Prime Test
Time Limit: 6000MS
Memory Limit: 65536K
Total Submissions: 29193
Accepted: 7392
Case Time Limit: 4000MS
DescriptionGiven a big integer number, you are required to find out whether it's a prime number.
Input
The first line contains the number of test cases T (1 <= T <= 20 ), then the following T lines each contains an integer number N (2 <= N < 2^54).
Output
For each test case, if N is a prime number, output a line containing the word "Prime", otherwise, output a line containing the smallest prime factor of N.
Sample Input
2
5
10
Sample Output
Prime
2
Source
POJ Monthly
题目大意：T组数据，对于输入的N，若N为素数，输出"Prime"，否则输出N的最小素因子
思路：由于N的规模为2^54所以普通的素性推断果断过不了。
要用Miller Rabin素数測试来做。
而若N不为素数，则须要对N进行素因子分解。由于N为大数，考虑用Pollar Rho整数分解来做。
#include<stdio.h>
#include<stdlib.h>
#include<time.h>
#include<math.h>
#define MAX_VAL (pow(2.0,60))
//miller_rabbin素性測试
//__int64 mod_mul(__int64 x,__int64 y,__int64 mo)
//{
// __int64 t;
// x %= mo;
// for(t = 0; y; x = (x<<1)%mo,y>>=1)
// if(y & 1)
// t = (t+x) %mo;
//
// return t;
//}
__int64 mod_mul(__int64 x,__int64 y,__int64 mo)
{
__int64 t,T,a,b,c,d,e,f,g,h,v,ans;
T = (__int64)(sqrt(double(mo)+0.5));
t = T*T - mo;
a = x / T;
b = x % T;
c = y / T;
d = y % T;
e = a*c / T;
f = a*c % T;
v = ((a*d+b*c)%mo + e*t) % mo;
g = v / T;
h = v % T;
ans = (((f+g)*t%mo + b*d)% mo + h*T)%mo;
while(ans < 0)
ans += mo;
return ans;
}
__int64 mod_exp(__int64 num,__int64 t,__int64 mo)
{
__int64 ret = 1, temp = num % mo;
for(; t; t >>=1,temp=mod_mul(temp,temp,mo))
if(t & 1)
ret = mod_mul(ret,temp,mo);
return ret;
}
bool miller_rabbin(__int64 n)
{
if(n == 2)
return true;
if(n < 2 || !(n&1))
return false;
int t = 0;
__int64 a,x,y,u = n-1;
while((u & 1) == 0)
{
t++;
u >>= 1;
}
for(int i = 0; i < 50; i++)
{
a = rand() % (n-1)+1;
x = mod_exp(a,u,n);
for(int j = 0; j < t; j++)
{
y = mod_mul(x,x,n);
if(y == 1 && x != 1 && x != n-1)
return false;
x = y;
}
if(x != 1)
return false;
}
return true;
}
//PollarRho大整数因子分解
__int64 minFactor;
__int64 gcd(__int64 a,__int64 b)
{
if(b == 0)
return a;
return gcd(b, a % b);
}
__int64 PollarRho(__int64 n, int c)
{
int i = 1;
srand(time(NULL));
__int64 x = rand() % n;
__int64 y = x;
int k = 2;
while(true)
{
i++;
x = (mod_exp(x,2,n) + c) % n;
__int64 d = gcd(y-x,n);
if(1 < d && d < n)
return d;
if(y == x)
return n;
if(i == k)
{
y = x;
k *= 2;
}
}
}
void getSmallest(__int64 n, int c)
{
if(n == 1)
return;
if(miller_rabbin(n))
{
if(n < minFactor)
minFactor = n;
return;
}
__int64 val = n;
while(val == n)
val = PollarRho(n,c--);
getSmallest(val,c);
getSmallest(n/val,c);
}
int main()
{
int T;
__int64 n;
scanf("%d",&T);
while(T--)
{
scanf("%I64d",&n);
minFactor = MAX_VAL;
if(miller_rabbin(n))
printf("Prime
");
else
{
getSmallest(n,200);
printf("%I64d
",minFactor);
}
}
return 0;
}