POJ2429 GCD & LCM Inverse （大整数分解）

题目点我点我点我

题目大意：给你两个数a,b的最大公约数和最小公倍数，求a+b最小的组合a，b。

解题思路：直接套大整数分解模版。然后DFS即可。

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#include <stdio.h>
#include <string.h>
#include <iostream>
#include <algorithm>
#include <vector>
#include <queue>
#include <stack>
#include <set>
#include <map>
#include <string>
#include <math.h>
#include <stdlib.h>
#include <bitset>
using namespace std;

#define rep(i,a,b) for (int i=(a),_ed=(b);i<=_ed;i++)
#define per(i,a,b) for (int i=(b),_ed=(a);i>=_ed;i--)
#define pb push_back
#define mp make_pair
const int inf_int = 2e9;
const long long inf_ll = 2e18;
#define inf_add 0x3f3f3f3f
#define mod 1000000007
#define LL long long
#define ULL unsigned long long
#define MS0(X) memset((X), 0, sizeof((X)))
#define SelfType int
SelfType Gcd(SelfType p,SelfType q){return q==0?p:Gcd(q,p%q);}
SelfType Pow(SelfType p,SelfType q){SelfType ans=1;while(q){if(q&1)ans=ans*p;p=p*p;q>>=1;}return ans;}
#define Sd(X) int (X); scanf("%d", &X)
#define Sdd(X, Y) int X, Y; scanf("%d%d", &X, &Y)
#define Sddd(X, Y, Z) int X, Y, Z; scanf("%d%d%d", &X, &Y, &Z)
#define reunique(v) v.resize(std::unique(v.begin(), v.end()) - v.begin())
#define all(a) a.begin(), a.end()
typedef pair<int, int> pii;
typedef pair<long long, long long> pll;
typedef vector<int> vi;
typedef vector<long long> vll;
inline int read(){int ra,fh;char rx;rx=getchar(),ra=0,fh=1;while((rx<'0'||rx>'9')&&rx!='-')rx=getchar();if(rx=='-')fh=-1,rx=getchar();while(rx>='0'&&rx<='9')ra*=10,ra+=rx-48,rx=getchar();return ra*fh;}
//#pragma comment(linker, "/STACK:102400000,102400000")

const int Times = 10;
const LL INF = (LL)1<<61;
const int N = 550;

LL n, m, ct, cnt;
LL mini, mina,minb,ans;
LL fac
, num
;

LL gcd(LL a, LL b)
{
return b? gcd(b, a % b) : a;
}

LL multi(LL a, LL b, LL m)
{
LL ans = 0;
a %= m;
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 m = n - 1;
int k = 0;
while((m & 1) == 0)
{
k++;
m >>= 1;
}
for(int i=0; i<Times; i++)
{
LL a = rand() % (n - 1) + 1;
LL x = quick_mod(a, m, n);
LL y = 0;
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 i = 1, k = 2;
LL x = rand() % (n - 1) + 1;
LL y = x;
while(true)
{
i++;
x = (multi(x, x, n) + c) % n;
LL 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;
}
}
}

void find(LL n, int c)
{
if(n == 1) return;
if(Miller_Rabin(n))
{
fac[ct++] = n;
return ;
}
LL p = n;
LL k = c;
while(p >= n) p = pollard_rho(p, c--);
find(p, k);
find(n / p, k);
}

void dfs(LL dept, LL val)
{
if(dept == cnt)
{
LL a = val;
LL b = ans / val;
if(gcd(a,b)==1)
{
a *= n;
b *= n;
if(a+b<mini)
{
mini = a+b;
mina = a;
minb = b;
}
}
return ;
}
for(int i=0;i<=num[dept];i++)
{
if(val>mini)return;
dfs(dept + 1, val);
val *= fac[dept];
}
}

int main()
{
while(~scanf("%I64d%I64d", &n, &m))
{
if(n == m)
{
printf("%I64d %I64d\n",n,m);
continue;
}
mini = INF;
ct = cnt = 0;
ans = m / n;
find(ans, 120);
sort(fac, fac + ct);
num[0] = 1;
int k = 1;
for(int i=1; i<ct; i++)
{
if(fac[i] == fac[i-1])
++num[k-1];
else
{
num[k] = 1;
fac[k++] = fac[i];
}
}
cnt = k;
dfs(0, 1);
if(mina>minb)swap(mina,minb);
printf("%I64d %I64d\n",mina,minb);
}
return 0;
}