Segmented Sieve of Erastothenes C++ SPOJ [duplicate]

问题

I'm aware this has been asked before, but I cannot fully understand how to implement Segmented Sieve of Eratosthenes.

Problem

The input begins with the number t of test cases in a single line (t<=10). In each of the next t lines there are two numbers m and n (1 <= m <= n <= 1000000000, n-m<=100000) separated by a space. For every test case print all prime numbers p such that m <= p <= n, one number per line, test cases separated by an empty line.

My approach

I could implement Sieve of Eratosthenes and I can find prime numbers up to square root of n. But I'm not able to understand how to implement the "offset" that is being discussed on other sites. How to perform a Sieve on a selected partition?

#include <stdio.h>
#include <iostream>
#include <math.h>
using namespace std;

int main()
{
    int t;
    cin>>t;

    while(t--)
    {
        long long m,n;
        long long p[100001];
        bool primes[100000];

        cin>>m;
        cin>>n;
        long long square=sqrt(n);
        cout<<square;
        int j=0;
        int i;
        primes[0]=false;    
        primes[1]=false;

        for(i=2; i<n;i++)
            primes[i]=true;

        for(i=2; i<=square; i++)
        {
            if(primes[i]==true)
            {
                for(j=i+i; j<=n; j+=i)
                    primes[j]=false;
            }
        }

        for(i=m; i<n ; i++)
        {
            if(primes[i]==true)
            {
                cout<<i<<" \t";
                if(i >= m)
                {
                    p[j]=i;
                    j++;
                }
            }
        }

        for(i=0 ; i<j ; i++)
        {
            cout<<p[i]<<"\n";
        }
    }

    return 0;
}

回答1:

Consider a segment S : [a,b] and a prime p.

Note that the following code will eliminate all composites "corresponding" to prime p.

for(int i=ceil(a/p);i<=floor(b/p);++i) {
    new_primes[i*p-a]=false;

Extend this idea for all primes <= sqrt(b).

回答2:

First of all since you mentioned you are coding for SPOJ, I'll tell you that this is not going t work. Even if you somehow got a method to do SOE just from m to n, you would be performing such seives t times, which is going to give you TLE.

What is excpected is a simple precompute of SOE through the entire range, i.e. from 1 to 10^x. First outside your while loop perform SOE and store all primes into a vector. Then in your while loop simply display the required primes from the vector.

来源：https://stackoverflow.com/questions/23954313/segmented-sieve-of-erastothenes-c-spoj

标签

c++

primes

sieve-of-eratosthenes