hdu 2138 How many prime numbers
2015-02-17 16:58
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How many prime numbers
Time Limit: 3000/1000 MS (Java/Others) Memory Limit: 32768/32768 K (Java/Others)Total Submission(s): 7017 Accepted Submission(s): 2336
[align=left]Problem Description[/align]
Give you a lot of positive integers, just to find out how many prime numbers there are.
[align=left]Input[/align]
There are a lot of cases. In each case, there is an integer N representing the number of integers to find. Each integer won’t exceed 32-bit signed integer, and each of them won’t be less than 2.
[align=left]Output[/align]
For each case, print the number of prime numbers you have found out.
[align=left]Sample Input[/align]
3
2 3 4
[align=left]Sample Output[/align]
2
_____________________________
ACM STEPS里的...这题前面一道是求LCM....结果接下来就是这么一道。。。
朴素会超....筛法会爆....题目顺序真是按照难度来的?
于是想到 Miller-Rabin素数测试.......
这个方法是基于费马小定理
我的理解就是...
如果我要判断n是否为素数
只要取k个数 如果满足 a^(n-1)mod n =1 那么n就很可能为素数。
证明什么的...暂时还是算了吧...论文里貌似扯了一大堆
第一次用,竟然真的A了。。。。
感觉更好的办法也许是先打一个比较小的素数表,然后每次random选取若干个进行判断...那样应该更可靠些?
本来想WA掉之后再改的。。。没想到这么写就A掉了。。。。杭电数据略水?
#include <iostream> #include <cmath> #include <stdio.h> #include <cstring> using namespace std; typedef long long LL; LL power(LL m,LL n,LL k) { int b = 1; while (n > 0) { if (n & 1) b = (b*m)%k; n = n >> 1 ; m = (m*m)%k; } return b; } bool judge(LL n) { LL i; if (n<=3) return true; for (i=2;i<=ceil(sqrt(n))+1;i++) if (n %i==0) return false; return true; } int main() { LL i,n,x; while (scanf("%I64d",&n)!=EOF) { LL ans=0; for (i=1;i<=n;i++) { scanf("%I64d",&x); if ((power(61,x-1,x)==1)&&(power(11,x-1,x)==1)&&(power(31,x-1,x)==1) &&(power(97,x-1,x)==1)) ans++; } printf("%I64d\n",ans); } return 0; }
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