【bzoj1036】樹的統計 樹鏈剖分/LCT

AC通道：http://www.lydsy.com/JudgeOnline/problem.php?id=1036

【題解】

看到題目，發現是樹剖一眼題，所以就秒掉了。

#include<iostream>
#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<ctime>
#include<cmath>
#include<algorithm>
using namespace std;
typedef long long ll;
#define FILE "read"
#define MAXN 30010
#define INF 1000000000
#define up(i,j,n) for(int i=j;i<=n;++i)
#define dn(i,j,n) for(int i=j;i>=n;--i)
#define cmax(a,b) a=max(a,b)
#define cmin(a,b) a=min(a,b)
namespace INIT{
	char buf[1<<15],*fs,*ft;
	inline char getc(){return (fs==ft&&(ft=(fs=buf)+fread(buf,1,1<<15,stdin),fs==ft))?0:*fs++;}
	inline int read(){
		int x=0,f=1;  char ch=getchar();
		while(!isdigit(ch))  {if(ch=='-')  f=-1;  ch=getchar();}
		while(isdigit(ch))  {x=x*10+ch-'0';  ch=getchar();}
		return x*f;
	}
}using namespace INIT;
struct node{int y,next;}e[MAXN*2];
int n,m,z,len,Link[MAXN],size[MAXN],son[MAXN],w[MAXN],f[MAXN],top[MAXN],deep[MAXN],sum[MAXN*8],maxx[MAXN*8];
void insert(int x,int y){e[++len].next=Link[x];Link[x]=len;e[len].y=y;}
void dfs(int x){
	size[x]=1;  son[x]=0;
	for(int i=Link[x];i;i=e[i].next){
		if(e[i].y==f[x])  continue;
		deep[e[i].y]=deep[x]+1;  f[e[i].y]=x;
		dfs(e[i].y);  size[x]+=size[e[i].y];
		if(size[e[i].y]>size[son[x]])  son[x]=e[i].y;
	}
}
void dfs(int x,int temp){
	w[x]=++z;  top[x]=temp;
	if(son[x])  dfs(son[x],temp);
	for(int i=Link[x];i;i=e[i].next)
		if(e[i].y!=son[x]&&e[i].y!=f[x])  dfs(e[i].y,e[i].y);
}
void relord(int p) {sum[p]=sum[p<<1]+sum[p<<1|1]; maxx[p]=max(maxx[p<<1],maxx[p<<1|1]);}
void updata(int p,int l,int r,int x,int v){
	if(x>r||x<l)  return;
	if(l==r)  {maxx[p]=sum[p]=v; return;}
	int mid=(l+r)>>1;
	updata(p<<1,l,mid,x,v);  updata(p<<1|1,mid+1,r,x,v);
	relord(p);
}
int findmax(int p,int l,int r,int x,int y){
	if(x>r||y<l)  return -INF;
	if(x<=l&&y>=r)  return maxx[p];
	int mid=(l+r)>>1;
	return max(findmax(p<<1,l,mid,x,y),findmax(p<<1|1,mid+1,r,x,y));
}
int findsum(int p,int l,int r,int x,int y){
	if(x>r||y<l)  return 0;
	if(x<=l&&y>=r)  return sum[p];
	int mid=(l+r)>>1;
	return findsum(p<<1,l,mid,x,y)+findsum(p<<1|1,mid+1,r,x,y);
}
int askmax(int x,int y){
	int f1=top[x],f2=top[y],temp(-INF);
	while(f1!=f2){
		if(deep[f1]<deep[f2])  swap(f1,f2),swap(x,y);
		cmax(temp,findmax(1,1,z,w[f1],w[x]));
		x=f[f1];  f1=top[x];
	}
	if(deep[x]>deep[y])  swap(x,y);
	cmax(temp,findmax(1,1,z,w[x],w[y]));
	return temp;
}
int asksum(int x,int y){
	int f1=top[x],f2=top[y],temp(0);
	while(f1!=f2){
		if(deep[f1]<deep[f2])  swap(f1,f2),swap(x,y);
		temp+=findsum(1,1,z,w[f1],w[x]);
		x=f[f1];  f1=top[x];
	}
	if(deep[x]>deep[y])  swap(x,y);
	temp+=findsum(1,1,z,w[x],w[y]);
	return temp;
}
int main(){
	freopen(FILE".in","r",stdin);
	freopen(FILE".out","w",stdout);
	n=read();
	up(i,1,n-1) {int x=read(),y=read(); insert(x,y); insert(y,x);}
	dfs(1);  dfs(1,1);
	up(i,1,n) {int x=read(); updata(1,1,z,w[i],x);}
	m=read();
	up(i,1,m){
		char ch[10];  scanf("%s",ch);  int x=read(),y=read();
		if(ch[0]=='C') updata(1,1,z,w[x],y);
		else if(ch[1]=='M') printf("%d\n",askmax(x,y));
		else printf("%d\n",asksum(x,y));
	}
	return 0;
}

然後我發現這題被貼上了LCT的標籤，於是去搞了一發LCT，比樹剖要慢一些。

#include<iostream>
#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<ctime>
#include<cmath>
#include<algorithm>
using namespace std;
#define FILE "read"
#define MAXN 30010
#define INF 1000000000
#define up(i,j,n) for(int i=j;i<=n;++i)
#define dn(i,j,n) for(int i=j;i>=n;--i)
namespace INIT{
	char buf[1<<15],*fs,*ft;
	inline char getc(){return (fs==ft&&(ft=(fs=buf)+fread(buf,1,1<<15,stdin),fs==ft))?0:*fs++;}
	inline int read(){
		int x=0,f=1;  char ch=getchar();
		while(!isdigit(ch))  {if(ch=='-')  f=-1;  ch=getchar();}
		while(isdigit(ch))  {x=x*10+ch-'0';  ch=getchar();}
		return x*f;
	}
}using namespace INIT;
int n,m,v[MAXN],X[MAXN],Y[MAXN];
namespace Link_Cut_Tree{
	int maxx[MAXN],sum[MAXN],f[MAXN],q[MAXN],vis[MAXN],son[MAXN][2];
	bool get(int x){return son[f[x]][1]==x;}
	bool isroot(int x){return (f[x]==0||(son[f[x]][0]!=x&&son[f[x]][1]!=x));}
	void updata(int x){
		maxx[x]=max(maxx[son[x][0]],max(maxx[son[x][1]],v[x]));
		sum[x]=sum[son[x][0]]+sum[son[x][1]]+v[x];
	}
	void pushdown(int x){
		if(vis[x]){
			swap(son[x][0],son[x][1]);
			vis[son[x][0]]^=1;  vis[son[x][1]]^=1;
			vis[x]=0;
		}
	}
	void rotate(int x){
		int y=f[x],z=f[y],which=get(x);
		if(!isroot(y))  son[z][son[z][1]==y]=x;
		son[y][which]=son[x][which^1];  f[son[y][which]]=y;
		son[x][which^1]=y;  f[y]=x;  f[x]=z;
		updata(y);  updata(x);
	}
	void splay(int x){
		int top(0);  q[++top]=x;
		for(int i=x;!isroot(i);i=f[i])  q[++top]=f[i];
		dn(i,top,1)  pushdown(q[i]);
		for(int y=f[x];!isroot(x);rotate(x),y=f[x])
			if(!isroot(y))  rotate(get(x)==get(y)?y:x);
	}
	void access(int x){for(int temp(0);x;temp=x,x=f[x])splay(x),son[x][1]=temp,updata(x);}
	void reverse(int x){access(x);splay(x);vis[x]^=1;}
	void linkk(int x,int y){reverse(x);f[x]=y;}
	void split(int x,int y){reverse(x);access(y);splay(y);}
}
int main(){
	freopen(FILE".in","r",stdin);
	freopen(FILE".out","w",stdout);
	using namespace Link_Cut_Tree;
	n=read();  maxx[0]=-INF;
	up(i,1,n-1)  X[i]=read(),Y[i]=read();
	up(i,1,n)  v[i]=read(),sum[i]=maxx[i]=v[i];
	up(i,1,n-1)  linkk(X[i],Y[i]);
	m=read();
	up(i,1,m){
		char ch[10];  scanf("%s",ch); int x=read(),y=read();
		if(ch[1]=='H')  splay(x),v[x]=y,updata(x);
		else if(ch[1]=='M')  split(x,y),printf("%d\n",maxx[y]);
		else split(x,y),printf("%d\n",sum[y]);
	}
}