BZOJ 1767: [Ceoi2009]harbingers

树上斜率优化

#include<cstdio>
#include<algorithm>
using namespace std;
int cnt,n,top,v[100005],w[100005],last[100005],Dep[100005],Last_ID[100005],ID[100005];
long long F[100005];
struct node1{
	long long k,b;
}stack[100005],Last_val[100005];
struct node{
	int to,next,val;
}e[200005];
void add(int a,int b,int c){
	e[++cnt].to=b;
	e[cnt].next=last[a];
	e[cnt].val=c;
	last[a]=cnt;
}
double check(node1 a,node1 b){
	return ((double)a.b-b.b)/(b.k-a.k);
}
void insert(node1 line,int x){
	int L=1,R=top;
	if (top<=1 || check(stack[top],stack[top-1])<check(stack[top],line)) ID[x]=top+1;
	else{
		while (L<R){
			int mid=(L+R)>>1;
			double X;
			if (mid==1) X=-1ll<<60;
			else X=check(stack[mid],stack[mid-1]);
			double Y=check(line,stack[mid]);
			if (X>Y) R=mid;
			else L=mid+1;
		}
		ID[x]=L;
	}
	Last_ID[x]=top;
	Last_val[x]=stack[ID[x]];
	top=ID[x];
	stack[ID[x]]=line;
}
void solve(int x){
	int L=1,R=top;
	while (L<R){
		int mid=(L+R)>>1;
		double l,r;
		if (mid==1) l=-1ll<<60;
		else l=check(stack[mid],stack[mid-1]);
		if (mid==top) r=1ll<<60;
		else r=check(stack[mid],stack[mid+1]);
		if (v[x]>=l && v[x]<=r){
			L=mid;
			break;
		}
		else if (v[x]<l) R=mid-1;
		else L=mid+1;
	}
	F[x]=stack[L].k*v[x]+stack[L].b;
	F[x]+=1ll*Dep[x]*v[x]+w[x];
	//for (int i=1; i<=top; i++)
	//	F[x]=min(F[x],-1ll*Dep[stack[i]]*v[x]+F[stack[i]]);
//	printf("ans:%d %d %lld\n",x,-Dep[x],F[x]);
	insert((node1){-Dep[x],F[x]},x);
}
void dfs(int x,int fa,int dep){
	Dep[x]=dep;
	solve(x);
	for (int i=last[x]; i; i=e[i].next){
		int V=e[i].to;
		if (V==fa) continue;
		dfs(V,x,dep+e[i].val);
	}
	stack[ID[x]]=Last_val[x];
	top=Last_ID[x];
}
int main(){
	scanf("%d",&n);
	for (int i=1; i<n; i++){
		int x,y,z;
		scanf("%d%d%d",&x,&y,&z);
		add(x,y,z);
		add(y,x,z);
	}
	for (int i=2; i<=n; i++) scanf("%d%d",&w[i],&v[i]);
	dfs(1,0,0);
	for (int i=2; i<=n; i++)
		printf("%lld ",F[i]);
	return 0;
}