[luoguP3690] 【模板】Link Cut Tree

传送门

处理路径 xor 和的时候可以维护子树 xor 和，先提取出路径，再把一个点 splay 到最上方，直接取子树 xor 和即可。

更新一个点权时可以先提取出根到这个点的路径，把这个点 splay 到最上方，然后 update 即可。

——代码

 #include <cstdio>
 #include <iostream>
 #define N 300001
 #define get(x) (son[f[x]][1] == (x))
 #define swap(x, y) ((x) ^= (y) ^= (x) ^= (y))
 #define isroot(x) (son[f[x]][0] ^ (x) && son[f[x]][1] ^ (x))

 int n, m;
 int a[N], sum[N], son[N][], rev[N], f[N], s[N];

 inline int read()
 {
     int x = , f = ;
     char ch = getchar();
     for(; !isdigit(ch); ch = getchar()) if(ch == '-') f = -;
     for(; isdigit(ch); ch = getchar()) x = (x << ) + (x << ) + ch - '';
     return x * f;
 }

 inline void update(int x)
 {
     if(x)
     {
         sum[x] = a[x];
         if(son[x][]) sum[x] ^= sum[son[x][]];
         if(son[x][]) sum[x] ^= sum[son[x][]];
     }
 }

 inline void pushdown(int x)
 {
     if(x && rev[x])
     {
         swap(son[x][], son[x][]);
         if(son[x][]) rev[son[x][]] ^= ;
         if(son[x][]) rev[son[x][]] ^= ;
         rev[x] = ;
     }
 }

 inline void rotate(int x)
 {
     int old = f[x], oldf = f[old], wh = get(x);

     if(!isroot(old))
         son[oldf][get(old)] = x;
     f[x] = oldf;

     son[old][wh] = son[x][wh ^ ];
     f[son[old][wh]] = old;

     son[x][wh ^ ] = old;
     f[old] = x;

     update(old);
     update(x);
 }

 inline void splay(int x)
 {
     int i, fa, t = ;
     s[++t] = x;
     for(i = x; !isroot(i); i = f[i]) s[++t] = f[i];
     for(i = t; i >= ; i--) pushdown(s[i]);
     for(; !isroot(x); rotate(x))
         if(!isroot(fa = f[x]))
             rotate(get(x) ^ get(fa) ? x : fa);
 }

 inline void access(int x)
 {
     for(int t = ; x; t = x, x = f[x]) splay(x), son[x][] = t, update(x);
 }

 inline void reverse(int x)
 {
     access(x);
     splay(x);
     rev[x] ^= ;
 }

 inline int query(int x, int y)
 {
     reverse(x);
     access(y);
     splay(y);
     return sum[y];
 }

 inline int find(int x)
 {
     access(x);
     splay(x);
     while(son[x][]) x = son[x][];
     return x;
 }

 inline void link(int x, int y)
 {
     reverse(x);
     f[x] = y;
     access(x);
 }

 inline void cut(int x, int y)
 {
     reverse(x);
     access(y);
     splay(y);
     son[y][] = f[x] = ;
     update(y);
 }

 inline void change(int x, int y)
 {
     access(x);
     splay(x);
     a[x] = y;
     update(x);
 }

 int main()
 {
     int i, x, y, z;
     n = read();
     m = read();
     for(i = ; i <= n; i++) a[i] = read();
     for(i = ; i <= m; i++)
     {
         z = read();
         x = read();
         y = read();
         if(z == ) printf("%d\n", query(x, y));
         if(z == )
             if(find(x) ^ find(y))
                 link(x, y);
         if(z == )
             if(find(x) == find(y))
                 cut(x, y);
         if(z == ) change(x, y);
     }
 }