标签：des style blog http io ar color os sp
素数的测试:Miller测试进行k次,将合数当成素数处理的错误概率最多不会超过4^(-k).
参考博客：http://blog.sina.com.cn/s/blog_6f71bea30100okag.html
PS：需要人品啊。
| Time Limit: 6000MS | Memory Limit: 65536K | |
| Total Submissions: 29406 | Accepted: 7479 | |
| Case Time Limit: 4000MS | ||
Description
Input
Output
Sample Input
2 5 10
Sample Output
Prime 2
#include <algorithm>
#include <iostream>
#include <stdlib.h>
#include <string.h>
#include <iomanip>
#include <stdio.h>
#include <string>
#include <queue>
#include <cmath>
#include <time.h>
#include <stack>
#include <map>
#include <set>
#define eps 1e-8
#define M 1000100
///#define LL long long
#define LL __int64
#define INF 0x3f3f3f
#define PI 3.1415926535898
#define mod 1000000007
#define MAX (pow(2.0, 60))
#define TIME 12
#define C 240
const int maxn = 110;
using namespace std;
LL Min;
LL gcd(LL x, LL y)
{
if(y == 0) return x;
return gcd(y, x%y);
}
LL mod_mult(LL a, LL b, LL n) ///计算(a*b) mod n
{
LL s = 0;
a = a % n;
while (b)
{
if (b & 1)
{
s += a;
if (s >= n)
s -= n;
}
a = a << 1;
if (a >= n)
a -= n;
b = b >> 1;
}
return s;
}
LL mod_exp(LL a, LL b, LL n) ///计算(a^b) mod n
{
LL d = 1;
a = a % n;
while (b >= 1)
{
if (b & 1) d = mod_mult(d, a, n);
a = mod_mult(a, a, n);
b = b >> 1;
}
return d;
}
bool Wintess(LL a, LL n) ///以a为基对n进行Miller测试并实现二次探测
{
LL m, x, y;
int i, j = 0;
m = n - 1;
while (m % 2 == 0) ///计算(n-1)=m*(2^j)中的j和m,j=0时m=n-1,不断的除以2直至n为奇数
{
m = m >> 1;
j++;
}
x = mod_exp(a, m, n);
for (i = 1; i <= j; i++)
{
y = mod_exp(x, 2, n);
if ((y == 1) && (x != 1) && (x != n - 1)) ///二次探测
return true; ///返回true时,n是合数
x = y;
}
if (y != 1)
return true;
return false;
}
bool miller_rabin(int times,LL n) ///对n进行s次的Miller测试
{
LL a;
int i;
if (n == 1)
return false;
if (n == 2)
return true;
if (n % 2 == 0)
return false;
srand(time(NULL));
for (i = 1; i <= times; i++)
{
a = rand() % (n - 1) + 1;
if (Wintess(a, n))
return false;
}
return true;
}
LL Pollard(LL n, int c) ///对n进行因字分解,找出n的一个因子,注意该因子不一定是最小的
{
LL i, k, x, y, d;
srand(time(NULL));
i = 1;
k = 2;
x = rand() % n;
y = x;
while (true)
{
i++;
x = (mod_mult(x, x, n) + c) % n;
d = gcd(y - x, n);
if (d > 1 && d < n)
return d;
if (y == x) ///该数已经出现过,直接返回即可
return n;
if (i == k)
{
y = x;
k = k << 1;
}
}
}
void get_small(LL n, int c) ///找出最小的素数因子
{
LL m;
if(n == 1) return;
if(miller_rabin(TIME, n))
{
if(n < Min) Min = n;
return;
}
m = n;
///while(m == n) m = Pollard(n, c--);
while (m == n) //找出n的一个因子
m = Pollard(n, c--);
get_small(m, c);
get_small(n/m, c);
}
int main()
{
int T;
LL n;
cin >>T;
while(T--)
{
scanf("%I64d",&n);
Min = MAX;
if(miller_rabin(TIME, n))
{
puts("Prime");
continue;
}
get_small(n, C);
printf("%I64d\n",Min);
}
return 0;
}
POJ 1811 Prime Test（费马小定理+二次探测定理）
标签：des style blog http io ar color os sp
原文地址：http://blog.csdn.net/xu12110501127/article/details/41358697
