歐幾里得擴展,並且找出最小cost
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
//====================================================================||
// ||
// ||
// Author : 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("failed\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("failed\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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