[BZOJ1492][NOI2007][CDQ分治][斜率优化][DP]货币兑换Cash

#include <cstdio>
#include <iostream>
#include <algorithm>
#include <cmath>
#define N 100010
#define inf 1<<30
#define eps 1e-9

using namespace std;

int n,s,head,tail;
int q
;
double f
;
struct days{
double a,b,r,x,y,k;
int g;
friend bool operator <(days a,days b){
return a.x<b.x+eps||(fabs(a.x-b.x)<=eps&&a.y<b.y+eps);
}
}d
,id
,p
;

inline bool cmp(days a,days b){
return a.k<b.k;
}

inline double getk(int x,int y){
if(!x) return -inf;
if(!y) return inf;
if(fabs(p[x].x-p[y].x)<=eps) return -inf;
return (p[x].y-p[y].y)/(p[x].x-p[y].x);
}

void solve(int l,int r){
int mid=l+r>>1,t1=l,t2=mid+1;
if(l==r){
f[l]=max(f[l-1],f[l]);
p[l].y=f[l]/(d[l].a*d[l].r+d[l].b);
p[l].x=p[l].y*d[l].r;
return;
}
for(int i=l;i<=r;i++)
if(d[i].g<=mid) id[t1++]=d[i];
else id[t2++]=d[i];
for(int i=l;i<=r;i++) d[i]=id[i];
solve(l,mid);
int head=1,tail=0;
for(int i=l;i<=mid;i++){
while(head<tail&&getk(q[tail],q[tail-1])+eps<getk(i,q[tail])) tail--;
q[++tail]=i;
}
for(int i=r;i>mid;i--){
while(head<tail&&d[i].k<getk(q[head],q[head+1])+eps) head++;
f[d[i].g]=max(f[d[i].g],p[q[head]].x*d[i].a+p[q[head]].y*d[i].b);
}
solve(mid+1,r);
t1=l,t2=mid+1;
for(int i=l;i<=r;i++)
if((p[t1]<p[t2]||t2>r)&&t1<=mid) id[i]=p[t1++];
else id[i]=p[t2++];
for(int i=l;i<=r;i++) p[i]=id[i];
}

int main(){
scanf("%d%d",&n,&s); f[0]=s;
for(int i=1;i<=n;i++){
scanf("%lf%lf%lf",&d[i].a,&d[i].b,&d[i].r);
d[i].k=-d[i].a/d[i].b;
d[i].g=i;
}
sort(d+1,d+1+n,cmp);
solve(1,n);
printf("%.3lf\n",f
);
}