PKU 2429 GCD & LCM Inverse
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;
}