洛谷3703 [SDOI2017] 树点染色 【LCT】【线段树】

题目分析：

　　操作一很明显等价于LCT上的access操作，操作二是常识，操作三转化到dfs序上求最大值也是常识。access的时候顺便在线段树中把对应部分-1，把右子树的子树+1即可。

代码：

 #include<bits/stdc++.h>
 using namespace std;

 const int maxn = ;

 int num,n,m;

 vector <int> g[maxn];

 int f[maxn],dep[maxn],dfsin[maxn],dfsout[maxn];

 class SegmentTree{
 private:
     int data[maxn<<],lazy[maxn<<],maxx[maxn<<];
     void push_down(int now){
     int L = (now<<),R = (now<<|);
     data[L] += lazy[now]; maxx[L] += lazy[now]; lazy[L] += lazy[now];
     data[R] += lazy[now]; maxx[R] += lazy[now]; lazy[R] += lazy[now];
     lazy[now] = ;
     }
 public:
     void Add(int now,int tl,int tr,int l,int r,int d){
     if(lazy[now]&&tl!=tr) push_down(now);
     if(tl >= l && tr <= r){
         data[now] += d; lazy[now] += d;maxx[now] += d; return;
     }
     if(tl > r || tr < l) return;
     int mid = (tl+tr)/;
     Add(now<<,tl,mid,l,r,d);
     Add(now<<|,mid+,tr,l,r,d);
     maxx[now] = max(maxx[now<<],maxx[now<<|]);
     }
     int Query(int now,int tl,int tr,int l,int r){
     if(lazy[now]&&tl!=tr) push_down(now);
     if(tl >= l && tr <= r) return maxx[now];
     if(tl > r || tr < l) return ;
     int mid = (tl+tr)/;
     int ans = max(Query(now<<,tl,mid,l,r),Query(now<<|,mid+,tr,l,r));
     maxx[now] = max(maxx[now<<],maxx[now<<|]);
     return ans;
     }
 }T;

 class LinkCutTree{
 private:
     int ch[maxn][],fa[maxn],data[maxn];
     stack <int> sta;

     int is_root(int now){return ch[fa[now]][]!=now&&ch[fa[now]][]!=now;}

     void r0(int now,int dr){
     int son = ch[now][dr],pa = fa[now],gp = fa[pa];
     int tag = is_root(pa);
     ch[pa][dr^] = son; fa[son] = pa;
     ch[now][dr] = pa; fa[pa] = now; fa[now] = gp;
     if(tag == ) return;
     if(ch[gp][] == pa) ch[gp][] = now;
     else ch[gp][] = now;
     }

     void splay(int now){
     while(!is_root(now)){
         int pa = fa[now],gp = fa[pa];
         if(is_root(pa)){
         if(ch[pa][] == now) r0(now,);
         else r0(now,);
         }else{
         if(ch[gp][] == pa){
             if(ch[pa][] == now) r0(pa,),r0(now,);
             else r0(now,),r0(now,);
         }else{
             if(ch[pa][] == now) r0(now,),r0(now,);
             else r0(pa,),r0(now,);
         }
         }
     }
     }
 public:
     void access(int now){
     int p = now,last = ;
     while(p != ){
         splay(p);
         int zz = ch[p][]; while(ch[zz][]) zz = ch[zz][];
         if(zz)T.Add(,,n,dfsin[zz],dfsout[zz],);
         int lt = p; while(ch[lt][]) lt = ch[lt][];
         T.Add(,,n,dfsin[lt],dfsout[lt],-);
         ch[p][] = last;
         last = p; p = fa[p];
     }
     T.Add(,,n,,n,);
     }
     void BuildLCT(){
     for(int i=;i<=n;i++) data[i] = dep[i];
     for(int i=;i<=n;i++) fa[i] = f[i];
     }
 }LCT;

 void read(){
     scanf("%d%d",&n,&m);
     for(int i=;i<n;i++){
     int u,v; scanf("%d%d",&u,&v);
     g[u].push_back(v); g[v].push_back(u);
     }
 }

 int RMQ[maxn<<][],app[maxn][],euler[maxn<<],nE;

 void dfs(int now,int fa,int dp){
     f[now] = fa; dep[now] = dp;
     euler[++nE] = now; app[now][] = app[now][] = nE;
     dfsin[now] = dfsout[now] = ++num;
     T.Add(,,n,dfsin[now],dfsin[now],dp);
     for(int i=;i<g[now].size();i++){
     int p = g[now][i];
     if(p == fa) continue;
     dfs(p,now,dp+);
     dfsout[now] = dfsout[p];
     euler[++nE] = now; app[now][] = nE;
     }
 }

 void BuildRMQ(){
     for(int i=;i<=nE;i++) RMQ[i][] = euler[i];
     for(int k=;(<<k)<=nE;k++){
     for(int i=;i<=nE;i++){
         if(i+(<<k-) > nE) {RMQ[i][k] = RMQ[i][k-];continue;}
         if(dep[RMQ[i][k-]] < dep[RMQ[i+(<<k-)][k-]]){
         RMQ[i][k] = RMQ[i][k-];
         }else RMQ[i][k] = RMQ[i+(<<k-)][k-];
     }
     }
 }

 int QueryLCA(int u,int v){
     int fst = min(app[u][],app[v][]),sec = max(app[u][],app[v][]);
     int len = sec-fst+,k = ;
     while((<<k+) <= len) k++;
     if(dep[RMQ[fst][k]] < dep[RMQ[sec-(<<k)+][k]]) return RMQ[fst][k];
     else return RMQ[sec-(<<k)+][k];
 }

 void init(){
     dfs(,,);
     BuildRMQ();
     LCT.BuildLCT();
 }

 void getdist(){
     int u,v; scanf("%d%d",&u,&v);
     int lca = QueryLCA(u,v);
     u = dfsin[u],v = dfsin[v],lca = dfsin[lca];
     int ans = T.Query(,,n,u,u)+T.Query(,,n,v,v);
     ans = ans - *T.Query(,,n,lca,lca) + ;
     printf("%d\n",ans);
 }

 void Query(){
     int u; scanf("%d",&u);
     int ans = T.Query(,,n,dfsin[u],dfsout[u]);
     printf("%d\n",ans);
 }

 void work(){
     for(int i=;i<=m;i++){
     int cas; scanf("%d",&cas);
     if(cas == ){int x;scanf("%d",&x);LCT.access(x);}
     else if(cas == ) getdist();
     else if(cas == ) Query();
     }
 }

 int main(){
     read();
     init();
     work();
     return ;
 }