洛谷P3703 树点涂色

题意：

解：

发现我们每次染的都是不同的颜色，那么用lct维护的话一个颜色就会在一个splay里。染色是access。

维护每个节点到根路径上的虚边数量。

虚边的切换只会在access和link中出现。于是access的时候顺便修改那个子树。lct上啥也不用维护。

查询链可以用两端点减去lca。

 #include <bits/stdc++.h>

 const int N = , INF = 0x3f3f3f3f;

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

 int e[N], n, siz[N], pos[N], id[N], d[N], num, top[N], father[N], son[N]; /// tree
 int fa[N], s[N][], stk[N], Top; /// lct
 bool rev[N];
 int large[N << ], tag[N << ]; /// seg

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

 void DFS_1(int x, int f) { /// father siz son d
     siz[x] = ;
     fa[x] = father[x] = f;
     for(int i = e[x]; i; i = edge[i].nex) {
         int y = edge[i].v;
         if(y == f) continue;
         d[y] = d[x] + ;
         DFS_1(y, x);
         siz[x] += siz[y];
         if(siz[y] > siz[son[x]]) {
             son[x] = y;
         }
     }
     return;
 }

 void DFS_2(int x, int f) { /// top id pos
     top[x] = f;
     pos[x] = ++num;
     id[num] = x;
     if(son[x]) DFS_2(son[x], f);
     for(int i = e[x]; i; i = edge[i].nex) {
         int y = edge[i].v;
         if(y == father[x] || y == son[x]) continue;
         DFS_2(y, y);
     }
     return;
 }

 inline void Pushdown(int o) {
     if(tag[o]) {
         int ls = o << , rs = o <<  | ;
         tag[ls] += tag[o];
         tag[rs] += tag[o];
         large[ls] += tag[o];
         large[rs] += tag[o];
         tag[o] = ;
     }
     return;
 }

 void build(int l, int r, int o) {
     if(l == r) {
         large[o] = d[id[r]];
         return;
     }
     int mid = (l + r) >> ;
     build(l, mid, o << );
     build(mid + , r, o <<  | );
     large[o] = std::max(large[o << ], large[o <<  | ]);
     return;
 }

 void add(int L, int R, int v, int l, int r, int o) {
     if(L <= l && r <= R) {
         large[o] += v;
         tag[o] += v;
         return;
     }
     Pushdown(o);
     int mid = (l + r) >> ;
     if(L <= mid) add(L, R, v, l, mid, o << );
     if(mid < R) add(L, R, v, mid + , r, o <<  | );
     large[o] = std::max(large[o << ], large[o <<  | ]);
     return;
 }

 int getMax(int L, int R, int l, int r, int o) {
     if(L <= l && r <= R) return large[o];
     int mid = (l + r) >> , ans = -INF;
     Pushdown(o);
     if(L <= mid) ans = std::max(ans, getMax(L, R, l, mid, o << ));
     if(mid < R) ans = std::max(ans, getMax(L, R, mid + , r, o <<  | ));
     return ans;
 }

 int ask(int p, int l, int r, int o) {
     if(l == r) return large[o];
     Pushdown(o);
     int mid = (l + r) >> ;
     if(p <= mid) return ask(p, l, mid, o << );
     else return ask(p, mid + , r, o <<  | );
 }

 inline void pushdown(int x) {
     if(rev[x]) {
         std::swap(s[x][], s[x][]);
         if(s[x][]) rev[s[x][]] ^= ;
         if(s[x][]) rev[s[x][]] ^= ;
         rev[x] = ;
     }
     return;
 }

 inline void pushup(int x) {
     return;
 }

 inline bool no_root(int x) {
     return (s[fa[x]][] == x) || (s[fa[x]][] == x);
 }

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

     fa[x] = z;
     if(no_root(y)) {
         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 y = x;
     stk[++Top] = y;
     while(no_root(y)) {
         y = fa[y];
         stk[++Top] = y;
     }
     while(Top) {
         pushdown(stk[Top]);
         Top--;
     }

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

 inline void change(int x, int v) {
     pushdown(x);
     while(s[x][]) {
         x = s[x][];
         pushdown(x);
     }
     /// x
     add(pos[x], pos[x] + siz[x] - , v, , n, );
     return;
 }

 inline void access(int x) {
     int y = ;
     while(x) {
         splay(x);
         if(s[x][]) change(s[x][], );
         if(y) change(y, -);
         s[x][] = y;
         pushup(x);
         y = x;
         x = fa[x];
     }
     return;
 }

 inline int lca(int x, int y) {
     while(top[x] != top[y]) {
         if(d[top[x]] < d[top[y]]) {
             y = father[top[y]];
         }
         else {
             x = father[top[x]];
         }
     }
     return d[x] < d[y] ? x : y;
 }

 inline int ask(int x, int y) {
     //printf("ask : %d %d lca %d \n", x, y, lca(x, y));
     //printf("ask : %d + %d - 2 * %d \n", ask(pos[x], 1, n, 1), ask(pos[y], 1, n, 1), ask(pos[lca(x, y)], 1, n, 1));
     return ask(pos[x], , n, ) + ask(pos[y], , n, ) -  * ask(pos[lca(x, y)], , n, );
 }

 inline int query(int x) {
     return getMax(pos[x], pos[x] + siz[x] - , , n, );
 }

 int main() {
     int m;
     scanf("%d%d", &n, &m);
     for(int i = , x, y; i < n; i++) {
         scanf("%d%d", &x, &y);
         add(x, y); add(y, x);
     }
     /// init
     DFS_1(, );
     DFS_2(, );
     build(, n, );

     for(int i = , f, x, y; i <= m; i++) {
         scanf("%d%d", &f, &x);
         if(f == ) { /// change
             access(x);
         }
         else if(f == ) {
             scanf("%d", &y);
             printf("%d\n", ask(x, y) + );
         }
         else { /// f == 3
             printf("%d\n", query(x) + );
         }
     }
     return ;
 }

AC代码