【POJ】1811 Prime Test

rabin_miller判断素数，pollard rho求质因式分解。别人的模板。

/* 4344 */
#include <iostream>
#include <sstream>
#include <string>
#include <map>
#include <queue>
#include <set>
#include <stack>
#include <vector>
#include <deque>
#include <algorithm>
#include <cstdio>
#include <cmath>
#include <ctime>
#include <cstring>
#include <climits>
#include <cctype>
#include <cassert>
#include <functional>
#include <iterator>
#include <iomanip>
using namespace std;
//#pragma comment(linker,"/STACK:102400000,1024000")

#define sti                set<int>
#define stpii            set<pair<int, int> >
#define mpii            map<int,int>
#define vi                vector<int>
#define pii                pair<int,int>
#define vpii            vector<pair<int,int> >
#define rep(i, a, n)     for (int i=a;i<n;++i)
#define per(i, a, n)     for (int i=n-1;i>=a;--i)
#define clr                clear
#define pb                 push_back
#define mp                 make_pair
#define fir                first
#define sec                second
#define all(x)             (x).begin(),(x).end()
#define SZ(x)             ((int)(x).size())
#define lson            l, mid, rt<<1
#define rson            mid+1, r, rt<<1|1

#define LL                __int64 
#define Times            10

LL n, mn;

LL random(LL n) {
    return (double) rand() / RAND_MAX * n + 0.5;
}

LL multi(LL a, LL b, LL mod) {
    LL ret = 0;
    
    while (b) {
        if (b & 1)
            ret = (ret + a) % mod;
        b >>= 1;
        a = (a + a) % mod;
    }
    
    return ret;
}

LL pow(LL a, LL b, LL mod) {
    LL ret = 1;
    
    while (b) {
        if (b & 1)
            ret = multi(ret, a, mod);
        b >>= 1;
        a = multi(a, a, mod);
    }
    
    return ret;
}

bool witness(LL a, LL n) {
    LL d = n - 1;
    
    while (!(d & 1))
        d >>= 1;
    
    LL t = pow(a, d, n);
    while (d!=n-1 && t!=1 && t!=n-1) {
        t = multi(t, t, n);
        d <<= 1;
    }
    
    return t==n-1 || (d&1);
}

bool miller_rabin(LL n) {
    if (n == 2)
        return true;
    
    if (n<2 || (n&1)==0)
        return false;
    
    rep(i, 0, Times) {
        LL a = random(n-2) + 1;
        if (!witness(a, n))
            return false;
    }
    
    return true;
}

LL pollard_rho(LL n, int c) {
    LL x, y, d, i = 1, k = 2;
    x = random(n-2) + 1;
    y = x;
    
    while (1) {
        ++i;
        x = (multi(x, x, n) + c) % n;
        d = __gcd(y-x, n);
        if (1<d && d<n)
            return d;
        
        if (y == x)
            return n;
        
        if (i == k) {
            y = x;
            k <<= 1;
        }
    }
}

void find(LL n, int c) {
    if (n == 1)
        return ;
    
    if (miller_rabin(n)) {
        mn = min(mn, n);
        return ;
    }
    
    LL p = n;
    while (p >= n)
        p = pollard_rho(p, c--);
    find(p, c);
    find(n/p, c);
}

void solve() {
    mn = n;
    if (miller_rabin(n)) {
        puts("Prime");
        return ;
    }
    
    find(n, 12312);
    printf("%I64d
", mn);
}

int main() {
    ios::sync_with_stdio(false);
    #ifndef ONLINE_JUDGE
        freopen("data.in", "r", stdin);
        freopen("data.out", "w", stdout);
    #endif
    
    int t;
    
    scanf("%d", &t);
    while (t--) {
        scanf("%I64d", &n);
        solve();
    }
    
    #ifndef ONLINE_JUDGE
        printf("time = %d.
", (int)clock());
    #endif
    
    return 0;
}