【BZOJ 1036】【ZJOI 2008】树的统计

此题为树链剖分的裸题。 代码如下，使用常用的轻重链剖分。

/**************************************************************
	Problem: 1036
	User: Evensgn
	Language: C++
	Result: Accepted
	Time:2468 ms
	Memory:5772 kb
****************************************************************/

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

using namespace std;

const int MaxE = 30000 + 5, MaxN = 30000 + 5;

int n, q, topH, W[MaxN], f[MaxN], dep[MaxN], top[MaxN], son[MaxN], h[MaxN], size[MaxN], A[MaxN];

int Ans;

struct treeNode
{
	int sum, max;
} T[MaxN * 4];

struct edge
{
	int u, v;
	edge *next;
} E[MaxE * 2], *P = E, *point[MaxN];

inline void addedge(int x, int y)
{
	++P; P -> u = x; P -> v = y; P -> next = point[x]; point[x] = P;
}

int DFS_1(int now, int depth, int fa)
{
	f[now] = fa;
	dep[now] = depth;
	int sonSize, maxSonSize = 0;
	size[now] = 1;
	for (edge *j = point[now]; j; j = j -> next)
	{
		if (j -> v != f[now])
		{
			sonSize = DFS_1(j -> v, depth + 1, now);
			size[now] += sonSize;
			if (maxSonSize < sonSize)
			{
				son[now] = j -> v;
				maxSonSize = sonSize;
			}
		}
	}
	return size[now];
}

void DFS_2(int now)
{
	if (now != son[f[now]]) top[now] = now;
	else top[now] = top[f[now]];
	h[now] = ++topH;
	A[h[now]] = W[now];
	if (son[now]) DFS_2(son[now]);
	for (edge *j = point[now]; j; j = j -> next)
		if (j -> v != son[now] && j -> v != f[now]) DFS_2(j -> v);
}

int max(int a, int b)
{
	if (a > b) return a;
	return b;
}

void update(int x)
{
	T[x].sum = T[x * 2].sum + T[x * 2 + 1].sum;
	T[x].max = max(T[x * 2].max, T[x * 2 + 1].max);
}

void buildTree(int x, int s, int t)
{
	if (s == t)
	{
		T[x].sum = A[s];
		T[x].max = A[s];
		return;
	}
	int m = (s + t) >> 1;
	buildTree(x * 2, s, m);
	buildTree(x * 2 + 1, m + 1, t);
	update(x);
}

void change(int x, int s, int t, int loc, int num)
{
	if (s == t)
	{
		T[x].sum = num;
		T[x].max = num;
		return;
	}
	int m = (s + t) >> 1;
	if (loc <= m) change(x * 2, s, m, loc, num);
	else change(x * 2 + 1, m + 1, t, loc, num);
	update(x);
}

int getMax(int x, int s, int t, int l, int r)
{
	if (l <= s && r >= t)
		return T[x].max;
	int m = (s + t) >> 1, ans = -999999999;
	if (l <= m) ans = max(ans, getMax(x * 2, s, m, l, r));
	if (r >= m + 1) ans = max(ans, getMax(x * 2 + 1, m + 1, t, l, r));
	return ans;
}

int getSum(int x, int s, int t, int l, int r)
{
	if (l <= s && r >= t)
		return T[x].sum;
	int m = (s + t) >> 1, ans = 0;
	if (l <= m) ans += getSum(x * 2, s, m, l, r);
	if (r >= m + 1) ans += getSum(x * 2 + 1, m + 1, t, l, r);
	return ans;
}

void queryMax(int s, int t)
{
	int f1, f2;
	f1 = 0; f2 = 1;
	while (f1 != f2)
	{
		f1 = top[s];
		f2 = top[t];
		if (f1 != f2)
		{
			if (dep[f1] >= dep[f2])
			{
				Ans = max(Ans, getMax(1, 1, n, h[f1], h[s]));
				s = f[f1];
			}
			else
			{
				Ans = max(Ans, getMax(1, 1, n, h[f2], h[t]));
				t = f[f2];
			}
		}
		else
		{
			if (s == t) Ans = max(Ans, getMax(1, 1, n, h[s], h[s]));
			else
			{
				if (dep[s] >= dep[t]) Ans = max(Ans, getMax(1, 1, n, h[t], h[s]));
				else Ans = max(Ans, getMax(1, 1, n, h[s], h[t]));
			}
		}
	}
}

void querySum(int s, int t)
{
	int f1, f2;
	f1 = 0; f2 = 1;
	while (f1 != f2)
	{
		f1 = top[s];
		f2 = top[t];
		if (f1 != f2)
		{
			if (dep[f1] >= dep[f2])
			{
				Ans += getSum(1, 1, n, h[f1], h[s]);
				s = f[f1];
			}
			else
			{
				Ans += getSum(1, 1, n, h[f2], h[t]);
				t = f[f2];
			}
		}
		else
		{
			if (s == t) Ans += getSum(1, 1, n, h[s], h[s]);
			else
			{
				if (dep[s] >= dep[t]) Ans += getSum(1, 1, n, h[t], h[s]);
				else Ans += getSum(1, 1, n, h[s], h[t]);
			}
		}
	}
}

int main()
{
//	freopen("1.in", "r", stdin);
	scanf("%d", &n);
	int a, b;
	char flag[10];
	for (int i = 1; i <= n - 1; i++)
	{
		scanf("%d%d", &a, &b);
		addedge(a, b);
		addedge(b, a);
	}
	for (int i = 1; i <= n; i++) scanf("%d", &W[i]);
	DFS_1(1, 1, 0);
	topH = 0; top[1] = 1; DFS_2(1);
	buildTree(1, 1, n);
	scanf("%d", &q);
	for (int i = 1; i <= q; i++)
	{
		scanf("%s%d%d", flag, &a, &b);
		if (!strcmp(flag, "QMAX"))
		{
			Ans = -999999999;
			queryMax(a, b);
			printf("%d\n", Ans);
		}
		else if (!strcmp(flag, "QSUM"))
		{
			Ans = 0;
			querySum(a, b);
			printf("%d\n", Ans);
		}
		else         //Change one node
		{
			change(1, 1, n, h[a], b);
		}
	}
	return 0;
}

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