[wikioi]没有上司的舞会

树形DP。用F[k][0]和F[k][1]表示某节点不选和选了之后子树的最大值。那么：
f[i][0]=sigma(max(f[k][0],f[k][1]))
f[i][1]=sigma(f[k][0])+v[i]
解题中用了备忘录。一开始要先找树根。

#include <cstdio>
#include <iostream>
#include <algorithm>
#include <memory.h>
#include <vector>
#define MAX(a, b) a>b?a:b
#define LEN 6005
using namespace std;

int F[LEN][2]; // dp state, F[i][0] for i not selected, F[i][1] for i selected
int R[LEN];
bool isRoot[LEN];
int opt(int x, int y, vector<vector<int> > &tree) {
	if (F[x][y] != -1) {
		return F[x][y];
	}
	if (y == 0) {
		int sum = 0;
		for (int i = 0; i < tree[x].size(); i++) {
			sum += MAX(opt(tree[x][i], 0, tree), opt(tree[x][i], 1, tree));
		}
		F[x][y] = sum;
		return sum;
	}
	else if (y == 1) {
		int sum = R[x];
		for (int i = 0; i < tree[x].size(); i++) {
			sum += opt(tree[x][i], 0, tree);
		}
		F[x][y] = sum;
		return sum;
	}
	else return 0;
}

int main()
{
    memset(F, 0, sizeof(F));
	memset(R, 0, sizeof(R));
	memset(isRoot, true, sizeof(isRoot));
	int n;
    cin >> n;
	vector<vector<int> > tree(n+1);
	for (int i = 1; i <= n; i++) {
		cin >> R[i];
	}
	int x, y;
	for (int i = 1; i <= n-1; i++) {
		cin >> x >> y;
		tree[y].push_back(x);
		isRoot[x] = false;
	}
	cin >> x >> y; // skip 0, 0

	for (int i = 1; i <= n; i++) {
		for (int j = 0; j <= 1; j++) {
			F[i][j] = -1;
		}
	}
	int root = 0;
	for (int i = 1; i <= n; i++) {
		if (isRoot[i]) {
			root = i;
			break;
		}
	}
	int ans = MAX(opt(root, 0, tree), opt(root, 1, tree));
	cout << ans << endl;
    return 0;
}