POJ 2429 GCD & amp; LCM Inverse pollard_rov big factor decomposition

This question. Assume that the original numbers are a and B, after the GCD and LCM are given, we only need to ask the LCM/GCD factor to find the/gcd and B/gcd, and then we can find that there cannot be a common number between the two things. it is necessary to take all of the factors away and use the larger number of pollard_rov for decomposition. If the complexity is involved, assume that the decomposition factor is p, and the time used is O (sqrt (p). In general, it is much faster than the direct sqrt (n) decomposition.

#include <iostream>#include <cstdio>#include <cstdlib>#include <cmath>#include <algorithm>#include <ctime>#include <map>#define MAXN 10#define INF 1LL<<61#define C 16381using namespace std;typedef long long LL;LL gcd(LL a, LL b){    return b ? gcd(b, a % b) : a;}LL multi(LL a, LL b, LL m){     LL ans = 0;     while(b)     {         if(b & 1)         {             ans = (ans + a) % m;             b--;         }         b >>= 1;         a = (a + a) % m;     }     return ans;}LL quick_mod(LL a, LL b, LL m){     LL ans = 1;     a %= m;     while(b)     {         if(b & 1)         {             ans = multi(ans, a, m);             b--;         }         b >>= 1;         a = multi(a, a, m);     }     return ans;}bool Miller_Rabin(LL n){    if(n == 2) return true;    if(n < 2 || !(n & 1)) return false;    LL a, m = n - 1, x, y;    int k = 0;    while((m & 1) == 0)    {        k++;        m >>= 1;    }    for(int i = 0; i < MAXN; i++)    {        a = rand() % (n - 1) + 1;        x = quick_mod(a, m, n);        for(int j = 0; j < k; j++)        {            y = multi(x, x, n);            if(y == 1 && x != 1 && x != n - 1) return false;            x = y;        }        if(y != 1) return false;    }    return true;}LL Pollard_rho(LL n, LL c){     LL x, y, d, i = 1, k = 2;     y = x = rand() % (n - 1) + 1;     while(true)     {         i++;         x = (multi(x, x, n) + c) % n;         d = gcd((y - x + n) % n, n);         if(1 < d && d < n) return d;         if(y == x) return n;         if(i == k)         {             y = x;             k <<= 1;         }     }}LL fac[555];int cnt;map<LL, int>mp;void find(LL n, int c){     if(n == 1) return;     if(Miller_Rabin(n))     {         mp[n]++;         return ;     }     LL p = n;     LL k = c;     while(p >= n) p = Pollard_rho(p, c--);     find(p, k);     find(n / p,k);}int main(){    LL a, b;    while(scanf("%I64d%I64d", &a, &b) != EOF)    {        cnt = 0;        LL tmp = b / a;        if(a == b)        {            printf("%I64d %I64d\n", a, b);            continue;        }        mp.clear();        find(tmp, C);        cnt = 0;        for(map<LL, int>:: iterator it = mp.begin(); it != mp.end(); it++)        {            LL t = 1;            for(int j = 0; j < it -> second; j++)                t = t * (it -> first);            fac[cnt++] = t;        }        //for(int i = 0; i < cnt; i++)           // printf("%I64d\n", fac[i]);        LL ansa = INF, ansb = INF;        for(int i = 0; i < (1 << cnt); i++)        {            LL ta = 1;            for(int j = 0; j < cnt; j++)                if(i & (1 << j))                    ta *= fac[j];            if(ansa + ansb > ta + b / a / ta)                ansa = ta, ansb = b / a / ta;        }        if(ansa > ansb) swap(ansa, ansb);        printf("%I64d %I64d\n", ansa * a, ansb * a);    }return 0;}