学步园

大数分解pollard-rho

素数判定miller-rabin

#include<stdio.h>
#include<time.h>
#include<stdlib.h>
#define LL unsigned long long
#define nmax 2005
LL factor[nmax], num[nmax], minx, ans;
int flen, nnum;
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;
	ret = 1, a %= c;
	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 temp, a, x, y;
	int te, i, j;
	temp = n - 1;
	te = 0;
	while (!(temp & 1)) {
		temp >>= 1;
		te++;
	}
	srand(time(0));
	for (i = 0; i < times; i++) {
		a = rand() % (n - 1) + 1;
		x = modular_exp(a, temp, n);
		for (j = 0; j < te; 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;
	srand(time(0));
	x = rand() % (n - 1) + 1;
	y = x;
	i = 1;
	k = 2;
	while (1) {
		i++;
		x = (modular_multi(x, x, n) + c) % n;
		d = gcd(y - x, n);
		if ((d > 1) && (d < n)) {
			return d;
		}
		if (y == x) {
			return n;
		}
		if (i == k) {
			y = x;
			k <<= 1;
		}
	}
	return -1;
}
void findFactor(LL n, int c) {
	if (n == 1) {
		return;
	}
	if (miller_rabin(n, 6)) {
		factor[++flen] = n;
		return;
	}
	LL p = n;
	while (p >= n) {
		p = pollard_rho(p, c--);
	}
	findFactor(p, c);
	findFactor(n / p, c);

}
int cmp(const void *a, const void *b) {
	LL te = (*(LL *) a - *(LL *) b);
	if (te > 0) {
		return 1;
	} else if (te < 0) {
		return -1;
	}
	return 0;
}
void solve() {
	qsort(factor, flen + 1, sizeof(factor[0]), cmp);
	num[0] = factor[0];
	nnum = 0;
	int i;
	for (i = 0; i < flen; i++) {
		if (factor[i] == factor[i + 1]) {
			num[nnum] *= factor[i + 1];
		} else {
			num[++nnum] = factor[i + 1];
		}
	}
}
void dfs(int s, LL sn, LL n) {
	if (s == nnum + 1) {
		if (minx == -1 || (sn + n / sn < minx)) {
			if (gcd(sn, n / sn) == 1) {
				minx = sn + n / sn;
				ans = sn;
			}
		}
		return;
	}
	dfs(s + 1, sn * num[s], n);
	dfs(s + 1, sn, n);
}
int main() {
#ifndef ONLINE_JUDGE
	freopen("t.txt", "r", stdin);
#endif
	LL a, b, n, x, y;
	while (scanf("%lld %lld", &a, &b) != EOF) {
		if (a == b) {
			printf("%lld %lld\n", a, b);
			continue;
		}
		n = b / a;
		if (miller_rabin(n, 10)) {
			printf("%lld %lld\n", a, b);
			continue;
		}
		flen = -1;
		findFactor(n, 207);
		solve();
		minx = -1LL;
		dfs(0, 1LL, n);
		x = ans;
		y = n / ans;
		if (x > y) {
			n = x, x = y, y = n;
		}
		printf("%lld %lld\n", x * a, y * a);
	}
	return 0;
}