BZOJ 2809 APIO2012 dispatching Treap+启发式合并 / 可并堆

题目大意：给定一棵树，选定一棵子树中的一些点，薪水和不能超过m，求点的数量*子树根节点的领导能力的最大值

考虑对于每个节点，我们维护一种数据结构，在其中贪心寻找薪金小的雇佣。

每个节点暴力重建一定不行，我们考虑可并数据结构，每个节点将子节点的信息直接合并即可

可以用启发式合并的Treap，也可以用可并堆

今天特意去学了这玩应0.0 先写了左偏树 然后又写了下随机堆…… 后者速度上更快一些 不过建议从左偏树开始学起

总之平衡树常数各种大就是了0.0

Treap+启发式合并

#include<cstdio>
#include<cstring>
#include<iostream>
#include<algorithm>
#define M 100100
using namespace std;
typedef long long ll;
struct abcd{
	abcd *ls,*rs;
	int key;
	int cnt,siz;
	ll num,sum;
	abcd (ll x,int y);
	void Maintain();
}*null=new abcd(0,0),*tree[M];
struct edge{
	int to,next;
}table[M];
int head[M],tot;
int n,root;
ll m,ans,leadership[M];
void Add(int x,int y)
{
	table[++tot].to=y;
	table[tot].next=head[x];
	head[x]=tot;
}
abcd :: abcd(ll x,int y)
{
	ls=rs=null;
	sum=x*y;
	num=x;
	cnt=siz=y;
	key=y?rand():0;
}
void abcd :: Maintain()
{
	siz=ls->siz+rs->siz+cnt;
	sum=ls->sum+rs->sum+num*cnt;
}
void Zig(abcd *&x)
{
	abcd *y=x->ls;
	x->ls=y->rs;
	y->rs=x;
	x=y;
	x->rs->Maintain();
}
void Zag(abcd *&x)
{
	abcd *y=x->rs;
	x->rs=y->ls;
	y->ls=x;
	x=y;
	x->ls->Maintain();
}
void Insert(abcd *&x,ll y,int z)
{
	if(x==null)
	{
		x=new abcd(y,z);
		return ;
	}
	if(y==x->num)
		x->cnt+=z;
	else if(y<x->num)
	{
		Insert(x->ls,y,z);
		if(x->ls->key>x->key)
			Zig(x);
	}
	else
	{
		Insert(x->rs,y,z);
		if(x->rs->key>x->key)
			Zag(x);
	}
	x->Maintain();
}
int Query(abcd *x,ll y)
{
	if(x==null)
		return 0;
	ll temp=x->ls->sum;int re=0;
	if(y<=temp)	return Query(x->ls,y);
	re+=x->ls->siz;y-=temp;
	if(y<=x->num*x->cnt)
		return re+y/x->num;
	re+=x->cnt;y-=x->num*x->cnt;
	return re+Query(x->rs,y);
}
void Decomposition(abcd *&x,int y)
{
	if(x==null)
		return ;
	Decomposition(x->ls,y);
	Decomposition(x->rs,y);
	Insert(tree[y],x->num,x->cnt);
	delete x;
	x=null;
}
void Tree_DP(int x)
{
	int i;
	for(i=head[x];i;i=table[i].next)
	{
		Tree_DP(table[i].to);
		if(tree[x]->siz<tree[table[i].to]->siz)
			swap(tree[x],tree[table[i].to]);
		Decomposition(tree[table[i].to],x);
	}
	ans=max(ans,leadership[x]*Query(tree[x],m));
}
int main()
{
	
	//freopen("2809.in","r",stdin);
	//freopen("2809.out","w",stdout);
	
	int i,fa;
	ll x;
	cin>>n>>m;
	for(i=1;i<=n;i++)
	{
		scanf("%d%lld%lld",&fa,&x,&leadership[i]);
		if(!fa) root=i;
		else Add(fa,i);
		tree[i]=new abcd(x,1);
	}
	Tree_DP(root);
	cout<<ans<<endl;
}
//lld!!

左偏树

#include<cstdio>
#include<cstring>
#include<iostream>
#include<algorithm>
#define M 100100
using namespace std;
struct abcd{
	abcd *ls,*rs;
	int num,h;
	abcd(int x); 
}*null=new abcd(0),*tree[M];
struct edge{
	int to,next;
}table[M];
int head[M],tot;
int n,m,root,leadership[M],sum[M],size[M];
long long ans;
void Add(int x,int y)
{
	table[++tot].to=y;
	table[tot].next=head[x];
	head[x]=tot;
}
abcd :: abcd(int x)
{
	ls=rs=null;
	num=x;
	if(x) h=0;
	else h=-1;
}
abcd* Merge(abcd *x,abcd *y)
{
	if(x==null) return y;
	if(y==null) return x;
	if(x->num<y->num)
		swap(x,y);
	x->rs=Merge(x->rs,y);
	if(x->ls->h<x->rs->h)
		swap(x->ls,x->rs);
	x->h=x->rs->h+1;
	return x;
}
void Tree_DP(int x)
{
	int i;
	for(i=head[x];i;i=table[i].next)
	{
		Tree_DP(table[i].to);
		tree[x]=Merge(tree[x],tree[table[i].to]);
		sum[x]+=sum[table[i].to];
		size[x]+=size[table[i].to];
		while(sum[x]>m)
		{
			sum[x]-=tree[x]->num;
			--size[x];
			tree[x]=Merge(tree[x]->ls,tree[x]->rs);
		}
	}
	ans=max(ans,(long long)size[x]*leadership[x]);
}
int main()
{
	int i,fa,x;
	cin>>n>>m;
	for(i=1;i<=n;i++)
	{
		scanf("%d%d%d",&fa,&x,&leadership[i]);
		if(!fa) root=i;
		else Add(fa,i);
		tree[i]=new abcd(x);
		sum[i]=x;
		size[i]=1;
	}
	Tree_DP(root);
	cout<<ans<<endl;
}

随机堆

#include<cstdio>
#include<cstring>
#include<iostream>
#include<algorithm>
#define M 100100
using namespace std;
struct abcd{
	abcd *ls,*rs;
	int num;
	abcd(int x); 
}*null=new abcd(0),*tree[M];
struct edge{
	int to,next;
}table[M];
bool son;
int head[M],tot;
int n,m,root,leadership[M],sum[M],size[M];
long long ans;
void Add(int x,int y)
{
	table[++tot].to=y;
	table[tot].next=head[x];
	head[x]=tot;
}
abcd :: abcd(int x)
{
	ls=rs=null;
	num=x;
}
abcd* Merge(abcd *x,abcd *y)
{
	if(x==null) return y;
	if(y==null) return x;
	if(x->num<y->num)
		swap(x,y);
	if(son^=1)
		x->rs=Merge(x->rs,y);
	else
		x->ls=Merge(x->ls,y);
	return x;
}
void Tree_DP(int x)
{
	int i;
	for(i=head[x];i;i=table[i].next)
	{
		Tree_DP(table[i].to);
		tree[x]=Merge(tree[x],tree[table[i].to]);
		sum[x]+=sum[table[i].to];
		size[x]+=size[table[i].to];
		while(sum[x]>m)
		{
			sum[x]-=tree[x]->num;
			--size[x];
			tree[x]=Merge(tree[x]->ls,tree[x]->rs);
		}
	}
	ans=max(ans,(long long)size[x]*leadership[x]);
}
int main()
{
	int i,fa,x;
	cin>>n>>m;
	for(i=1;i<=n;i++)
	{
		scanf("%d%d%d",&fa,&x,&leadership[i]);
		if(!fa) root=i;
		else Add(fa,i);
		tree[i]=new abcd(x);
		sum[i]=x;
		size[i]=1;
	}
	Tree_DP(root);
	cout<<ans<<endl;
}