C++ sieve of Eratosthenes with array [closed] - c++

Question

Closed. This question does not meet Stack Overflow guidelines. It is not currently accepting answers.
Questions asking for code must demonstrate a minimal understanding of the problem being solved. Include attempted solutions, why they didn't work, and the expected results. See also: Stack Overflow question checklist
Closed 9 years ago.
Improve this question
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.

Answer 1

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.

Answer 2

From Algorithms and Data Structures
#include<iostream>
#include<cmath>
#include<cstring>
using namespace std;
void runEratosthenesSieve(int upperBound) {
int upperBoundSquareRoot = (int)sqrt((double)upperBound);
bool *isComposite = new bool[upperBound + 1];
memset(isComposite, 0, sizeof(bool) * (upperBound + 1));
for (int m = 2; m <= upperBoundSquareRoot; m++) {
if (!isComposite[m]) {
cout << m << " ";
for (int k = m * m; k <= upperBound; k += m)
isComposite[k] = true;
}
}
for (int m = upperBoundSquareRoot; m <= upperBound; m++)
if (!isComposite[m])
cout << m << " ";
delete [] isComposite;
}
int main()
{
runEratosthenesSieve(1000);
}
You don't want to use STL, but that's not a good idea
STL makes life much simpler.
Still consider this implementation using std::map
int max = 100;
S sieve;
for(int it=2;it < max;++it)
sieve.insert(it);
for(S::iterator it = sieve.begin();it != sieve.end();++it)
{
int prime = *it;
S::iterator x = it;
++x;
while(x != sieve.end())
if (((*x) % prime) == 0)
sieve.erase(x++);
else
++x;
}
for(S::iterator it = sieve.begin();it != sieve.end();++it)
std::cout<<*it<<std::endl;