Prime Test
Time Limit: 6000ms
Case Time Limit: 4000ms
Memory Limit: 65536KB
This problem will be judged on PKU. Original ID: 181164-bit integer IO format: %lld Java class name: Main
Given 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 < 254).
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
解题：Miller-Rabbin + Pollard-rho
1 #include <cstdio> 2 #include <ctime> 3 #include <cstdlib> 4 using namespace std; 5 typedef long long LL; 6 const int maxn = 1001; 7 LL mul(LL a,LL b,LL mod) { 8 if(!a) return 0; 9 return ((a&1)*b%mod + (mul(a>>1,b,mod)<<1)%mod)%mod; 10 } 11 LL quickPow(LL a,LL d,LL n) { 12 LL ret = 1; 13 while(d) { 14 if(d&1) ret = mul(ret,a,n); 15 d >>= 1; 16 a = mul(a,a,n); 17 } 18 return ret; 19 } 20 bool check(LL a,LL d,LL n) { 21 if(n == a) return true; 22 while(~d&1) d >>= 1; 23 LL t = quickPow(a,d,n); 24 while(d < n-1 && t != 1 && t != n-1) { 25 t = mul(t,t,n); 26 d <<= 1; 27 } 28 return (d&1) || t == n-1; 29 } 30 bool isP(LL n) { 31 if(n == 2) return true; 32 if(n < 2 || 0 == (n&1)) return false; 33 static int p[5] = {2,3,7,61,24251}; 34 for(int i = 0; i < 5; ++i) 35 if(!check(p[i],n-1,n)) return false; 36 return true; 37 } 38 LL gcd(LL a,LL b) { 39 if(a < 0) return gcd(-a,b);//特别注意，没这个TLE 40 return b?gcd(b,a%b):a; 41 } 42 LL Pollard_rho(LL n,LL c) { 43 LL i = 1,k = 2,x = rand()%n,y = x; 44 while(true) { 45 x = (mul(x,x,n) + c)%n; 46 LL d = gcd(y - x,n); 47 if(d != 1 && d != n) return d; 48 if(y == x) return n; 49 if(++i == k) { 50 y = x; 51 k <<= 1; 52 } 53 } 54 } 55 LL Fac[maxn],tot; 56 void factorization(LL n) { 57 if(isP(n)) { 58 Fac[tot++] = n; 59 return; 60 } 61 LL p = n; 62 while(p >= n) p = Pollard_rho(p,rand()%(n-1)+1); 63 factorization(p); 64 factorization(n/p); 65 } 66 int main() { 67 int kase; 68 LL x; 69 scanf("%d",&kase); 70 while(kase--) { 71 scanf("%I64d",&x); 72 if(isP(x)) puts("Prime"); 73 else { 74 tot = 0; 75 LL ret = x; 76 factorization(x); 77 for(int i = 0; i < tot; ++i) 78 if(ret > Fac[i]) ret = Fac[i]; 79 printf("%I64d ",ret); 80 } 81 } 82 return 0; 83 }