题面
题解
看\(mashirosky\)大佬的题解吧……这里
//minamoto
#include<bits/stdc++.h>
#define R register
#define inf 0x3f3f3f3f
#define inline __inline__ __attribute__((always_inline))
#define fp(i,a,b) for(R int i=(a),I=(b)+1;i<I;++i)
#define fd(i,a,b) for(R int i=(a),I=(b)-1;i>I;--i)
#define go(u) for(int i=head[u],v=e[i].v;i;i=e[i].nx,v=e[i].v)
using namespace std;
char buf[1<<21],*p1=buf,*p2=buf;
inline char getc(){return p1==p2&&(p2=(p1=buf)+fread(buf,1,1<<21,stdin),p1==p2)?EOF:*p1++;}
int read(){
R int res,f=1;R char ch;
while((ch=getc())>'9'||ch<'0')(ch=='-')&&(f=-1);
for(res=ch-'0';(ch=getc())>='0'&&ch<='9';res=res*10+ch-'0');
return res*f;
}
double readdb()
{
R double x=0,y=0.1,f=1;R char ch;
while((ch=getc())>'9'||ch<'0')(ch=='-')&&(f=-1);
for(x=ch-'0';(ch=getc())>='0'&&ch<='9';x=x*10+ch-'0');
for(ch=='.'&&(ch=getc());ch>='0'&&ch<='9';x+=(ch-'0')*y,y*=0.1,ch=getc());
return x*f;
}
const int N=10005;const double eps=1e-13;
inline int sgn(R double x){return x<-eps?-1:x>eps;}
double s[N],k[N],vp[N],v[N],mx[N],E;
int n;
bool ck(double lam){
double res=0,l,r,mid;
fp(i,1,n){
l=max(0.0,vp[i]),r=mx[i],mid;
while(sgn(r-l)>0){
mid=(l+r)*0.5;
(sgn(2*lam*mid*mid*k[i]*(mid-vp[i])+1)>=0)?l=mid:r=mid;
}
v[i]=l,res+=k[i]*(v[i]-vp[i])*(v[i]-vp[i])*s[i];
if(sgn(E-res)<0)return false;
}
return true;
}
int main(){
// freopen("testdata.in","r",stdin);
n=read(),E=readdb();
fp(i,1,n){
s[i]=readdb(),k[i]=readdb(),vp[i]=readdb();
mx[i]=sgn(s[i])?sqrt(E/k[i]/s[i])+vp[i]:inf;
}
double l=-inf,r=0,mid;
while(sgn(r-l)>0){
mid=(l+r)*0.5;
ck(mid)?l=mid:r=mid;
}
ck(r);
double res=0;
fp(i,1,n)res+=s[i]/v[i];
printf("%.8lf\n",res);
return 0;
}