[模板]ETT

解：splay维护括号序列，就是进子树一次出子树一次。树上每个点直接记录这两个点的编号。

建树的时候按照分配的编号建树。

 #include <bits/stdc++.h>
 typedef long long LL;
 #define gc pa==pb&&(pb=(pa=buf)+fread(buf,1,100000,stdin),pa==pb)?EOF:*pa++
 static char buf[],*pa(buf),*pb(buf);
 template <class T> inline void read(T &x) {
     x = ;
     register char c(gc);
     while((c<''||c>'')&&c!='-')
         c=gc;
     register int f(c=='-'?c=gc,-:);
     while(c>=''&&c<='')
         x=x*+c-,c=gc;
     x*=f;
     return;
 }

 const int N = ;
 const LL INF = 0x3f3f3f3f3f3f3f3fll;

 struct Edge {
     int nex, v;
 }edge[N]; int tp;

 int fa[N], op[N], ed[N], s[N][], root, stk[N], top;
 LL large[N], val[N], Val[N], tag[N];
 int e[N], num = , n, id[N];

 inline void add(int x, int y) {
     tp++;
     edge[tp].v = y;
     edge[tp].nex = e[x];
     e[x] = tp;
     return;
 }

 void DFS(int x, int f) {
     id[++num] = x;
     op[x] = num;
     for(int i = e[x]; i; i = edge[i].nex) {
         int y = edge[i].v;
         if(y == f) continue;
         DFS(y, x);
     }
     id[++num] = x;
     ed[x] = num;
     return;
 }

 inline void pushup(int x) {
     large[x] = std::max(large[s[x][]], large[s[x][]]);
     large[x] = std::max(large[x], val[x]);
     if(!fa[x]) root = x;
     return;
 }

 inline void pushdown(int x) {
     if(tag[x]) {
         if(s[x][]) {
             tag[s[x][]] += tag[x];
             val[s[x][]] += tag[x];
             large[s[x][]] += tag[x];
         }
         if(s[x][]) {
             tag[s[x][]] += tag[x];
             val[s[x][]] += tag[x];
             large[s[x][]] += tag[x];
         }
         tag[x] = ;
     }
     return;
 }

 void out(int x = root) {
     pushdown(x);
     if(s[x][]) {
         out(s[x][]);
     }
     printf("%d ", id[x]);
     if(s[x][]) {
         out(s[x][]);
     }
     return;
 }

 inline void rotate(int x) {
     int y = fa[x];
     int z = fa[y];
     bool f = (s[y][] == x);

     fa[x] = z;
     if(z) {
         s[z][s[z][] == y] = x;
     }
     s[y][f] = s[x][!f];
     if(s[x][!f]) {
         fa[s[x][!f]] = y;
     }
     s[x][!f] = y;
     fa[y] = x;

     pushup(y);
     return;
 }

 inline void splay(int x, int g = ) {
     int y = x;
     stk[top = ] = y;
     while(fa[y]) {
         y = fa[y];
         stk[++top] = y;
     }
     while(top) {
         pushdown(stk[top]);
         top--;
     }

     y = fa[x];
     int z = fa[y];
     while(y != g) {
         if(z != g) {
             (s[z][] == y) ^ (s[y][] == x) ?
             rotate(x) : rotate(y);
         }
         rotate(x);
         y = fa[x];
         z = fa[y];
     }
     pushup(x);
     return;
 }

 inline int getLP() {
     pushdown(root);
     int p = s[root][];
     while(s[p][]) {
         p = s[p][];
         pushdown(p);
     }
     return p;
 }

 inline int getRP() {
     pushdown(root);
     int p = s[root][];
     while(s[p][]) {
         p = s[p][];
         pushdown(p);
     }
     return p;
 }

 int build(int l, int r, int f) {
     int mid = (l + r) >> ;
     //int x = np(f, Val[id[mid]]);
     fa[mid] = f;
     val[mid] = large[mid] = Val[id[mid]];
     if(l < mid) s[mid][] = build(l, mid - , mid);
     if(mid < r) s[mid][] = build(mid + , r, mid);
     pushup(mid);
     return mid;
 }

 inline void Add(int x, LL v) {
     splay(op[x]);
     int a = getLP();
     splay(ed[x]);
     int b = getRP();
     splay(b);
     splay(a, b);
     int z = s[a][];
     tag[z] += v;
     large[z] += v;
     val[z] += v;
     pushup(a);
     pushup(b);
     return;
 }

 int main() {

     int q, rt, x; LL y;
     read(n); read(q); read(rt);
     for(register int i = ; i <= n; i++) {
         read(Val[i]);
     }
     for(register int i = ; i < n; i++) {
         read(x); read(y);
         add(x, y); add(y, x);
     }

     DFS(rt, );

     /*for(int i = 1; i <= num + 1; i++) {
         printf("%d ", id[i]);
     }
     puts("");*/

     Val[] = val[] = -INF;
     root = build(, num + , );

     //out(), puts("");

     for(int i = , f; i <= q; i++) {
         read(f); read(x);
         if(f == ) { /// out max subtree x
             splay(op[x]);
             int a = getLP();
             splay(ed[x]);
             int b = getRP();
             splay(b);
             splay(a, b);
             printf("%lld\n", large[s[a][]]);
         }
         else if(f == ) { /// subtree x += y
             read(y);
             Add(x, y);
         }
         else if(f == ) { /// change fa[x] -> y
             read(y);
             splay(op[x]);
             int a = getLP();
             splay(ed[x]);
             int b = getRP();

             /*printf("%d op = %d ed = %d \n", x, op[x], ed[x]);
             printf("a=%d %d  b=%d %d \n", a, id[a], b, id[b]);*/

             splay(b);
             splay(a, b);
             int z = s[a][];
             s[a][] = fa[z] = ;
             pushup(a);
             pushup(b);
             splay(op[y]);
             int t = getRP();
             splay(t, op[y]);
             s[t][] = z; fa[z] = t;
             pushup(t);
             pushup(op[y]);
         }
         //out(), puts("");
     }

     return ;
 }

AC代码