I'd like to code the famous Sieve of Eratosthenes in C++ using just array as it would be a set where I can delete some elements on the way to find out primes numbers. I don't want to use STL (vector, set)... Just array! How can I realize it?
I try to explain why I don't want to use STL set operator: I'm learning C++ from the very beginning and I think STL is of course useful for programmers but built on standard library, so I'd like to use former operators and commands. I know that everything could be easier with STL.
The key to the sieve of Eratosthenes's efficiency is that it does not, repeat not, delete ⁄ remove ⁄ throw away ⁄ etc. the composites as it enumerates them, but instead just marks them as such.
Keeping all the numbers preserves our ability to use a number's value as its address in this array and thus directly address it: array[n]. This is what makes the sieve's enumeration and marking off of each prime's multiples efficient, when implemented on modern random-access memory computers (just as with the integer sorting algorithms).
To make that array simulate a set, we give each entry two possible values, flags: on and off, prime or composite, 1 or 0. Yes, we actually only need one bit, not byte, to represent each number in the sieve array, provided we do not remove any of them while working on it.
And btw, vector<bool> is automatically packed, representing bools by bits. Very convenient.