NOI2007货币兑换

用Splay维护凸包

以后还是建议用CDQ吧。

Splay比较难调试

/*
@Date    : 2019-08-18 08:04:31
@Author  : Adscn (adscn@qq.com)
@Link    : https://www.cnblogs.com/LLCSBlog
*/
#include<bits/stdc++.h>
using namespace std;
#define IL inline
#define RG register
#define gi getint()
#define gc getchar()
#define File(a) freopen(a".in","r",stdin);freopen(a".out","w",stdout)
IL int getint()
{
	RG int xi=0;
	RG char ch=gc;
	bool f=0;
	while(ch<'0'||ch>'9')ch=='-'?f=1:f,ch=gc;
	while(ch>='0'&&ch<='9')xi=(xi<<1)+(xi<<3)+ch-48,ch=gc;
	return f?-xi:xi;
}
template<typename T>
IL void pi(T k,char ch=0)
{
	if(k<0)k=-k,putchar('-');
	if(k>=10)pi(k/10,0);
	putchar(k%10+'0');
	if(ch)putchar(ch);
}
const int N=1e5+7;
const double eps=1e-8;
double dp[N],A[N],B[N],R[N];
__inline__ __attribute__((always_inline))
int dcmp(double x){
	if(fabs(x)<eps)return 0;
	return x<0?-1:1;
}
namespace SplayTree{
	struct node;
	typedef node * tree;
	struct node{
		tree ch[2],par;
		double lk,rk;//lk>rk
		double x,y;
		node(){}
		node(const node &b,tree p){x=b.x,y=b.y,par=p,ch[0]=ch[1]=NULL;}
		inline bool operator == (const node &b)const{return dcmp(x-b.x)==0&&dcmp(y-b.y)==0;}
	}*root=NULL;
	inline bool ws(tree x,tree p){return p?p->ch[1]==x:0;}
	inline void connect(tree x,tree p,bool wh){x?(x->par=p):0,(p?p->ch[wh]:root)=x;}
	inline void rotate(tree x)
	{
		tree p=x->par,g=p->par;
		bool t=ws(x,p);
		connect(x,g,ws(p,g)),connect(x->ch[!t],p,t),connect(p,x,!t);
	}
	inline void Splay(tree x,tree y)
	{
		while(x&&x->par!=y)
		{
			tree p=x->par,g=p->par;
			if(g!=y)rotate(ws(x,p)^ws(p,g)?x:p);
			rotate(x);
		}
	}
	bool ok(tree x,double p){return x->lk+eps>=p&&x->rk<=p+eps;}
	tree find(double num)
	{
		tree x=root;
		while(x&&!ok(x,num))x=x->ch[x->lk>=num+eps];
		return Splay(x,NULL),x;
	}
	double slope(tree x,tree y){
		if(dcmp(x->x-y->x)==0)return -1e9;
		return (y->y-x->y)/(y->x-x->x);
	}
	tree pre(tree x)
	{
		tree y=x->ch[0],ret=y;
		while(y)
			if(y->lk+eps>=slope(x,y))ret=y,y=y->ch[1];
			else y=y->ch[0];
		return ret;
	}
	tree nxt(tree x)
	{
		tree y=x->ch[1],ret=y;
		while(y)
			if(y->rk<=slope(x,y)+eps)ret=y,y=y->ch[0];
			else y=y->ch[1];
		return ret;
	}
	inline void insert(node p)
	{
		if(!root)root=new node(p,NULL);
		else 
			for(tree x=root;x;x=x->ch[p.x>x->x+eps])
				if(!x->ch[p.x>x->x+eps]){
					x->ch[p.x>x->x+eps]=new node(p,x);
					Splay(x->ch[p.x>x->x+eps],NULL);
					return ;
				}
	}
	inline void free_(tree &x)
	{
		if(!x)return;
		free_(x->ch[0]),free_(x->ch[1]);
		delete x;
		x=NULL;
	}
	inline void update(node now){
		insert(now);
		tree x=root;
		assert(*root==now);
		if(x->ch[0]){
			tree p=pre(x);
			Splay(p,x);free_(p->ch[1]);
			x->lk=p->rk=slope(p,x);
		}
		else x->lk=1e9;
		if(x->ch[1]){
			tree p=nxt(x);
			Splay(p,x);free_(p->ch[0]);
			x->rk=p->lk=slope(p,x);
		}
		else x->rk=-1e9;
		if(x->lk<=x->rk+eps){
			root=x->ch[0];
			connect(x->ch[1],root,1),root->par=NULL;
			root->lk=slope(root,root->ch[1]);
			if(root->ch[1])root->ch[1]->rk=root->lk;
			delete x;
		}
	}
}
using namespace SplayTree;
int main(void)
{
	int n=gi;cin>>dp[0];
	for(int i=1;i<=n;++i)
	{
		scanf("%lf%lf%lf",A+i,B+i,R+i);
		tree j=find(-A[i]/B[i]);
		dp[i]=dp[i-1];
		if(j)dp[i]=max(dp[i-1],j->x*A[i]+j->y*B[i]);
		node nw;
		nw.y=dp[i]/(A[i]*R[i]+B[i]),nw.x=nw.y*R[i];
		update(nw);
	}
	printf("%.3lf
",dp[n]);
	return 0;
}