洛谷-P3178 [HAOI2015]树上操作（树链剖分）

题目链接：https://www.luogu.org/problemnew/show/P3178

题目大意：三种操作，按题目意思操作即可。

思路：树链剖分板子。单点修改，区间修改，区间查询。

ACCode：

//#pragma comment(linker, "/STACK:1024000000,1024000000")
  
#include<stdio.h>
#include<string.h> 
#include<math.h> 
   
#include<map>  
#include<set>
#include<deque> 
#include<queue> 
#include<stack> 
#include<bitset>
#include<string> 
#include<fstream>
#include<iostream> 
#include<algorithm> 
using namespace std; 
  
#define ll long long 
#define Pair pair<int,int>
//#define max(a,b) (a)>(b)?(a):(b)
//#define min(a,b) (a)<(b)?(a):(b)
#define clean(a,b) memset(a,b,sizeof(a))// ??
//std::ios::sync_with_stdio(false);
//  register
const int MAXN=1e5+10;
const int INF32=0x3f3f3f3f;
const ll INF64=0x3f3f3f3f3f3f3f3f;
const ll mod=1e9+7;
const double PI=acos(-1.0);
const double EPS=1.0e-8;

class Segment{
	ll TreeSum[MAXN<<2],TreeMAX[MAXN<<2],Lazy[MAXN<<2],Size[MAXN<<2];
	
	void PushDown(int rt){
		if(Lazy[rt]==0) return ;
		TreeSum[rt<<1]=(TreeSum[rt<<1]+Size[rt<<1]*Lazy[rt]);
		TreeSum[rt<<1|1]=(TreeSum[rt<<1|1]+Size[rt<<1|1]*Lazy[rt]);
		
		Lazy[rt<<1]=(Lazy[rt<<1]+Lazy[rt]);
		Lazy[rt<<1|1]=(Lazy[rt<<1|1]+Lazy[rt]);
		Lazy[rt]=0;
	}
	public : void Intt(){
		clean(Lazy,0);clean(Size,0);
	}
	public : void Build(int l,int r,int rt,int a[]){
		Size[rt]=r-l+1;
//		printf("rt=%d l=%d r=%d Tree[rt]=%d\n",rt,l,r,Tree[rt]);
		if(l==r){
			TreeSum[rt]=1ll*a[l];//TreeMAX[rt]=a[l];
			return ;
		}int mid=(l+r)>>1;
		Build(l,mid,rt<<1,a);Build(mid+1,r,rt<<1|1,a);
		TreeSum[rt]=(TreeSum[rt<<1]+TreeSum[rt<<1|1]);
//		TreeMAX[rt]=max(TreeMAX[rt<<1],TreeMAX[rt<<1|1]);
	}
	public : void Update(int ql,int qr,int val,int l,int r,int rt){
		if(ql<=l&&r<=qr){
			TreeSum[rt]+=1ll*Size[rt]*val;//TreeMAX[rt]=val;
			Lazy[rt]+=val;
			return ;
		}int mid=(l+r)>>1;
		PushDown(rt);
		if(ql<=mid) Update(ql,qr,val,l,mid,rt<<1);
		if(qr>mid) Update(ql,qr,val,mid+1,r,rt<<1|1);
		TreeSum[rt]=(TreeSum[rt<<1]+TreeSum[rt<<1|1]);
//		TreeMAX[rt]=max(TreeMAX[rt<<1],TreeMAX[rt<<1|1]);
	}
	public : ll QuerySum(int ql,int qr,int l,int r,int rt){
		if(ql<=l&&r<=qr) return TreeSum[rt];
		PushDown(rt);
		int mid=(l+r)>>1;
		ll ans=0;
		if(ql<=mid) ans=(ans+QuerySum(ql,qr,l,mid,rt<<1));
		if(qr>mid) ans=(ans+QuerySum(ql,qr,mid+1,r,rt<<1|1));
		return ans;
	}
	public : int QueryMAX(int ql,int qr,int l,int r,int rt){
		if(ql<=l&&r<=qr) return TreeMAX[rt];
		int mid=(l+r)>>1;
		int ans=-INF32;
		if(ql<=mid) ans=max(ans,QueryMAX(ql,qr,l,mid,rt<<1));
		if(qr>mid) ans=max(ans,QueryMAX(ql,qr,mid+1,r,rt<<1|1));
		return ans;
	}
	public : void Show(int l,int r,int rt){
		printf("rt=%d l=%d r=%d TreeMAX[rt]=%d TreeSum[rt]=%d\n",rt,l,r,TreeMAX[rt],TreeSum[rt]);
		if(l==r) return ;
		int mid=(l+r)>>1;
		Show(l,mid,rt<<1);Show(mid+1,r,rt<<1|1);
	}
};
struct Node1{
	int v,val,nxt;
	Node1(int _v=0,int _val=0,int _nxt=0){
		v=_v;val=_val;nxt=_nxt;
	}
};
Segment Seg;
Node1 Edge[MAXN<<2];
int Head[MAXN],Ecnt;
int Deep[MAXN],Fa[MAXN],Size[MAXN],Son[MAXN];
int Idx[MAXN],Icnt;//重新标号 
int Top[MAXN];
int A[MAXN],B[MAXN];
int n,m;

void Intt(){
	Seg.Intt();
	clean(Head,-1);Ecnt=0;
	clean(Deep,0);clean(Fa,-1);clean(Size,0);clean(Son,-1);
	Icnt=0;
}
void AddEdge(int u,int v,int val){
	Edge[Ecnt]=Node1(v,val,Head[u]);
	Head[u]=Ecnt++;
}
int DFS1(int u,int fa,int dep){
	Deep[u]=dep;
	Fa[u]=fa;
	Size[u]=1;
	int maxson=-1;
	for(int i=Head[u];i+1;i=Edge[i].nxt){
		int temp=Edge[i].v;
		if(temp==fa) continue;
		Size[u]+=DFS1(temp,u,dep+1);
		if(Size[temp]>maxson){
			maxson=Size[temp];
			Son[u]=temp;
		}
	}return Size[u];
}
void DFS2(int u,int topfa){
	Idx[u]=++Icnt;
//	cout<<"u,Idx[u]"<<u<<" "<<Idx[u]<<endl;
	Top[u]=topfa;
	B[Idx[u]]=A[u];
	if(Son[u]==-1) return ;
	DFS2(Son[u],topfa);
	for(int i=Head[u];i+1;i=Edge[i].nxt){
		int temp=Edge[i].v;
		if(Idx[temp]==0){
			DFS2(temp,temp);
		}
	}
}
void UpdateDot(int u,int val){
	Seg.Update(Idx[u],Idx[u],val,1,n,1);
}
void UpdateSubTree(int u,int val){
	int l=Idx[u],r=Idx[u]+Size[u]-1;
	Seg.Update(l,r,val,1,n,1);
}
ll QuerySum(int l,int r){
	ll ans=0;
	while(Top[l]!=Top[r]){
		if(Deep[Top[l]]<Deep[Top[r]]) swap(l,r);
		ans+=Seg.QuerySum(Idx[Top[l]],Idx[l],1,n,1);
		l=Fa[Top[l]];
	}
	if(Deep[l]>Deep[r]) swap(l,r);
	ans+=Seg.QuerySum(Idx[l],Idx[r],1,n,1);
	return ans;
}
int main(){
	scanf("%d%d",&n,&m);Intt();
	for(int i=1;i<=n;++i){
		scanf("%d",&A[i]);
	}
	for(int i=1;i<n;++i){
		int x,y;scanf("%d%d",&x,&y);
		AddEdge(x,y,1);AddEdge(y,x,1);
	}
	DFS1(1,-1,1);
//	cout<<"DFS2:"<<endl;
	DFS2(1,1);
//	cout<<"Icnt: "<<Icnt<<endl;
//	for(int i=1;i<=n;++i){
//		cout<<"i,Idx[i],Size[i]: "<<i<<" "<<Idx[i]<<" "<<Size[i]<<endl;
//	}
	Seg.Build(1,n,1,B);
//	Seg.Show(1,n,1);
	for(int i=1;i<=m;++i){
		int oper;scanf("%d",&oper);
		if(oper==1){//x z,节点u的权值+z 
			int x,z;scanf("%d%d",&x,&z);
			UpdateDot(x,z);
		}
		else if(oper==2){//x z。x为根节点的子树所有点+z 
			int x,z;scanf("%d%d",&x,&z);
			UpdateSubTree(x,z);
		}
		else if(oper==3){//x，节点x到根节点的Sum 
			int x;scanf("%d",&x);
			printf("%lld\n",QuerySum(1,x));
		}
	}
}