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| #include<bits/stdc++.h>
using namespace std;
const double eps=1e-12;
double s;
int a,b,c;
double x,y,z;
double ff(double x,double y)
{
double z=s-x-y;
double ans=0;
if(z!=0) ans=c*log(z);
else if(z==0&&c!=0) ans=0;
if(y!=0) ans+=b*log(y);
else if(y==0&&b!=0) ans=0;
return ans;
}
double f(double x)
{
double low=0.0;
double up=s-x;
double m1,m2;
int tot=0;
while(tot<=100)
{
tot++;
m1=low+(up-low)/3.0;
m2=up-(up-low)/3.0;
if(ff(x,m1)+eps<=ff(x,m2))
low=m1;
else
up=m2;
}
y=(m1+m2)/2;
double ans=ff(x,y);
if(x!=0) ans+=a*log(x);
else if(x==0&&a!=0) ans=0;
return ans;
}
double three_devide(double low,double up)
{
double m1,m2;
int tot=0;
while(tot<=100)
{
tot++;
m1=low+(up-low)/3.0;
m2=up-(up-low)/3.0;
if(f(m1)+eps<=f(m2))
low=m1;
else
up=m2;
}
return (m1+m2)/2;
}
int main()
{
scanf("%lf",&s);
scanf("%d%d%d",&a,&b,&c);
x=three_devide(0.0,s);
z=f(x);
z=s-x-y;
printf("%.10f %.10f %.10f",x,y,z);
return 0;
}
|