POJ 2486 Apple Tree

Description

Wshxzt is a lovely girl. She likes apple very much. One day HX takes her to an apple tree. There are N nodes in the tree. Each node has an amount of apples. Wshxzt starts her happy trip at one node. She can eat up all the apples in the nodes she reaches. HX is a kind guy. He knows that eating too many can make the lovely girl become fat. So he doesn’t allow Wshxzt to go more than K steps in the tree. It costs one step when she goes from one node to another adjacent node. Wshxzt likes apple very much. So she wants to eat as many as she can. Can you tell how many apples she can eat in at most K steps.

Input

There are several test cases in the input 
Each test case contains three parts. 
The first part is two numbers N K, whose meanings we have talked about just now. We denote the nodes by 1 2 ... N. Since it is a tree, each node can reach any other in only one route. (1<=N<=100, 0<=K<=200) 
The second part contains N integers (All integers are nonnegative and not bigger than 1000). The ith number is the amount of apples in Node i. 
The third part contains N-1 line. There are two numbers A,B in each line, meaning that Node A and Node B are adjacent. 
Input will be ended by the end of file. 

Note: Wshxzt starts at Node 1.

Output

For each test case, output the maximal numbers of apples Wshxzt can eat at a line.

Sample Input

2 1 
0 11
1 2
3 2
0 1 2
1 2
1 3

Sample Output

11
2

Source

POJ Contest,Author:magicpig@ZSU

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树形DP~

因为走到一个叶子节点后要原路返回才能走到下一个节点，所以记录的f数组要多加一维状态记录是否会返回该点，则f[i][j][k]就表示从点i向子节点走了j步，如果k==1，则表示没有回到该点，k==0则表示回到该点。

状态转移方程就是f[u][i][1]=max(f[u][i][1],f[u][i-j][0]+f[kkz][j-1][1]);
  f[u][i][1]=max(f[u][i][1],f[u][i-j][1]+f[kkz][j-2][0]);
  f[u][i][0]=max(f[u][i][0],f[u][i-j][0]+f[kkz][j-2][0]);

（f数组不能开太大，否则会T的。）

#include
#include
#include
using namespace std;

int n,k,x,y,akz,w[10001],ne[10001],fi[10001],fa[10001],f[101][201][2],cnt;

void add(int u,int v)
{
	w[++cnt]=v;ne[cnt]=fi[u];fi[u]=cnt;
}

void findd(int u)
{
	for(int kkzv=fi[u];kkzv;kkzv=ne[kkzv])
	  if(w[kkzv]!=fa[u])
	  {
		int kkz=w[kkzv];fa[kkz]=u;
		findd(kkz);
		for(int i=k;i>=1;i--)
		  for(int j=1;j<=i;j++)
		  {
		  	f[u][i][1]=max(f[u][i][1],f[u][i-j][0]+f[kkz][j-1][1]);
		  	f[u][i][1]=max(f[u][i][1],f[u][i-j][1]+f[kkz][j-2][0]);
		  	f[u][i][0]=max(f[u][i][0],f[u][i-j][0]+f[kkz][j-2][0]);
		  }
	  }
}

int main()
{
	while(scanf("%d%d",&n,&k)!=EOF)
	{
		memset(f,0,sizeof(f));
		for(int i=1;i<=n;i++)
		{
			scanf("%d",&akz);fi[i]=0;
			for(int j=0;j<=k;j++) f[i][j][0]=f[i][j][1]=akz;
		}
		cnt=0;
		for(int i=1;i