PIC 10A

(Sec. 3a-3d)

C++ Programming and Problem Solving

Instructor: Ivo Dinov, Asst. Prof.Neurology, Mathematics, Statistics

 http://www.math.ucla.edu/~dinov/10a.3.01s/

Due Date:

Monday, 8:00 PM, June 04, 2001

Please, submit your homework electronically using the "submit" system. Please try to follow the "good programming" conventions we discussed in class. Write modular code and include all of your functions in the same CPP file as your main.

• (HW_8_1.cpp/exe) (The Sieve of Eratosthenes Algorithm) A prime integer is any integer that is evenly divisible only by itself and 1. The Sieve of Eratosthenes is a method of finding prime numbers. It operates as follows:
1. Create an array with all elements initialized to 1 (true). Array elements with prime subscripts will remain 1. All other array elements will eventually be set to zero;
2. Starting with array subscript 2 (subscript 1 must be prime), every time an array element is found whose value is 1, loop through the remainder of the array and set to zero every element whose subscript is a multiple of the subscript for the element with value 1. For example, for array subscript 2, all elements beyond 2 in the array that are multiples of 2 will be set to zero (subscripts 4, 6, 8, 10, etc.); for array subscript 3, all elements beyond 3 in the array that are multiples of 3 will be set to zero (subscripts 6, 9, 12, 15, etc.); and so on.

When this process is complete, the array elements that are still set to one indicate that the subscript is a prime number. Finally, all subscripts for which the array elements remain equal to 1 should be printed. Write a program that uses an array of 1000 elements to determine and print the prime numbers between 1 and 999. Ignore element 0 of the array. [You should remember that prime numbers are the core of all robust public encryption systems, information encoding/decoding, just like in the example we discussed in class. The problem is that large primes, say of 50 digits, are extremely difficult to find.]

More about Prime Numbers could be found here!

Sample Run: (no user input is allowed/expected)
%> Prime number machine!
%> These are all prime numbers in the range [1 ; 1000]
%> 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
%> 739 743 751 757 761 769 773 787 797 809
%> 811 821 823 827 829 839 853 857 859 863
%> 877 881 883 887 907 911 919 929 937 941
%> 947 953 967 971 977 983 991 997
%> Goodbye!

\Ivo D. Dinov, Ph.D., Department of Neurology and Program in Computing, UCLA School of Medicine/