素数筛选高效算法

用普通的筛法，1000 0000 的数，需要用时1600ms左右。

#include <stdio.h>
#include <string.h>
#include <math.h>
 
char dp[10000010];
 
const int inf = 10000001;
int t = sqrt(inf);
 
inline void  prime (   )
{
  int i, j, k = 0,p;
  dp[1] = -1;
  for (i = 2; i <= t; i++)
    if( dp[i] != -1)
    {
    //p = inf / i;
    for (j = 2; j <= inf / i  ; j ++)
        dp[i * j] = -1;
    }
}
         
int main( )
{
  int N, k, i;
  prime (  );
  while(scanf("%d", &N) != EOF)
  {
     
      
    for  (i =2; i < N; i++)
      if (dp[i]!= -1)
      printf("%d\n",i);
   }
   return 0;
  }
   

而用如下筛法,则只需440ms左右。强大啊，也只需要开500 0000的数组。偶数不用筛了，筛过的也不用筛了。(thanks  tao  -_-) .

#include <stdio.h>
#include <string.h>
#include <math.h>

int dp[5000010] = {0};

int main( )
{
    int N,i, j, k, n;
    while (scanf("%d", &N) != EOF ) {
    n = sqrt( N +1);
    for ( i = 3;i <= n; i += 2) {
        if (dp[i >> 1])
                 continue;
        int x = i << 1;
        for( j = i * i; j <= N; j += x)
            dp[j >> 1] = 1;
    }
             printf("2\n");    
             int t = (N +1) / 2;
        for ( i = 1; i < t ; i++)  {
            if(dp[i]) 
               continue;
             printf("%d\n",(i << 1 )+ 1);
        }
}
   return 0;    

}