POJ 2486 Apple Tree(树形DP)

总结

1. 这里 dp[][][] 不是恰好走 k 步, 而是最多走 k 步. 恰好和最多的区别就在于 dp 数组的初始化上了

代码

/*
 * source.cpp
 *
 *  Created on: Apr 7, 2014
 *      Author: sangs
 */

#include <stdio.h>
#include <iostream>
#include <string>
#include <vector>
#include <memory.h>
#include <algorithm>
#include <math.h>
using namespace std;


int val[1000];
int dp[500][500][2];
vector<int> graph[1000];

/*
 * dp[u][t][0] start from u and end at u, maximum income in t steps
 * dp[u][t][1] .............not end at u, maximum income in .......
 * dp[u][t][0] = max(dp[u][t][0], dp[u][t-2-k][0] + dp[v][k][0]) v is child of u
 * dp[u][t][1] = max(dp[u][t][1], dp[u][t-1-k][0] + dp[v][k][1]) v is child of u and girl end at v
 * dp[u][t][1] = max(dp[u][t][1], dp[u][t-2-k][1] + dp[v][k][0]) v is child of u and girl end at another child of u
 */
void solve_dp(int u, int pre, int vmax) {
	for(int i = 0; i <= vmax; i ++) // at most k steps, not exactly k steps
		dp[u][i][0] = dp[u][i][1] = val[u];

	for(size_t i = 0; i < graph[u].size(); i ++) {
		int v = graph[u][i];
		if(v == pre) continue;

		solve_dp(v, u, vmax);

		for(int j = vmax;  j >= 0; j --) {
			for(int k = 0; k <= j; k ++) {
				dp[u][j+2][0] = max(dp[u][j][0], dp[u][j-k][0] + dp[v][k][0]);
				dp[u][j+1][1] = max(dp[u][j][1], dp[u][j-k][0] + dp[v][k][1]);
				dp[u][j+2][1] = max(dp[u][j][1], dp[u][j-k][1] + dp[v][k][0]);
			}
		}
	}
}

int main() {
	freopen("input.txt", "r", stdin);
	int n, T;
	while(scanf("%d%d", &n, &T) != EOF) {
		for(int i = 1; i <= n; i ++)
			scanf("%d", val+i);

		for(int i =1; i <= n; i ++)
			graph[i].clear();

		memset(dp, 0, sizeof(dp));

		for(int i = 1; i <= n-1; i ++) {
			int from, to;
			scanf("%d%d", &from, &to);
			graph[from].push_back(to);
			graph[to].push_back(from);
		}

		solve_dp(1, -1, T);
		cout << dp[1][T][1] << endl;
	}
    return 0;
}