【ZJOI2008】树的统计（树链剖分）

传送门

Solution:

就是树链剖分入门题啦~

// luogu-judger-enable-o2
#include<bits/stdc++.h>
#define N 30005
#define M 200005
#define lson now<<1
#define rson now<<1|1
#define INF 0x7fffffff
using namespace std;
int n,tot,first[N],val[N];
int father[N],size[N],maxson[N],depth[N],top[N],id[N],sign,wnew[N];
int ans=0;
struct Edge
{
	int to,next;
}edge[2*N];
inline void addedge(int x,int y)
{
	tot++;
	edge[tot].to=y;
	edge[tot].next=first[x];
	first[x]=tot;
}
struct node
{
	int l,r,sum,maxv;
}tree[4*N];
inline void build(int l,int r,int now)
{
	tree[now].l=l,tree[now].r=r,tree[now].sum=0,tree[now].maxv=0;
	if(l==r)
	{
		tree[now].sum=wnew[l];
		tree[now].maxv=wnew[l];
		return;
	}
	int m=(l+r)>>1;
	build(l,m,lson);
	build(m+1,r,rson);
	
	tree[now].sum=tree[lson].sum+tree[rson].sum;
	tree[now].maxv=max(tree[lson].maxv,tree[rson].maxv);
}
inline void update(int now,int x,int k)
{
	if(tree[now].l==x&&tree[now].r==x)
	{
		tree[now].sum=k;
		tree[now].maxv=k;
		return;
	}
	int m=(tree[now].l+tree[now].r)>>1;
	if(x<=m) update(lson,x,k);
	else update(rson,x,k);
	
	tree[now].sum=tree[lson].sum+tree[rson].sum;
	tree[now].maxv=max(tree[lson].maxv,tree[rson].maxv);
}
inline void query_sum(int l,int r,int now)
{
	if(l<=tree[now].l&&tree[now].r<=r) 
	{
		ans+=tree[now].sum;
		return;
	}
	int m=(tree[now].l+tree[now].r)>>1;
	if(l<=m)	query_sum(l,r,lson);
	if(r>m)	query_sum(l,r,rson);
}
inline void query_max(int l,int r,int now)
{
	if(l<=tree[now].l&&tree[now].r<=r) 
	{
		ans=max(ans,tree[now].maxv);
		return;
	}
	int m=(tree[now].l+tree[now].r)>>1;
	if(l<=m)	query_max(l,r,lson);
	if(r>m)	query_max(l,r,rson);
}
inline void dfs1(int now,int fa)
{
	father[now]=fa;
	size[now]=1;
	depth[now]=depth[fa]+1;
	for(int u=first[now];u;u=edge[u].next)
	{
		int vis=edge[u].to;
		if(vis==fa)	continue;
		dfs1(vis,now);
		size[now]+=size[vis];
		if(size[vis]>size[maxson[now]])	maxson[now]=vis;
	}
}
inline void dfs2(int now,int topf)
{
	id[now]=++sign;
	top[now]=topf;
	wnew[sign]=val[now];
	if(maxson[now])	dfs2(maxson[now],topf);
	for(int u=first[now];u;u=edge[u].next)
	{
		int vis=edge[u].to;
		if(vis==father[now]||vis==maxson[now])	continue;
		dfs2(vis,vis);
	}
}
inline int qmax(int x,int y)
{
	int ret=-INF;
	while(top[x]!=top[y])
	{
		if(depth[top[x]]<depth[top[y]])	swap(x,y);//默认x比y深 
	
		ans=-INF;
		query_max(id[top[x]],id[x],1);
		ret=max(ret,ans);
	
		x=father[top[x]];
	}
	if(depth[x]<depth[y]) swap(x,y);
	
	ans=-INF;
	query_max(id[y],id[x],1);
	return max(ret,ans);
}
inline int qsum(int x,int y)
{
	int ret=0;
	while(top[x]!=top[y])
	{
		if(depth[top[x]]<depth[top[y]])	swap(x,y);//默认x比y浅
	
		ans=0;
		query_sum(id[top[x]],id[x],1);
		ret+=ans;
	
		x=father[top[x]];
	}
	if(depth[x]<depth[y]) swap(x,y);
	
	ans=0;
	query_sum(id[y],id[x],1);
	ret+=ans;
	
	return ret;
}
int main()
{
	cin>>n;
	for(int i=1;i<=n-1;i++)
	{
		int x,y;
		cin>>x>>y;
		addedge(x,y);
		addedge(y,x);
	}
	for(int i=1;i<=n;i++)	cin>>val[i];
	dfs1(1,0);
	dfs2(1,1);
	build(1,n,1);
	int Q;
	cin>>Q;
	while(Q--)
	{
		string s;
		int x,y;
		cin>>s>>x>>y;
		if(s=="CHANGE")	update(1,id[x],y);
		if(s=="QMAX") cout<<qmax(x,y)<<'\n';
		if(s=="QSUM") cout<<qsum(x,y)<<'\n';
	}
	return  0;
}