poj2429 GCD & LCM Inverse

用miller_rabin 和 pollard_rho对大数因式分解，再用dfs寻找答案即可。

http://poj.org/problem?id=2429

 #include <cstdio>
 #include <cstring>
 #include <algorithm>
 #include <cmath>
 using namespace std;
 typedef __int64 LL;
 const int maxn = ;
 const int times = ;
 LL prime[maxn], k;
 int cnt[maxn];
 LL c, d, pm, mid;

 void dfs(int pos, LL t){
     if(pos == k){
         if(pm < t) pm = t;
         return;
     }
     LL tem = ;
     int c = cnt[pos];
     while(c--) tem *= prime[pos];
     dfs(pos + , t);
     if(t * tem <= mid) dfs(pos + , t * tem);
 }

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

 LL multi(LL a, LL b, LL mod){
     a %= mod, b %= mod;
     LL ans = ;
     while(b){
         if(b & ) ans += a, ans %= mod;
         b >>= ;
         a <<= ;
         a %= mod;
     }
     return ans;
 }

 LL power(LL a, LL p, LL mod){
     a %= mod;
     LL ans = ;
     while(p){
         if(p & ) ans = multi(ans, a, mod), ans %= mod;
         p >>= ;
         a = multi(a, a, mod);
         a %= mod;
     }
     return ans;
 }

 LL gcd(LL a, LL b){
     if(!b) return a;
     return gcd(b, a % b);
 }

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

 bool miller_rabin(LL n){
     if(n == ) return ;
     if(n <  || !(n & )) return ;
     for(int i = ; i < times; i++){
         LL p = random(n - ) + ;
         if(!witness(p, n)) return ;
     }
     return ;
 }

 LL pollard_rho(LL n, LL t){
     LL x = random(n - ) + ;
     LL y = x, i = , k = , d;
     while(){
         ++i;
         x = (multi(x, x, n) + t) % n;
         d = gcd(y - x, n);
         if( < d && d < n) return d;
         if(x == y) return n;
         if(i == k){
             y = x;
             k <<= ;
         }
     }
 }

 void solve(){
     LL m = d / c;
     LL m1 = m;
     mid = (LL)sqrt(m);
     k = ;
     memset(cnt, , sizeof cnt);
     if(m %  == ){
         prime[k++] = ;
         while(m %  == ) m >>= , ++cnt[k - ];
     }
     while(!miller_rabin(m) && m > ){
         int seed = ;
         LL p1 = m;
         while(p1 >= m || !miller_rabin(p1)) p1 = pollard_rho(m, seed--);
         prime[k++] = p1;
         while(m % p1 == ) m /= p1, ++cnt[k - ];
     }
     if(m != ) prime[k++] = m, ++cnt[k - ];
     pm = ;
     dfs(, );
     LL qm = m1 / pm;
     printf("%I64d %I64d\n", pm * c, qm * c);
 }

 int main(){
     //freopen("in.txt", "r", stdin);
     //freopen("out.txt", "w", stdout);
     while(~scanf("%I64d%I64d", &c, &d)) solve();
     return ;
 }