Sieve of Eratosthenes used to determine prime numbers. A bool array in taken and initialized to false
first of all it starts with 2 and updates index of bool array of all multiples of 2 to be true..
like 4,6,8..but not 2 which is kept false. next false number is picked which is 3..and all its multiples are updated true like 6,9,12,15...updated true but 3 is kept false
similarly it is followed..
all numbers in the end which are false are primes.
then next false number is picked
int main() { static bool b[100000];
for(int i=2;i<=30000;i+=1)
{
if(!b[i])
{for(int j=2;j*i<30000;j++)
{
b[i*j]=true;}
}
} for(int i=2;i<30000;i++)
{
if(!b[i])
{
printf("%d",i);}
}
return 0;
}
We can reduce the number of iterations.
We only need to iterate i from 2 to sqrt(N), where N is the upper bound.
And j can start from i.
Check this code.
This is because any composite number has a divisor that does not exceed its square root.
(proof: Let n be a composite. There exists a, b (1 < a <= b < n) s.t. a*b=n. Then a must be less than or equal to sqrt(n))
Actually it's not the asymptotic optimization.
What is asymptotic optimization?
Sieve of Eratosthenes works in
your optimization don't make it better.
I just said we can reduce the number of iterations. I didn't say I optimized it nor my code has better time complexity.
Your code is not really most optimized. See my code: http://pastebin.com/fi2f9HCN
Could you tell me which part is different?
I used j+=i instead of j++ in
for (int j=i*i; j<N; j+=i)And because global array is initialized by zero, I named my array NonPrime instead of IsPrime to avoidfor (int i = 1; i <= N; i++) is_prime[i]=1;.P/S: I got TLE in one problem use this sieve. By a trade-off between readablity and performance. My following code run faster 3x.
First loop means we remove numbers 6k, 6k+2, 6k+3, 6k+4. Second loop means we try to iterate 5, 7, 11, 13, 17, 19, ... (6k-1 and 6k+1)
I got it. Thanks!
If you just want to generate prime number in [1,n], you can try this simple algorithm. It's running time is O(n).
your suggestions are welcomed. Guys i am just beginner programmer.This is my very first post.It may not be best solution but i posted it for beginner programmers(easy to understand) and my future reference.
Thanks for your suggestions in the matter.
:D :D