Assignment 1

Andy WangCOP 4530: Data Structures,

Algorithms, and Generic Programming

Scope of Assignment 1 Class implementation BitVector implementation BitVector application Multi-file compilation Library compilation

Deliverables sieve.h, sieve.cpp, bitvector.cpp, main.cpp

Makefile Hardcopy of development log

Daily journal Features implemented, bugs fixed, help

obtained from other people Due in class on Sept 15

Sieve Algorithm Find all prime numbers <= n Observation

If n is not prime It is divisible by a prime number <=

sqrt(n)

Sieve Algorithm Example: Sieve 9

1. Create a bit vector b of 10 elements0 0 0 0 0 0 0 0 0 0

2. Set all bits of b 1 1 1 1 1 1 1 1 1 1

3. Unset b[0] and b[1], since the smaller prime number is 2 0 0 1 1 1 1 1 1 1 1

Sieve Algorithm

4. for (k = 2; k <= sqrt(10); ++k)

0 1 2 3 4 5 6 7 8 90 0 1 1 1 1 1 1 1 1

k

Sieve Algorithm

4. for (k = 2; k <= sqrt(10); ++k)for (j = 2*k; j <= 10; j +=

k)

0 1 2 3 4 5 6 7 8 90 0 1 1 1 1 1 1 1 1

k j

Sieve Algorithm

4. for (k = 2; k <= sqrt(10); ++k)for (j = 2*k; j <= 10; j +=

k)

Unset b[j];

0 1 2 3 4 5 6 7 8 90 0 1 1 0 1 1 1 1 1

k j

Sieve Algorithm

4. for (k = 2; k <= sqrt(10); ++k)for (j = 2*k; j <= 10; j +=

k)

Unset b[j];

0 1 2 3 4 5 6 7 8 90 0 1 1 0 1 1 1 1 1

k j

Sieve Algorithm

4. for (k = 2; k <= sqrt(10); ++k)for (j = 2*k; j <= 10; j +=

k)

Unset b[j];

0 1 2 3 4 5 6 7 8 90 0 1 1 0 1 0 1 1 1

k j

Sieve Algorithm

4. for (k = 2; k <= sqrt(10); ++k)for (j = 2*k; j <= 10; j +=

k)

Unset b[j];

0 1 2 3 4 5 6 7 8 90 0 1 1 0 1 0 1 1 1

k j

Sieve Algorithm

4. for (k = 2; k <= sqrt(10); ++k)for (j = 2*k; j <= 10; j +=

k)

Unset b[j];

0 1 2 3 4 5 6 7 8 90 0 1 1 0 1 0 1 0 1

k j

Sieve Algorithm

4. for (k = 2; k <= sqrt(10); ++k)for (j = 2*k; j <= 10; j +=

k)

Unset b[j];

0 1 2 3 4 5 6 7 8 90 0 1 1 0 1 0 1 0 1

k

Sieve Algorithm

4. for (k = 2; k <= sqrt(10); ++k)for (j = 2*k; j <= 10; j +=

k)

Unset b[j];

0 1 2 3 4 5 6 7 8 90 0 1 1 0 1 0 1 0 1

k

Sieve Algorithm

4. for (k = 2; k <= sqrt(10); ++k)for (j = 2*k; j <= 10; j +=

k)

Unset b[j];

0 1 2 3 4 5 6 7 8 90 0 1 1 0 1 0 1 0 1

k j

Sieve Algorithm

4. for (k = 2; k <= sqrt(10); ++k)for (j = 2*k; j <= 10; j +=

k)

Unset b[j];

0 1 2 3 4 5 6 7 8 9 0 0 1 1 0 1 0 1 0 1

k j

Sieve Algorithm

4. for (k = 2; k <= sqrt(10); ++k)for (j = 2*k; j <= 10; j +=

k)

Unset b[j];

0 1 2 3 4 5 6 7 8 90 0 1 1 0 1 0 1 0 1

k j

Sieve Algorithm

4. for (k = 2; k <= sqrt(10); ++k)for (j = 2*k; j <= 10; j +=

k)

Unset b[j];

0 1 2 3 4 5 6 7 8 90 0 1 1 0 1 0 1 0 0

k j

Sieve Algorithm

4. for (k = 2; k <= sqrt(10); ++k)for (j = 2*k; j <= 10; j +=

k)

Unset b[j];

0 1 2 3 4 5 6 7 8 90 0 1 1 0 1 0 1 0 0

k

Sieve Algorithm

4. for (k = 2; k <= sqrt(10); ++k)for (j = 2*k; j <= 10; j +=

k)

Unset b[j];

0 1 2 3 4 5 6 7 8 90 0 1 1 0 1 0 1 0 0