[BZOJ 3052] [wc2013] 糖果公园 【树上莫队】

#include <iostream>
#include <cstdlib>
#include <cstdio>
#include <cstring>
#include <cmath>
#include <algorithm>

using namespace std;

inline void Read(int &Num)
{
	char c = getchar();
	bool Neg = false;
	while (c < ‘0‘ || c > ‘9‘) 
	{
		if (c == ‘-‘) Neg = true;
		c = getchar();
	}
	Num = c - ‘0‘; c = getchar();
	while (c >= ‘0‘ && c <= ‘9‘)
	{
		Num = Num * 10 + c - ‘0‘;
		c = getchar();
	}
	if (Neg) Num = -Num;
}

typedef long long LL;

const int MaxN = 100000 + 5, MaxQ = 100000 + 5;

int n, m, q, BlkSize, Top, Index, ID_Index, Chg_Index, Qt;
int V[MaxN], W[MaxN], Col[MaxN], Father[MaxN], ID[MaxN], Depth[MaxN], S[MaxN], Cnt[MaxN], Jump[MaxN][20], Ti[MaxN];

LL Ans;
LL AnsA[MaxQ];

bool InPath[MaxN];

struct Edge
{
	int v;
	Edge *Next;
} E[MaxN * 2], *P = E, *Point[MaxN];

inline void AddEdge(int x, int y)
{
	++P; P -> v = y;
	P -> Next = Point[x]; Point[x] = P;
}

void DFS(int x, int Fa, int Dep)
{
	Father[x] = Fa; Depth[x] = Dep;
	int Bottom = Top;
	for (Edge *j = Point[x]; j; j = j -> Next)
	{
		if (j -> v == Fa) continue;
		DFS(j -> v, x, Dep + 1);
		if (Top - Bottom >= BlkSize)
		{
			++ID_Index;
			while (Top > Bottom)
				ID[S[Top--]] = ID_Index;
		}
	}
	S[++Top] = x;
}

struct Query
{
	int x, y, vx, vy, tl, Idx;
} Q[MaxQ];

inline bool Cmp(Query q1, Query q2)
{
	if (q1.vx != q2.vx) return q1.vx < q2.vx;
	if (q1.vy != q2.vy) return q1.vy < q2.vy;
	return q1.tl < q2.tl;
}

struct Chg
{
	int Pos, Num, Prev;
} C[MaxQ];

inline void ChangeCol(int Num, int f)
{
	if (f == -1)
	{	
		Ans -= (LL)V[Num] * (LL)W[Cnt[Num]];
		--Cnt[Num];
	}
	else
	{
		++Cnt[Num];
		Ans += (LL)V[Num] * (LL)W[Cnt[Num]];
	}
}

void ChangeTL(int x, int y)
{
	if (x == y) return;
	if (x < y) 
	{
		for (int i = x + 1; i <= y; ++i)
		{
			if (InPath[C[i].Pos])
			{
				ChangeCol(Col[C[i].Pos], -1);
				ChangeCol(C[i].Num, 1);
			}
			Col[C[i].Pos] = C[i].Num;
		}
	}
	else
	{
		for (int i = x; i > y; --i)
		{
			if (InPath[C[i].Pos])
			{
				ChangeCol(Col[C[i].Pos], -1);
				ChangeCol(C[i].Prev, 1);
			}
			Col[C[i].Pos] = C[i].Prev;
		}
	}
}

inline void Reverse(int x)
{
	if (InPath[x]) 
	{
		InPath[x] = false;
		ChangeCol(Col[x], -1);
	}
	else 
	{
		InPath[x] = true;
		ChangeCol(Col[x], 1);
	}
}

void Change(int x, int y)
{
	while (x != y)
	{
		if (Depth[x] < Depth[y]) swap(x, y);
		Reverse(x); 
		x = Father[x];		
	}
}

int LCA(int x, int y)
{
	if (Depth[x] < Depth[y]) swap(x, y);
	int Dif = Depth[x] - Depth[y];
	for (int i = 0; i <= 18; ++i)
		if (Dif & (1 << i)) x = Jump[x][i];
	if (x == y) return x;
	for (int i = 18; i >= 0; --i)
		if (Jump[x][i] != Jump[y][i])
		{
			x = Jump[x][i];
			y = Jump[y][i];
		}
	return Father[x];
}

void Prepare()
{
	for (int i = 1; i <= n; ++i) Jump[i][0] = Father[i];
	for (int j = 1; j <= 18; ++j)
		for (int i = 1; i <= n; ++i)
			Jump[i][j] = Jump[Jump[i][j - 1]][j - 1];
}

int main()
{
	Read(n); Read(m); Read(q);
	for (int i = 1; i <= m; ++i) Read(V[i]);
	for (int i = 1; i <= n; ++i) Read(W[i]);
	int a, b;
	for (int i = 1; i <= n - 1; ++i) 
	{
		Read(a); Read(b);
		AddEdge(a, b);
		AddEdge(b, a);
	}
	for (int i = 1; i <= n; ++i) Read(Col[i]);
	BlkSize = (int)pow(n, 0.667);
	DFS(1, 0, 0);
	while (Top > 0) ID[S[Top--]] = ID_Index;
	Prepare();
	for (int i = 1; i <= n; ++i) Ti[i] = Col[i];
	int f;
	for (int i = 1; i <= q; ++i)
	{
		Read(f); Read(a); Read(b);
		if (f == 0)
		{
			++Chg_Index;
			C[Chg_Index].Prev = Ti[a];
			Ti[a] = b;
			C[Chg_Index].Pos = a;
			C[Chg_Index].Num = b;
		}
		else
		{
			++Qt;
			Q[Qt].x = a; Q[Qt].y = b;
			Q[Qt].vx = ID[a]; Q[Qt].vy = ID[b];
			Q[Qt].tl = Chg_Index;
			Q[Qt].Idx = Qt;
		}
	}
	sort(Q + 1, Q + Qt + 1, Cmp);
	Ans = 0ll;
	ChangeTL(0, Q[1].tl);
	Change(Q[1].x, Q[1].y);
	int t = LCA(Q[1].x, Q[1].y);
	Reverse(t);	
	AnsA[Q[1].Idx] = Ans;	
	Reverse(t);
	for (int i = 2; i <= Qt; ++i)
	{
		ChangeTL(Q[i - 1].tl, Q[i].tl);
		Change(Q[i - 1].x, Q[i].x);
		Change(Q[i - 1].y, Q[i].y);
		t = LCA(Q[i].x, Q[i].y);
		Reverse(t);
		AnsA[Q[i].Idx] = Ans;	
		Reverse(t);
	}
	for (int i = 1; i <= Qt; ++i) printf("%lld\n", AnsA[i]);
	return 0;
}