poj 3728(LCA + dp)

题目链接：http://poj.org/problem?id=3728

思路：题目的意思是求树上a -> b的路径上的最大收益（在最小值买入，在最大值卖出）。

我们假设路径a - > b 之间的LCA(a, b) = f, 并且另up[a]表示a - > f之间的最大收益，down[a]表示f - > a之间的最大收益，dp_max[a]表示a - > f之间的最大值，dp_min[a]表示a - > f之间的最小值，于是可以得出关系： ans[id] = max(max(up[a], down[b]), dp_max[b] - dp_min[a])。

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

const int MAX_N = (50000 + 5000);
const int MAX_M = (MAX_N << 2);
const int inf = 0x3f3f3f3f;
int NE1, NE2, NE3, head1[MAX_N], head2[MAX_N], head3[MAX_N];

void Init()
{
	NE1 = NE2 = NE3 = 0;
	memset(head1, -1, sizeof(head1));
	memset(head2, -1, sizeof(head2));
	memset(head3, -1, sizeof(head3));

}

int N, Q, ans[MAX_N], value[MAX_N], vis[MAX_N];

struct Edge1 {
	int v, next;
} edge1[MAX_M];

void Insert1(int u, int v)
{
	edge1[NE1].v = v;
	edge1[NE1].next = head1[u];
	head1[u] = NE1++;
}

struct Edge {
	int v, id, next;
} edge2[MAX_M], edge3[MAX_M];

void Insert2(int u, int v, int id, int flag)
{
	if (!flag) {
		edge2[NE2].v = v;
		edge2[NE2].id = id;
		edge2[NE2].next = head2[u];
		head2[u] = NE2++;
	} else {
		edge3[NE3].v = v;
		edge3[NE3].id = id;
		edge3[NE3].next = head3[u];
		head3[u] = NE3++;
	}
}

int parent[MAX_N];
int up[MAX_N], down[MAX_N], dp_max[MAX_N], dp_min[MAX_N];

int find(int x)
{
	if (x == parent[x]) {
		return x;
	}

	int fa = parent[x];
	parent[x] = find(parent[x]);

	up[x] = max(max(up[x], up[fa]), dp_max[fa] - dp_min[x]);
	down[x] = max(max(down[x], down[fa]), dp_max[x] - dp_min[fa]);
	dp_max[x] = max(dp_max[x], dp_max[fa]);
	dp_min[x] = min(dp_min[x], dp_min[fa]);

	return parent[x];
}

struct Node {
	int u, v;
} node[MAX_N];

void Tarjan(int u)
{
	vis[u] = 1;
	parent[u] = u;
	//Q;
	for (int i = head2[u]; ~i; i = edge2[i].next) {
		int v = edge2[i].v, id = edge2[i].id;
		if (!vis[v]) continue;
		int fa = find(v);
		Insert2(fa, v, id, 1);
	}

	for (int i = head1[u]; ~i; i = edge1[i].next) {
		int v = edge1[i].v;
		if (vis[v]) continue;
		Tarjan(v);
		parent[v] = u;
	}

	//edge3
	for (int i = head3[u]; ~i; i = edge3[i].next) {
		int id = edge3[i].id;
		find(node[id].u);
		find(node[id].v);
		ans[id] = max(max(up[node[id].u], down[node[id].v]), dp_max[node[id].v] - dp_min[node[id].u]);
	}
}


int main()
{
	while (~scanf("%d", &N)) {
		for (int i = 1; i <= N; ++i) {
			scanf("%d", &value[i]);
			up[i] = down[i] = 0;
			dp_max[i] = dp_min[i] = value[i];
		}

		Init();

		for (int i = 1; i < N; ++i) {
			int u, v;
			scanf("%d %d", &u, &v);
			Insert1(u, v);
			Insert1(v, u);
		}

		scanf("%d", &Q);
		for (int i = 1; i <= Q; ++i) {
			scanf("%d %d", &node[i].u, &node[i].v);
			Insert2(node[i].u, node[i].v, i, 0);
			Insert2(node[i].v, node[i].u, i, 0);
		}

        memset(vis, 0, sizeof(vis));
		Tarjan(1);

		for (int i = 1; i <= Q; ++i) printf("%d
", ans[i]);
	}
	return 0;
}