poj 3006 Dirichlet's Theorem on Arithmetic Progressions

最新推荐文章于 2020-04-19 11:15:59 发布

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最新推荐文章于 2020-04-19 11:15:59 发布

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本文介绍了解决POJ3006问题的方法，该问题是关于求解算术级数中第n个质数的问题。文章详细阐述了如何通过编程实现Dirichlet定理，并给出了具体的代码示例。

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poj 3006 Dirichlet's Theorem onArithmetic Progressions

Dirichlet's Theorem on Arithmetic Progressions

Time Limit: 1000MS	Memory Limit: 65536K
Total Submissions: 19133	Accepted: 9609

Description

If a and d arerelatively prime positive integers, the arithmetic sequence beginningwith a and increasing by d, i.e., a, a + d, a +2d, a + 3d, a + 4d, ...,contains infinitely many prime numbers. This fact is known as Dirichlet'sTheorem on Arithmetic Progressions, which had been conjectured by Johann CarlFriedrich Gauss (1777 - 1855) and was proved by Johann Peter Gustav LejeuneDirichlet (1805 - 1859) in 1837.

For example, thearithmetic sequence beginning with 2 and increasing by 3, i.e.,

2, 5, 8, 11, 14,17, 20, 23, 26, 29, 32, 35, 38, 41, 44, 47, 50, 53, 56, 59, 62, 65, 68, 71, 74,77, 80, 83, 86, 89, 92, 95, 98, ... ,

containsinfinitely many prime numbers

2, 5, 11, 17, 23,29, 41, 47, 53, 59, 71, 83, 89, ... .

Your mission,should you decide to accept it, is to write a program to find the nthprime number in this arithmetic sequence for given positive integers a, d,and n.

Input

The input is asequence of datasets. A dataset is a line containing three positiveintegers a, d, and n separated by aspace. a and d are relatively prime. You mayassume a <= 9307, d <= 346, and n <=210.

The end of theinput is indicated by a line containing three zeros separated by a space. It isnot a dataset.

Output

The output shouldbe composed of as many lines as the number of the input datasets. Each lineshould contain a single integer and should never contain extra characters.

The output integercorresponding to a dataset a, d, n shouldbe the nth prime number among those contained in the arithmeticsequence beginning with a and increasing by d.

FYI, it is knownthat the result is always less than 106 (one million) underthis input condition.

Sample Input

367 186 151

179 10 203

271 37 39

103 230 1

27 104 185

253 50 85

1 1 1

9075 337 210

307 24 79

331 221 177

259 170 40

269 58 102

0 0 0

Sample Output

92809

6709

12037

103

93523

14503

899429

5107

412717

22699

25673

涉及素数的题目貌似没有什么好办法，直接打印素数用的时候再取出来即可。

打表参考：http://blog.youkuaiyun.com/dinosoft/article/details/5829550

代码：

//poj 3006 Dirichlet's Theorem on Arithmetic Progressions
#include <cstdio>
#include <cstring>
constint max=1000500;
bool is_prime[max];
int prime[max];
int top=0;
void intitPrime(){
    memset(is_prime,true,sizeof is_prime);
    for(int i=2; i<max; i++){
       if(is_prime[i])
            prime[top++]= i;
       for(int j=0; j<top&&i*prime[j]<max; j++){
            is_prime[i*prime[j]]=false;
           if(i%prime[j]==0)break;
       }
    }
}
 
int main(int argc,charconst*argv[])
{
    intitPrime();
    freopen("in.txt","r", stdin);
    int a, b, n;
    while(scanf("%d %d%d",&a,&b,&n)!= EOF &&(a| b| n)){
       int i;
       for(i= a; i< max&&n>0; i += b){
           if(is_prime[i]) n--;
       }
        printf("%d\n", i);
    }
    return0;
}