Red Huang

Red Huang

uva 10090

歐幾里得擴展,並且找出最小成本

ax+by=c

讓 a 最小 或讓 a 最大 因為斜率為正,所以不會有答案在中心點的問題

//====================================================================||  
//                                                                    ||  
//                                                                    ||  
//                         作者 : GCA                               ||  
//                  6AE7EE02212D47DAD26C32C0FE829006                  ||  
//====================================================================||  
#include <iostream>  
#include <cstdio>  
#include <cstring>  
#include <algorithm>  
#include <cmath>  
#include <climits>  
#include <vector>  
#include <set>  
#include <map>  
#include <queue>  
#include <cctype>  
#include <utility>  
using namespace std;  
#ifdef ONLINE\_JUDGE  
#define ll "%lld"  
#else  
#define ll "%I64d"  
#endif  
typedef unsigned int uint;  
typedef long long int Int;  
#define Set(a,s) memset(a,s,sizeof(a))  
#define Write(w) freopen(w,"w",stdout)  
#define Read(r) freopen(r,"r",stdin)  
#define Pln() printf("\\n")  
#define I\_de(x,n)for(int i=0;i<n;i++)printf("%d ",x\[i\]);Pln()  
#define De(x)printf(#x"%d\\n",x)  
#define For(i,x)for(int i=0;i<x;i++)  
#define CON(x,y) x##y  
#define Pmz(dp,nx,ny)for(int hty=0;hty<ny;hty++){for(int htx=0;htx<nx;htx++){\\  
    printf("%d ",dp\[htx\]\[hty\]);}Pln();}  
#define M 55  
#define PII pair<int,int\>  
#define PB push\_back  
#define oo ((Int)1<<61)  
#define Set\_oo 0x3f  
#define Is\_debug true  
#define debug(...) if(Is\_debug)printf("DEBUG: "),printf(\_\_VA\_ARGS\_\_)  
#define FOR(it,c) for(\_\_typeof((c).begin()) it=(c).begin();it!=(c).end();it++)  
#define eps 1e-6  
bool xdy(double x,double y){return x>y+eps;}  
bool xddy(double x,double y){return x>y-eps;}  
bool xcy(double x,double y){return x<y-eps;}  
bool xcdy(double x,double y){return x<y+eps;}  
int min3(int x,int y,int z){  
    int tmp=min(x,y);  
    return min(tmp,z);  
}  
int max3(int x,int y,int z){  
    int tmp=max(x,y);  
    return max(tmp,z);  
}  
Int n;  
Int n1,n2,c1,c2;  
Int x,y;  
Int exegcd(Int a,Int b){  
    if(b==0){  
        x=1;  
        y=0;  
        return a;  
    }else{  
        Int r=exegcd(b,a%b);  
        Int t=x;  
        x=y;  
        y=t-(a/b)\*y;  
        return r;  
    }  
}  
void solve(){  
    Int gcd=exegcd(n1,n2);  
    Int tmp=n/gcd;  
    if(n%gcd!=0){  
        printf("失敗\\n");  
        return;  
    }  
    Int lcm=n1\*n2/gcd;  
    x\*=tmp;  
    y\*=tmp;  
    Int tx=x;  
    Int ty=y;  
    Int mincost=oo;  
    Int ansx=-1;  
    Int ansy=-1;  
    Int kx=lcm/n1;  
    Int ky=lcm/n2;  
//    debug("%lld %lld\\n",x,y);  
    if(tx<0){  
        tx=-tx;  
        Int k2=tx/kx;  
        if(tx%kx)k2++;  
        tx=k2\*kx-tx;  
        ty-=k2\*ky;  
    }  
    if(ty<0){  
        ty=-ty;  
        Int k2=ty/ky;  
        if(ty%ky)k2++;  
        ty=k2\*ky-ty;  
        tx-=k2\*kx;  
    }  
    x=tx;y=ty;  
    if(x<0||y<0){  
        printf("失敗\\n");  
        return;  
    }  
    Int k2=tx/kx;  
    tx-=kx\*k2;  
    ty+=ky\*k2;  
//    debug("%lld %lld\\n",tx,ty);  
    Int cost=c1\*tx+c2\*ty;  
    if(cost<mincost){  
        mincost=cost;  
        ansx=tx;  
        ansy=ty;  
    }  
    tx=x;ty=y;  
    k2=ty/ky;  
    tx+=kx\*k2;  
    ty-=ky\*k2;  
    cost=c1\*tx+c2\*ty;  
//    debug("%lld %lld %lld\\n",tx,ty,mincost);  
    if(cost<mincost){  
        cost=mincost;  
        ansx=tx;  
        ansy=ty;  
    }  
  
  
    printf("%lld %lld\\n",ansx,ansy);  
  
}  
int main() {  
    ios\_base::sync\_with\_stdio(0);  
    while(~scanf("%lld",&n)&&n){  
        scanf("%lld%lld%lld%lld",&c1,&n1,&c2,&n2);  
        solve();  
    }  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
}  

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