标签：blog http os 数据 io for 代码 div
埃拉托色尼选筛法(the Sieve of Eratosthenes)简称埃氏筛法，是古希腊数学家埃拉托色尼(Eratosthenes 274B.C.～194B.C.)提出的一种筛选法。 是针对自然数列中的自然数而实施的，用于求一定范围内的质数，它的容斥原理之完备性条件是p=H~。
#include <stdio.h>
#include <stdlib.h>
#define SIZE 10000
#define TRUE 1
#define FALSE 0
int
main()
{
char sieve[ SIZE ]; /* the sieve */
char *sp; /* pointer to access the sieve */
int number; /* number we’re computing */
/*
** Set the entire sieve to TRUE.
*/
for( sp = sieve; sp < &sieve[ SIZE ]; )
*sp++ = TRUE;
/*
Solution 6.4 continued . . .
Pointers on C—Instructor′s Guide 33
** Process each number from 3 to as many as the sieve holds. (Note: the
** loop is terminated from inside.)
*/
for( number = 3; ; number += 2 ){
/*
** Set the pointer to the proper element in the sieve, and stop
** the loop if we’ve gone too far.
*/
sp = &sieve[0]+(number-3) / 2;
if( sp >= &sieve[ SIZE ] )
break;
/*
** Now advance the pointer by multiples of the number and set
** each subsequent entry FALSE.
*/
while( sp += number, sp < &sieve[ SIZE ] )
*sp = FALSE;
}
/*
** Go through the entire sieve now and print the numbers corresponding
** to the locations that remain TRUE.
*/
number=2;
printf( "%8d", number );
for( number = 3, sp = &sieve[ 0 ];
sp < &sieve[ SIZE ];
number += 2, sp++ ){
if( *sp )
printf( "%8d", number );
}
return EXIT_SUCCESS;
}
由于除了2之外，所有偶数都不是质数，所以令数组中的元素只对应奇数，可使程序的空间效率提高一倍。
n（数组下标） 0 1 2 3 4 5 6 7 8 9 10
s（奇数） 3 5 7 9 11 13 15 17 19 21 23
显然s=2*n+3 由于n增加1时，s增加2.
所以对s进行筛选时
读取3，然后将2*3=6的倍数删去（因为是对奇数进行筛选）——》对n将3k+0的数删去
所以对下标n进行筛选时，可删去3k，1+5k，2+7k。。。。。
for( number = 3; ; number += 2 ){
/*
** Set the pointer to the proper element in the sieve, and stop
** the loop if we’ve gone too far.
*/
sp = &sieve[0]+(number-3) / 2;
if( sp >= &sieve[ SIZE ] )
break;
/*
** Now advance the pointer by multiples of the number and set
** each subsequent entry FALSE.
*/
while( sp += number, sp < &sieve[ SIZE ] )
*sp = FALSE;
}
Eratosrhenes筛选法,布布扣,bubuko.com
标签：blog http os 数据 io for 代码 div
原文地址：http://www.cnblogs.com/eesnake/p/3874157.html
