COP 3330 - Programming Assignment #6
Due: Friday, July 24 (11:59PM)
Objective
To gain experience with bitwise operations, used inside a class. Also
will provide further practice with dynamic allocation.
Task
You will implement a class called BitArray, which will
simulate a list of bits of any size, which can be individually set,
cleared, flipped, and queried. You will also implement a function that is
to be used by a sample test program, which uses the Sieve of Eratosthenes
technique (with the bit array) to find prime numbers.
Details
Download these starter files:
- bitarray.h -- declaration
of the BitArray class, listing out its primary interface (public
functions)
- main7.cpp -- a sample
program for finding prime numbers
The BitArray class
Implement the BitArray class, defining all specified public
member functions, in the file bitarray.cpp. Here are some
details about the BitArray class:
- A bit array is to be implemented with an underlying array of type
unsigned char. 'Unsigned' because we are only interested in
bits, not in negatives, and type char because it is the
smallest integer type. The concept of a BitArray object is that
it will store an array of bits (in the smallest storage space needed),
indexed starting at 0, just like with normal arrays.
- The array of characters should be created dynamically. The primary
constructor has one parameter, which indicates how many bits
are needed. The constructor should allocate the minimum number of
cells needed for this many bits.
Also, have the
constructor initialize all bits to 0. Example:
BitArray xy(35); // builds storage for at least 35 bits
// if we assume 1 byte char, this takes 5
// characters, for a total of 40 bits
- The Length() function should return the total number of bits
in the allocated array. In the example above (assuming 1 byte char),
this is 40
- While type char is commonly 8 bits on most machines
today, you may not assume that this is always the case. Structure
your class so that it is versatile enough to handle different platforms
(where type char might differ in size). But always use the
minimum number of char elements when creating the array. Hint:
sizeof() is a function call that returns the exact number of
bytes taken by a variable or type on a given machine:
int size = sizeof(int); // tells how many bytes for an int
// on current machine
Suggestion: Use a constant to store the size of an unsigned char in the
program, for modifiable computations later. If using only inside the
class, a static const is best.
- Because dynamic allocation is used, the BitArray class should
implement an appropriate destructor, copy constructor, and assignment
operator (for deep copy and appropriate cleanup)
- The functions Set(), Unset(), Flip(), and Query() represent
the different things that can be done with one bit. Each function takes
in an index number -- the index of the bit in question.
- Set() should set that bit to 1, without affecting any
others
- Unset() should set that bit to 0, without affecting any
others
- Flip() should change that bit to its opposite, without
affecting any others
- Query() should return true if that bit is
currently 1, and it should return false if that bit is
currently 0
- The operator overloads:
- operator<< -- the insertion operator should be written
to do output of a BitArray object. Format is the entire array,
printed as one continuous sequence of bits, inside parintheses. See
example outputs from test program
- operator== and operator!= -- usual inequality
operators. Entire arrays must match for them to be equal
- General:
- You may add private functions to the class if you like, and you may
add private constants. You may not change the public interface or the
underlying storage (dynamic array of unsigned char).
- Note that NOT ALL features of the BitArray class are tested in the
provided main7.cpp sample program. It is up to you to test all
BitArray features.
Sieve of Eratosthenes
A common algorithm to find prime numbers is the
Sieve of
Eratosthenes.
The main7.cpp program provided already sets up a BitArray object
of desired size. Then it calls upon a function named
Sieve.
Write the Sieve() function in a file
called sieve.h. Do not change main7.cpp in any way. The
Sieve() function should follow the Sieve of Eratosthenes
pattern. The general algorithm is as follows:
- Start by initializing all bits in the array to 1.
- Each index of the bit array will represent one non-negative
integer. Your algorithm should mark all non-prime numbers by
setting these bits back to 0, proceeding as follows:
- 0 and 1 are never prime. Unset these bits to 0
- The next "uncleared" bit is prime. Leave this bit as a 1, but change
all multiples of this value (not counting itself) to 0
- Move to the next "uncleared" bit and repeat
- This process only needs to repeat up to the square root of the
array's length. (Example: If we are checking for the prime numbers
from 0 through 500, then we can stop when we've reached sqrt(500),
which is 22.36. Once we've reached an "uncleared" bit that is 23 or
more, we know we've cleared all the non-primes
- The remaining bits (which are still 1) indicate the primes.
You can find the sqrt() (square root) function in the library
<cmath>.
Sample Runs
These are sample runs of the main7.cpp program, the Sieve program to find
primes. Remember to write your own driver(s) to test other functions in
class BitArray (such as comparison operators, copy constructor,
etc).
Note that in the sample runs, the bit array really is printing on one
line -- but it will probably show on screen wrapped around to multiple
lines
Sample run 1
Enter a positive integer for the maximum value: 345
The bit array looks like this:
(0011010100010100010100010000010100000100010100010000010000010100000100010100000
10001000001000000010001010001010001000000000000010001000001010000000001010000010
00001000100000100000101000000000101000101000000000001000000000001000101000100000
10100000000010000010000010000010100000100010100000000010000000000000100010100010
000000000000100000100000000010100)
Primes less than 345:
2 3 5 7 11 13 17 19
23 29 31 37 41 43 47 53
59 61 67 71 73 79 83 89
97 101 103 107 109 113 127 131
137 139 149 151 157 163 167 173
179 181 191 193 197 199 211 223
227 229 233 239 241 251 257 263
269 271 277 281 283 293 307 311
313 317 331 337
Goodbye!
Sample run 2
Enter a positive integer for the maximum value: 800
The bit array looks like this:
(0011010100010100010100010000010100000100010100010000010000010100000100010100000
10001000001000000010001010001010001000000000000010001000001010000000001010000010
00001000100000100000101000000000101000101000000000001000000000001000101000100000
10100000000010000010000010000010100000100010100000000010000000000000100010100010
00000000000010000010000000001010001000001000000010000010000010001000001000000010
00100000001000000000101000000000101000001000100000100000001000101000100000000000
10000000100010000000100010000010000000000010100000000000000000100000100000000010
00001000001010000010000000001000001000001010000010000010001010000000000010000000
00101000100000100000101000000000001000100000100000001000000000100000001000000000
10000000100000100000100010000000100000100010000000100010000000000000100000000010
0)
Primes less than 800:
2 3 5 7 11 13 17 19
23 29 31 37 41 43 47 53
59 61 67 71 73 79 83 89
97 101 103 107 109 113 127 131
137 139 149 151 157 163 167 173
179 181 191 193 197 199 211 223
227 229 233 239 241 251 257 263
269 271 277 281 283 293 307 311
313 317 331 337 347 349 353 359
367 373 379 383 389 397 401 409
419 421 431 433 439 443 449 457
461 463 467 479 487 491 499 503
509 521 523 541 547 557 563 569
571 577 587 593 599 601 607 613
617 619 631 641 643 647 653 659
661 673 677 683 691 701 709 719
727 733 739 743 751 757 761 769
773 787 797
Goodbye!
Submitting
Submit the files via blackboard:
bitarray.h
bitarray.cpp
sieve.h