section in vectest.c, compile, and run. The driver will print out the contents of the set.

d. Inserting

Write insert(). Now you will need to modify one of the bits (in one of the bytes). Think carefully about how to do this using bit operations. Notice the driver requires a two-byte vector, and it inserts 5 and 9--thus, one bit in the first byte and one bit in the second byte. Uncomment, compile, and test.

e. Removing

By now, removing and element shouldn't be that bad. (The function is called removeV() because one of the libraries we include already had a remove() function.)

4. Whole-set operations

One thing that sets apart the operations union, intersection, difference, and complement is that they do not modify their operand bit vectors, but rather create new ones. For each of these, you will have to allocate new bit vectors to represent the results.

a. Complement

We'll do complement first, since it needs only one operand. Make a new bit vector to return (same size as the operand), and make all its bits to be the opposite of the bits in the operand. For efficiency, don't do this one bit at a time. Do it for each byte as a whole using C's bit-wise negation operator, ~ In other words, loop through the bytes, setting each byte in the new bit vector to be the bit-wise negation of the equivalent byte in the old bit vector. Don't worry that this will also affect the unused bits in the last byte--- since they're unused, it won't do any harm to negate them as well.

Notice that you had to calculate the number of bytes again, based on the number of bits. When you do something twice, it's a sign there should be a separate function to calculate that. Write a function numBytes() that takes a number of bits and calculates the bytes required. Replace that calculation in complement() and createBitVector() with calls to that function.

Uncomment, compile, test.

b. Union

Next, implement union. This also can be done efficiently with a bitwise operator. (Why is the method called unionV()? Well, union is actually a reserved word in C. I called this function unionV() for "vector".) Uncomment, compile, test.

c. Intersection

Are you getting the hang of this? Intersection should be easy now.

d. Difference

Finally, compute set difference. Uncomment, compile, test.

Part C. The Sieve of Eratosthenes

Now let's use the bit-vector set you wrote in part B in a real application. The Sieve of Eratosthenes is a method for finding prime numbers. One makes a list of integers from 2 up to some specified largest number. We will cross off numbers as we find them not to be prime. Initially assume all numbers are prime, which is true at least for the first number in the list, 2. Then, starting with 2, repeatedly

Thus in the first iteration, we'll cross off every even number; in the second iteration, we'll cross off every multiple of 3; etc.

Complete the program sieve.c so that it uses one of your bit vectors to keep track of the numbers in the sieve. Your program should

To turn in

Please turn in all the files you modified (hmstring.c, bitvec.c, and sieve.c) to the turn-in directory for this project:

cp (some file) /cslab.all/ubuntu/cs245/turnin/(your user id)/proj4

DUE: 5:00 pm Wednesday, Mar 26, 2014.


Thomas VanDrunen
Last modified: Tue Nov 13 16:37:28 CST 2012