[BZOJ3052][UOJ#58][WC2013]糖果公园

#include <iostream>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <cctype>
#include <algorithm>
#include <cmath>
using namespace std;

const int BufferSize = 1 << 16;
char buffer[BufferSize], *Head, *Tail;
inline char Getchar() {
	if(Head == Tail) {
		int l = fread(buffer, 1, BufferSize, stdin);
		Tail = (Head = buffer) + l;
	}
	return *Head++;
}
int read() {
	int x = 0, f = 1; char c = Getchar();
	while(!isdigit(c)){ if(c == ‘-‘) f = -1; c = Getchar(); }
	while(isdigit(c)){ x = x * 10 + c - ‘0‘; c = Getchar(); }
	return x * f;
}

#define maxn 100010
#define maxm 200010
#define maxq 100010
#define maxlog 18
#define LL long long

int n, C, m, head[maxn], nxt[maxm], to[maxm], colv[maxn], timv[maxn], col[maxn];

void AddEdge(int a, int b) {
	to[++m] = b; nxt[m] = head[a]; head[a] = m;
	swap(a, b);
	to[++m] = b; nxt[m] = head[a]; head[a] = m;
	return ;
}

int Bsiz, S[maxn], top, cb, blid[maxn];
int fa[maxn], dep[maxn], clo, mnp[maxlog][maxn<<1], dfn[maxn];
void build(int u) {
	mnp[0][dfn[u] = ++clo] = u;
	int bot = top;
	for(int e = head[u]; e; e = nxt[e]) if(to[e] != fa[u]) {
		fa[to[e]] = u; dep[to[e]] = dep[u] + 1;
		build(to[e]);
		mnp[0][++clo] = u;
		if(top - bot >= Bsiz) {
			cb++;
			while(top > bot) blid[S[top--]] = cb;
		}
	}
	S[++top] = u;
	return ;
}
int Log[maxn<<1];
void rmq_init() {
	Log[1] = 0;
	for(int i = 2; i <= clo; i++) Log[i] = Log[i>>1] + 1;
	for(int j = 1; (1 << j) <= clo; j++)
		for(int i = 1; i + (1 << j) - 1 <= clo; i++) {
			int a = mnp[j-1][i], b = mnp[j-1][i+(1<<j-1)];
			mnp[j][i] = dep[a] < dep[b] ? a : b;
		}
	return ;
}
int lca(int a, int b) {
	int l = dfn[a], r = dfn[b];
	if(l > r) swap(l, r);
	int t = Log[r-l+1];
	a = mnp[t][l]; b = mnp[t][r-(1<<t)+1];
	return dep[a] < dep[b] ? a : b;
}

int q, cc, cq;
LL Ans[maxq];
struct Cmd {
	int id, col, clst;
	Cmd() {}
	Cmd(int _1, int _2, int _3): id(_1), col(_2), clst(_3) {}
} cs[maxq];
struct Que {
	int u, v, t, id;
	Que() {}
	Que(int _1, int _2, int _3, int _4): u(_1), v(_2), t(_3), id(_4) {}
	bool operator < (const Que& t) const {
		if(blid[u] != blid[t.u]) return blid[u] < blid[t.u];
		if(blid[v] != blid[t.v]) return blid[v] < blid[t.v];
		return this->t < t.t;
	}
} qs[maxq];

int U, V, T, tot[maxn];
LL ans;
bool tag[maxn];
void rev(int u) {
	if(tag[u]) ans -= (LL)timv[tot[col[u]]--] * colv[col[u]];
	else ans += (LL)timv[++tot[col[u]]] * colv[col[u]];
	tag[u] ^= 1;
	return ;
}
void change(int& node, int tar) {
	int c = lca(node, tar), To = tar;
	while(node != c) rev(node), node = fa[node];
	while(tar != c) rev(tar), tar = fa[tar];
	node = To;
	return ;
}

int main() {
	n = read(); C = read(); q = read();
	for(int i = 1; i <= C; i++) colv[i] = read();
	for(int i = 1; i <= n; i++) timv[i] = read();
	for(int i = 1; i < n; i++) {
		int a = read(), b = read();
		AddEdge(a, b);
	}
	for(int i = 1; i <= n; i++) col[i] = read();
	Bsiz = pow(n, 2.0 / 3);
	build(1);
	while(top) blid[S[top--]] = cb;
	rmq_init();
	
	for(int i = 1; i <= q; i++) {
		int tp = read();
		if(!tp) {
			int id = read(), co = read();
			cs[++cc] = Cmd(id, co, col[id]);
			col[id] = co;
		}
		else {
			int u = read(), v = read();
			cq++; qs[cq] = Que(u, v, cc, cq);
		}
	}
	for(int i = cc; i; i--) col[cs[i].id] = cs[i].clst;
	sort(qs + 1, qs + cq + 1);
	
	U = V = tot[col[1]] = tag[1] = 1; T = 0; ans = (LL)colv[col[1]] * timv[1];
	for(int i = 1; i <= cq; i++) {
		rev(lca(U, V)); rev(lca(qs[i].u, qs[i].v));
		change(U, qs[i].u);
		change(V, qs[i].v);
		while(T < qs[i].t) {
			T++;
			int u = cs[T].id;
			if(tag[u]) ans -= (LL)timv[tot[col[u]]--] * colv[col[u]];
			col[u] = cs[T].col;
			if(tag[u]) ans += (LL)timv[++tot[col[u]]] * colv[col[u]];
		}
		while(T > qs[i].t) {
			int u = cs[T].id;
			if(tag[u]) ans -= (LL)timv[tot[col[u]]--] * colv[col[u]];
			col[u] = cs[T].clst;
			if(tag[u]) ans += (LL)timv[++tot[col[u]]] * colv[col[u]];
			T--;
		}
		Ans[qs[i].id] = ans;
	}
	
	for(int i = 1; i <= cq; i++) printf("%lld\n", Ans[i]);
	
	return 0;
}