[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[100000],*pa(buf),*pb(buf);
template <class T> inline void read(T &x) {
    x = 0;
    register char c(gc);
    while((c<'0'||c>'9')&&c!='-')
        c=gc;
    register int f(c=='-'?c=gc,-1:1);
    while(c>='0'&&c<='9')
        x=x*10+c-48,c=gc;
    x*=f;
    return;
}

const int N = 400010;
const LL INF = 0x3f3f3f3f3f3f3f3fll;

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

int fa[N], op[N], ed[N], s[N][2], root, stk[N], top;
LL large[N], val[N], Val[N], tag[N];
int e[N], num = 1, 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][0]], large[s[x][1]]);
    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][0]) {
            tag[s[x][0]] += tag[x];
            val[s[x][0]] += tag[x];
            large[s[x][0]] += tag[x];
        }
        if(s[x][1]) {
            tag[s[x][1]] += tag[x];
            val[s[x][1]] += tag[x];
            large[s[x][1]] += tag[x];
        }
        tag[x] = 0;
    }
    return;
}

void out(int x = root) {
    pushdown(x);
    if(s[x][0]) {
        out(s[x][0]);
    }
    printf("%d ", id[x]);
    if(s[x][1]) {
        out(s[x][1]);
    }
    return;
}

inline void rotate(int x) {
    int y = fa[x];
    int z = fa[y];
    bool f = (s[y][1] == x);
    
    fa[x] = z;
    if(z) {
        s[z][s[z][1] == 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 = 0) {
    int y = x;
    stk[top = 1] = 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][1] == y) ^ (s[y][1] == 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][0];
    while(s[p][1]) {
        p = s[p][1];
        pushdown(p);
    }
    return p;
}

inline int getRP() {
    pushdown(root);
    int p = s[root][1];
    while(s[p][0]) {
        p = s[p][0];
        pushdown(p);
    }
    return p;
}

int build(int l, int r, int f) {
    int mid = (l + r) >> 1;
    //int x = np(f, Val[id[mid]]);
    fa[mid] = f;
    val[mid] = large[mid] = Val[id[mid]];
    if(l < mid) s[mid][0] = build(l, mid - 1, mid);
    if(mid < r) s[mid][1] = build(mid + 1, 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][1];
    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 = 1; i <= n; i++) {
        read(Val[i]);
    }
    for(register int i = 1; i < n; i++) {
        read(x); read(y);
        add(x, y); add(y, x);
    }
    
    DFS(rt, 0);
    
    /*for(int i = 1; i <= num + 1; i++) {
        printf("%d ", id[i]);
    }
    puts("");*/
    
    Val[0] = val[0] = -INF;
    root = build(1, num + 1, 0);
    
    //out(), puts("");
    
    for(int i = 1, f; i <= q; i++) {
        read(f); read(x);
        if(f == 3) { /// out max subtree x
            splay(op[x]);
            int a = getLP();
            splay(ed[x]);
            int b = getRP();
            splay(b);
            splay(a, b);
            printf("%lld
", large[s[a][1]]);
        }
        else if(f == 2) { /// subtree x += y
            read(y);
            Add(x, y);
        }
        else if(f == 1) { /// change fa[x] -> y
            read(y);
            splay(op[x]);
            int a = getLP();
            splay(ed[x]);
            int b = getRP();
            
            /*printf("%d op = %d ed = %d 
", x, op[x], ed[x]);
            printf("a=%d %d  b=%d %d 
", a, id[a], b, id[b]);*/
            
            splay(b);
            splay(a, b);
            int z = s[a][1];
            s[a][1] = fa[z] = 0;
            pushup(a);
            pushup(b);
            splay(op[y]);
            int t = getRP();
            splay(t, op[y]);
            s[t][0] = z; fa[z] = t;
            pushup(t);
            pushup(op[y]);
        }
        //out(), puts("");
    }
    
    return 0;
}