bzoj1095[ZJOI2007]Hide 捉迷藏
http://www.lydsy.com/JudgeOnline/problem.php?id=1095
好像有2种做法：线段树维护括号编码&动态树分治。
线段树维护括号编码：
这篇论文是讲得极好的。
#include<cstdio> #include<cstdlib> #include<iostream> #include<fstream> #include<algorithm> #include<cstring> #include<string> #include<cmath> #include<queue> #include<stack> #include<map> #include<utility> #include<set> #include<bitset> #include<vector> #include<functional> #include<deque> #include<cctype> #include<climits> #include<complex> //#include<bits/stdc++.h>适用于CF,UOJ，但不适用于poj using namespace std; typedef long long LL; typedef double DB; typedef pair<int,int> PII; typedef complex<DB> CP; #define mmst(a,v) memset(a,v,sizeof(a)) #define mmcy(a,b) memcpy(a,b,sizeof(a)) #define fill(a,l,r,v) fill(a+l,a+r+1,v) #define re(i,a,b) for(i=(a);i<=(b);i++) #define red(i,a,b) for(i=(a);i>=(b);i--) #define ire(i,x) for(typedef(x.begin()) i=x.begin();i!=x.end();i++) #define fi first #define se second #define m_p(a,b) make_pair(a,b) #define p_b(a) push_back(a) #define SF scanf #define PF printf #define two(k) (1<<(k)) template<class T>inline T sqr(T x){return x*x;} template<class T>inline void upmin(T &t,T tmp){if(t>tmp)t=tmp;} template<class T>inline void upmax(T &t,T tmp){if(t<tmp)t=tmp;} inline int sgn(DB x){if(abs(x)<1e-9)return 0;return(x>0)?1:-1;} const DB Pi=acos(-1.0); int gint() { int res=0;bool neg=0;char z; for(z=getchar();z!=EOF && z!='-' && !isdigit(z);z=getchar()); if(z==EOF)return 0; if(z=='-'){neg=1;z=getchar();} for(;z!=EOF && isdigit(z);res=res*10+z-'0',z=getchar()); return (neg)?-res:res; } LL gll() { LL res=0;bool neg=0;char z; for(z=getchar();z!=EOF && z!='-' && !isdigit(z);z=getchar()); if(z==EOF)return 0; if(z=='-'){neg=1;z=getchar();} for(;z!=EOF && isdigit(z);res=res*10+z-'0',z=getchar()); return (neg)?-res:res; } const int maxn=100000; int n; int now,info[maxn+100]; struct Tedge{int v,next;}edge[2*maxn+100]; int status[maxn+100],ge; void addedge(int u,int v){now++;edge[now].v=v;edge[now].next=info[u];info[u]=now;} int cnt,ty[3*maxn+100],pos[maxn+100]; void dfs(int u) { ty[++cnt]=-1; ty[++cnt]=u; pos[u]=cnt; int i,v; for(i=info[u],v=edge[i].v;i!=-1;i=edge[i].next,v=edge[i].v)if(!pos[v])dfs(v); ty[++cnt]=-2; } struct Tdata { int a,b; Tdata(int _a=0,int _b=0){a=_a;b=_b;} friend Tdata operator +(Tdata l,Tdata r){return (l.b<=r.a)?Tdata(l.a+r.a-l.b,r.b):Tdata(l.a,l.b-r.a+r.b);} friend bool operator ==(Tdata x,Tdata y){return x.a==y.a && x.b==y.b;} friend bool operator !=(Tdata x,Tdata y){return !(x==y);} }; Tdata null=Tdata(-1,-1); /* dist 子区间的最大值 whole 区间[l,r]的二元组(a,b) lp 右端点为黑点的a+b最大的前缀的二元组(a,b) rp 左端点为黑点的a+b最大的后缀的二元组(a,b) lm 右端点为黑点的b-a最大的前缀的二元组(a,b) rm 左端点为黑点的a-b最大的后缀的二元组(a,b) null表示不存在 */ struct Tnode { int dist; Tdata whole,lp,rp,lm,rm; void init(int x); }; void Tnode::init(int x) { int lcnt=(ty[x]==-2),rcnt=(ty[x]==-1); whole=Tdata(lcnt,rcnt); dist=-1; if(ty[x]>=1 && status[ty[x]]) lp=rp=lm=rm=whole; else lp=rp=lm=rm=null; } Tnode make_up(Tnode x,Tnode y) { Tnode res;Tdata p; res.whole=x.whole+y.whole; res.lp=x.lp; if(y.lp!=null) { p=x.whole+y.lp; if(res.lp==null || res.lp.a+res.lp.b<p.a+p.b)res.lp=p; } if(y.lm!=null) { p=x.whole+y.lm; if(res.lp==null || res.lp.a+res.lp.b<p.a+p.b)res.lp=p; } res.rp=y.rp; if(x.rp!=null) { p=x.rp+y.whole; if(res.rp==null || res.rp.a+res.rp.b<p.a+p.b)res.rp=p; } if(x.rm!=null) { p=x.rm+y.whole; if(res.rp==null || res.rp.a+res.rp.b<p.a+p.b)res.rp=p; } res.lm=x.lm; if(y.lm!=null) { p=x.whole+y.lm; if(res.lm==null || res.lm.b-res.lm.a<p.b-p.a)res.lm=p; } res.rm=y.rm; if(x.rm!=null) { p=x.rm+y.whole; if(res.rm==null || res.rm.a-res.rm.b<p.a-p.b)res.rm=p; } res.dist=max(x.dist,y.dist); if(x.rp!=null && y.lm!=null) { p=x.rp+y.lm; upmax(res.dist,p.a+p.b); } if(x.rm!=null && y.lp!=null) { p=x.rm+y.lp; upmax(res.dist,p.a+p.b); } return res; } Tnode tr[4*3*maxn+100]; void build(int rt,int l,int r) { if(l==r){tr[rt].init(l);return;} int mid=(l+r)>>1; build(rt<<1,l,mid); build(rt<<1|1,mid+1,r); tr[rt]=make_up(tr[rt<<1],tr[rt<<1|1]); } void update(int rt,int l,int r,int x) { if(l==r){tr[rt].init(l);return;} int mid=(l+r)/2; if(x<=mid)update(rt<<1,l,mid,x);else update(rt<<1|1,mid+1,r,x); tr[rt]=make_up(tr[rt<<1],tr[rt<<1|1]); } int main() { freopen("bzoj1095.in","r",stdin); freopen("bzoj1095.out","w",stdout); int i; n=gint(); now=-1;mmst(info,-1); re(i,1,n-1){int u=gint(),v=gint();addedge(u,v);addedge(v,u);} dfs(1); re(i,1,n)status[i]=1;ge=n; build(1,1,cnt); int Q;SF("%d\n",&Q); while(Q--) { char t;SF("%c",&t); if(t=='G') { if(ge==0)PF("-1\n");else if(ge==1) PF("0\n"); else PF("%d\n",tr[1].dist); } else { int x;SF("%d",&x); status[x]^=1; if(status[x])ge++;else ge--; update(1,1,cnt,pos[x]); } SF("\n"); } return 0; }
动态树分治：
首先，我们想平常树分治那样，找到一个重心。
然后将这个重心作为新的根，将它的所有儿子及其子树划分成大小相等的两个整体。（普通的树分治是一个儿子作为一个整体，但是这样合并的时候有点麻烦，如果只分成两个整体，合并就比较简单）
分别用一个堆维护这两个整体的黑点到重心的距离。
那么经过重心的最长的路径就是这两个堆的最大值之和。
递归处理这两个整体。
每个点最多属于$logn$个重心。
看程序比较好理解。
#include<cstdio> #include<cstdlib> #include<iostream> #include<fstream> #include<algorithm> #include<cstring> #include<string> #include<cmath> #include<queue> #include<stack> #include<map> #include<utility> #include<set> #include<bitset> #include<vector> #include<functional> #include<deque> #include<cctype> #include<climits> #include<complex> //#include<bits/stdc++.h>适用于CF,UOJ，但不适用于poj using namespace std; typedef long long LL; typedef double DB; typedef pair<int,int> PII; typedef complex<DB> CP; #define mmst(a,v) memset(a,v,sizeof(a)) #define mmcy(a,b) memcpy(a,b,sizeof(a)) #define fill(a,l,r,v) fill(a+l,a+r+1,v) #define re(i,a,b) for(i=(a);i<=(b);i++) #define red(i,a,b) for(i=(a);i>=(b);i--) #define ire(i,x) for(typedef(x.begin()) i=x.begin();i!=x.end();i++) #define fi first #define se second #define m_p(a,b) make_pair(a,b) #define p_b(a) push_back(a) #define SF scanf #define PF printf #define two(k) (1<<(k)) template<class T>inline T sqr(T x){return x*x;} template<class T>inline void upmin(T &t,T tmp){if(t>tmp)t=tmp;} template<class T>inline void upmax(T &t,T tmp){if(t<tmp)t=tmp;} inline int sgn(DB x){if(abs(x)<1e-9)return 0;return(x>0)?1:-1;} const DB Pi=acos(-1.0); int gint() { int res=0;bool neg=0;char z; for(z=getchar();z!=EOF && z!='-' && !isdigit(z);z=getchar()); if(z==EOF)return 0; if(z=='-'){neg=1;z=getchar();} for(;z!=EOF && isdigit(z);res=res*10+z-'0',z=getchar()); return (neg)?-res:res; } LL gll() { LL res=0;bool neg=0;char z; for(z=getchar();z!=EOF && z!='-' && !isdigit(z);z=getchar()); if(z==EOF)return 0; if(z=='-'){neg=1;z=getchar();} for(;z!=EOF && isdigit(z);res=res*10+z-'0',z=getchar()); return (neg)?-res:res; } const int maxn=100000; const int inf=0x3f3f3f3f; struct Priority_Queue { priority_queue<int>heap,delmark; void push(int x){heap.push(x);} void erase(int x){delmark.push(x);} void clear(){while(!delmark.empty() && !heap.empty() && delmark.top()==heap.top())heap.pop(),delmark.pop();} int top(){clear();return heap.empty()?-inf:heap.top();} void pop(){clear();heap.pop();} bool empty(){return heap.size()==delmark.size();} }; int n; int now[2],info[2][maxn+100]; struct Tedge{int v,next,kk,dis;}edge[2][3000000];//注意边数是nlogn int status[maxn+100]; void addedge(int k,int u,int v,int kk=0,int dis=0) { now[k]++; edge[k][now[k]].v=v; edge[k][now[k]].next=info[k][u]; if(k){edge[k][now[k]].kk=kk;edge[k][now[k]].dis=dis;} info[k][u]=now[k]; } int num; PII cd[maxn+100]; Priority_Queue Q[maxn+100][2]; int ans[maxn+100]; int sz[maxn+100],mx[maxn+100]; void getroot(int u,int fa,int all,int &rt) { sz[u]=1;mx[u]=0; int i,v; for(i=info[0][u],v=edge[0][i].v;i!=-1;i=edge[0][i].next,v=edge[0][i].v)if(v!=fa) { getroot(v,u,all,rt); sz[u]+=sz[v]; upmax(mx[u],sz[v]); } upmax(mx[u],all-sz[u]); if(!rt || mx[u]<mx[rt])rt=u; } void dfs(int u,int fa,int dis,int cur,int kind) { addedge(1,u,cur,kind,dis); Q[cur][kind].push(dis); int i,v; for(i=info[0][u],v=edge[0][i].v;i!=-1;i=edge[0][i].next,v=edge[0][i].v)if(v!=fa)dfs(v,u,dis+1,cur,kind); } void calc(int cur) { ans[cur]=max(ans[cd[cur].fi],ans[cd[cur].se]); if(!Q[cur][0].empty() && !Q[cur][1].empty())upmax(ans[cur],Q[cur][0].top()+Q[cur][1].top()); } int prep(int u,int all) { if(all<=2)return 0; int i,rt=0,tmp=0; getroot(u,-1,all,rt); getroot(rt,-1,all,tmp); int cur=++num,sum=0,v; for(i=info[0][rt],v=edge[0][i].v;i!=-1;i=edge[0][i].next,v=edge[0][i].v) { sum+=sz[v]; if(sum>=(all-1)/2 || edge[0][i].next==-1)break; } int st1=info[0][rt],ed1=i,st2=edge[0][ed1].next; edge[0][ed1].next=-1; dfs(rt,-1,0,cur,0); cd[cur].fi=prep(rt,sum+1); edge[0][ed1].next=info[0][rt]=st2; dfs(rt,-1,0,cur,1); cd[cur].se=prep(rt,all-sum); info[0][rt]=st1; calc(cur); return cur; } void update(int x) { int i,cur,dis,kind; for(i=info[1][x],cur=edge[1][i].v,dis=edge[1][i].dis,kind=edge[1][i].kk;i!=-1;i=edge[1][i].next,cur=edge[1][i].v,dis=edge[1][i].dis,kind=edge[1][i].kk) { if(status[x])Q[cur][kind].push(dis);else Q[cur][kind].erase(dis); calc(cur); } } int main() { freopen("bzoj1095.in","r",stdin); freopen("bzoj1095.out","w",stdout); int i; n=gint(); mmst(now,-1);mmst(info,-1); re(i,1,n-1){int u=gint(),v=gint();addedge(0,u,v);addedge(0,v,u);} re(i,1,n)status[i]=1; ans[0]=-inf; prep(1,n); int ge=n,T;SF("%d\n",&T); while(T--) { char z=getchar(); if(z=='G') { if(ge==0)PF("-1\n");else if(ge==1) PF("0\n");else PF("%d\n",ans[1]); } else { int x;SF("%d",&x); status[x]^=1; if(status[x])ge++;else ge--; update(x); } SF("\n"); } return 0; }
