pku 1811 Prime Test 大素数判定和大数分解

 

/*
 * pku1811.c
 *
 *  Created on: 2011-8-1
 *      Author: 王竹
 */

#include<stdio.h>
#include<stdlib.h>
#define LL long long
LL pmin;
LL modular_multi(LL a, LL b, LL c) {
    LL ret;
    ret = 0, a %= c;
    while (b) {
        if (b & 1) {
            ret += a;
            if (ret > c) {
                ret -= c;
            }
        }
        a <<= 1;
        if (a > c) {
            a -= c;
        }
        b >>= 1;
    }
    return ret;
}
LL modular_exp(LL a, LL b, LL c) {
    LL ret;
    a %= c, ret = 1;
    while (b) {
        if (b & 1) {
            ret = modular_multi(ret, a, c);
        }
        a = modular_multi(a, a, c);
        b >>= 1;
    }
    return ret;
}
int miller_rabin(LL n, int times) {
    if (n == 2) {
        return 1;
    }
    if ((n < 2) && (!(n & 1))) {
        return 0;
    }
    LL te, a, x, y;
    te = n - 1;
    int temp;
    temp = 0;
    while (!(te & 1)) {
        te >>= 1;
        temp++;
    }
    int i, j;
    for (i = 0; i < times; i++) {
        a = rand() % (n - 1) + 1;
        x = modular_exp(a, te, n);
        for (j = 0; j < temp; j++) {
            y = modular_multi(x, x, n);
            if ((y == 1) && (x != 1) && (x != (n - 1))) {
                return 0;
            }
            x = y;
        }
        if (x != 1) {
            return 0;
        }
    }
    return 1;
}
LL gcd(LL a, LL b) {
    LL te;
    if (a < b) {
        te = a, a = b, b = te;
    }
    if (b == 0) {
        return a;
    }
    while (b) {
        te = a % b;
        a = b;
        b = te;
    }
    return a;
}
LL pollard_rho(LL n, int c) {
    LL x, y, d, i, k;
    x = rand() % (n - 1) + 1;
    y = x;
    i = 1LL, k = 2LL;
    while (1) {
        i++;
        x = (modular_multi(x, x, n) + c) % n;
        
        d = gcd(y - x, n);
        if ((1 < d) && (d < n)) {
            return d;
        }
        if (x == y) {
            return n;
        }
        if (i == k) {
            k <<= 1;
            y = x;
        }
    }
    return -1;
}
void findFactor(LL n, int c) {
    if (n == 1) {
        return;
    }
    if (miller_rabin(n, 6)) {
        if (n < pmin) {
            pmin = n;
        }
        return;
    }
    LL p = n;
    while (p >= n) {
        p = pollard_rho(p, c--);
    }
    findFactor(p, c);
    findFactor(n / p, c);
}
int main() {
#ifndef ONLINE_JUDGE
    freopen("t.txt", "r", stdin);
#endif
    int T;
    LL n;
    while (scanf("%d", &T) != EOF) {
        while (T--) {
            scanf("%I64d", &n);
            if (miller_rabin(n, 10)) {
                printf("Prime\n");
                continue;
            }
            pmin = 1LL << 54;
            findFactor(n, 107);
            printf("%I64d\n", pmin);
        }
    }
    return 0;
}