[BZOJ 1492][NOI2007]货币兑换Cash（CDQ分治+斜率优化Dp）

#include<iostream>
#include<cstdio>
#include<cstring>
#include<cstdlib>
#include<cmath>
#include<algorithm>
#define MAXN 100005
#define eps 1e-9
const double INF=1e100;
using namespace std;
int n,s,stack[MAXN],top;
double a[MAXN],b[MAXN],R[MAXN],f[MAXN];
struct Node
{
    double s,x,y;
    int id;
    bool operator < (const Node& x) const
    {return s<x.s;}
}data[MAXN],t[MAXN];
double slope(int i,int j)
{
    if(fabs(data[j].x-data[i].x)<eps)return data[j].y>data[i].y?INF:-INF;
    return (data[j].y-data[i].y)/(data[j].x-data[i].x);
}
void merge(int l,int r)
{
    if(l==r)return;
    int mid=(l+r)>>1;
    int i=l,j=mid+1,k=l;
    while(i<=mid&&j<=r)
    {
        if(data[i].x<data[j].x)t[k++]=data[i++];
        else t[k++]=data[j++];
    }
    while(i<=mid)t[k++]=data[i++];
    while(j<=r)t[k++]=data[j++];
    for(int i=l;i<=r;i++)data[i]=t[i];
}
void solve(int l,int r)
{
    if(l==r)
    {
        f[l]=max(f[l],f[l-1]);
        data[l].y=f[l]/(R[l]*a[l]+b[l]);
        data[l].x=data[l].y*R[l];
        return;
    }
    int mid=(l+r)>>1;for(int i=l,j=mid+1,k=l;k<=r;k++)
    if(data[k].id<=mid)t[i++]=data[k];
    else t[j++]=data[k];
    for(int i=l;i<=r;i++)data[i]=t[i];
    solve(l,mid);
    top=0;
    for(int i=l;i<=mid;i++)
    {
        while(top>1&&slope(stack[top-1],stack[top])<eps+slope(stack[top],i))
        top--;
        stack[++top]=i;
    }
    for(int i=mid+1;i<=r;i++)
    {
        while(top>1&&data[i].s+eps>slope(stack[top-1],stack[top]))
        top--;
        f[data[i].id]=max(f[data[i].id],data[stack[top]].x*a[data[i].id]+data[stack[top]].y*b[data[i].id]);
    }
    solve(mid+1,r);
    merge(l,r);
}
int main()
{
    scanf("%d%lf",&n,&f[0]);
    for(int i=1;i<=n;i++)
    {
        scanf("%lf%lf%lf",&a[i],&b[i],&R[i]);
        data[i].id=i,data[i].s=-a[i]/b[i];
    }
    sort(data+1,data+1+n);
    solve(1,n);
    printf("%.3lf\n",f[n]);
    return 0;
}