【题解】LuoGu3313：[SDOI2014]旅行

原题传送门
此题不错，调了我3h，码力++
第一感觉肯定是树剖了，但是这里还需要关注教派不同的问题

想到对于每一个教派都开一棵线段树，维护区间最值与区间和
空间可能会存不下，所以需要动态开点

有许多细节问题

Code：

#include <bits/stdc++.h>
#define maxn 100010
using namespace std;
struct Edge{
	int to, next;
}edge[maxn << 1];
struct Seg{
	int l, r, val, sum;
}seg[maxn << 5];
int head[maxn], num, d[maxn], fa[maxn], size[maxn], son[maxn], id[maxn], cnt, rk[maxn], top[maxn];
int n, m, w[maxn], c[maxn], sz, rt[maxn];

inline int read(){
	int s = 0, w = 1;
	char c = getchar();
	for (; !isdigit(c); c = getchar()) if (c == '-') w = -1;
	for (; isdigit(c); c = getchar()) s = (s << 1) + (s << 3) + (c ^ 48);
	return s * w;
}

void add_edge(int x, int y){ edge[++num].to = y; edge[num].next = head[x]; head[x] = num; }

void dfs(int u){
	size[u] = 1, son[u] = -1;
	for (int i = head[u]; i; i = edge[i].next){
		int v = edge[i].to;
		if (v != fa[u]){
			fa[v] = u, d[v] = d[u] + 1;
			dfs(v);
			size[u] += size[v];
			if (son[u] == -1 || son[u] != -1 && size[son[u]] < size[v]) son[u] = v;
		}
	}
}

void dfs(int u, int x){
	id[u] = ++cnt, top[u] = x, rk[cnt] = u;
	if (son[u] == -1) return;
	dfs(son[u], x);
	for (int i = head[u]; i; i = edge[i].next){
		int v = edge[i].to;
		if (v != fa[u] && v != son[u]) dfs(v, v);
	}
}

void pushup(int rt){ 
	seg[rt].val = max(seg[seg[rt].l].val, seg[seg[rt].r].val);
	seg[rt].sum = seg[seg[rt].l].sum + seg[seg[rt].r].sum;
}

void clear(int rt){ seg[rt].val = seg[rt].sum = 0; }

void update(int &rt, int l, int r, int x, int y){
	if (!rt) rt = ++sz;
	if (l == r){
		seg[rt].val = seg[rt].sum = y;
		return;
	}
	int mid = (l + r) >> 1;
	if (mid >= x) update(seg[rt].l, l, mid, x, y); else update(seg[rt].r, mid + 1, r, x, y);
	pushup(rt);
}

void del(int rt, int l, int r, int x){
	if (!rt) return;
	if (l == r){
		clear(rt);
		return;
	}
	int mid = (l + r) >> 1;
	if (mid >= x) del(seg[rt].l, l, mid, x); else del(seg[rt].r, mid + 1, r, x);
	pushup(rt);
}

int querys(int rt, int tl, int tr, int l, int r){
	if (!rt) return 0;
	if (tl > r || tr < l) return 0;
	if (tl >= l && tr <= r) return seg[rt].sum;
	int mid = (tl + tr) >> 1;
	return querys(seg[rt].l, tl, mid, l, r) + querys(seg[rt].r, mid + 1, tr, l, r);
}

int querym(int rt, int tl, int tr, int l, int r){
	if (!rt) return 0;
	if (tl > r || tr < l) return 0;
	if (tl >= l && tr <= r) return seg[rt].val;
	int mid = (tl + tr) >> 1;
	return max(querym(seg[rt].l, tl, mid, l, r), querym(seg[rt].r, mid + 1, tr, l, r));
}

int main(){
	n = read(), m = read();
	for (int i = 1; i <= n; ++i) w[i] = read(), c[i] = read();
	for (int i = 1; i < n; ++i){
		int x = read(), y = read();
		add_edge(x, y); add_edge(y, x);
	}
	dfs(1); dfs(1, 1);
	for (int i = 1; i <= n; ++i) update(rt[c[rk[i]]], 1, n, i, w[rk[i]]);
	while (m--){
		char ch = getchar();
		for (; ch != 'C' && ch != 'Q'; ch = getchar());
		ch = getchar();
		int x = read(), y = read();
		if (ch == 'C'){
			del(rt[c[x]], 1, n, id[x]);
			c[x] = y;
			update(rt[c[x]], 1, n, id[x], w[x]);
		} else
		if (ch == 'W'){
			del(rt[c[x]], 1, n, id[x]);
			w[x] = y;
			update(rt[c[x]], 1, n, id[x], w[x]);
		} else
		if (ch == 'S'){
			int ans = 0, k = c[x];
			while (top[x] != top[y]){
				if (d[top[x]] < d[top[y]]) swap(x, y);
				ans += querys(rt[k], 1, n, id[top[x]], id[x]);
				x = fa[top[x]];
			}
			if (d[x] < d[y]) swap(x, y);
			ans += querys(rt[k], 1, n, id[y], id[x]);
			printf("%d\n", ans);
		} else{
			int ans = 0, k = c[x];
			while (top[x] != top[y]){
				if (d[top[x]] < d[top[y]]) swap(x, y);
				ans = max(ans, querym(rt[k], 1, n, id[top[x]], id[x]));
				x = fa[top[x]];
			}
			if (d[x] < d[y]) swap(x, y);
			ans = max(ans, querym(rt[k], 1, n, id[y], id[x]));
			printf("%d\n", ans);
		}
	}
	return 0;
}