【bzoj1036】树的统计 树链剖分/LCT

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

【题解】

看到题目，发现是树剖一眼题，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;}

然后我发现这题被贴上了LCT的标签，于是去搞了一发LCT，比树剖要慢一些。

#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]);}}