BZOJ1492：[NOI2007]货币兑换——题解

#include<iostream>
#include<cstring>
#include<cstdio>
#include<cmath>
#include<algorithm>
using namespace std;
typedef double dl;
const int N=1e5+5;
struct node{
    dl x,y;
    inline bool operator <(const node &b)const{
        return x<b.x||x==b.x&&y<b.y;
    }
}p[N],que[N];
int n,t[N],tmp[N];
dl f[N],a[N],b[N],rate[N],ans;
inline bool cmp(int x,int y){
    return a[x]*b[y]<a[y]*b[x];
}
inline bool slope(node k,node j,node i){
    return (j.x-i.x)*(k.y-i.y)-(j.y-i.y)*(k.x-i.x)<=0;
}
inline dl suan(node j,int i){
    return j.x*a[i]+j.y*b[i];
}
void cdq(int l,int r){
    if(l==r){
        f[l]=max(f[l],f[l-1]);
        ans=max(ans,f[l]);
        p[l].y=f[l]/(a[l]*rate[l]+b[l]);
        p[l].x=p[l].y*rate[l];
        return;
    }
    int mid=(l+r)>>1,idx1=l,idx2=mid+1,ql=1,qr=0;
    for(int i=l;i<=r;i++){
        if(t[i]<=mid)tmp[idx1++]=t[i];
        else tmp[idx2++]=t[i];
    }
    for(int i=l;i<=r;i++)t[i]=tmp[i];
    cdq(l,mid);
    for(int i=l;i<=mid;i++){
        while(qr>1&&slope(que[qr-1],que[qr],p[i]))qr--;
        que[++qr]=p[i];
    }
    for(int i=mid+1;i<=r;i++){
        int j=t[i];
        while(ql<qr&&suan(que[ql],j)<=suan(que[ql+1],j))ql++;
        f[j]=max(f[j],suan(que[ql],j));
    }
    cdq(mid+1,r);
    if(l==1&&r==n)return;
    ql=l,idx1=l,idx2=mid+1;
    while(ql<=r){
        if(idx2>r||idx1<=mid&&p[idx1]<p[idx2])que[ql++]=p[idx1++];
        else que[ql++]=p[idx2++];
    }
    for(int i=l;i<=r;i++)p[i]=que[i];
    return;
}
int main(){
    scanf("%d%lf",&n,&f[0]);
    for(int i=1;i<=n;i++){
        scanf("%lf%lf%lf",&a[i],&b[i],&rate[i]);
        t[i]=i;
    }
    sort(t+1,t+n+1,cmp);
    cdq(1,n);
    printf("%.3lf\n",ans);
    return 0;
}