POJ1463 树型动态规划

题意：

      给定一棵树，在某些节点上会放置士兵，使得任意一条边上的俩个节点至少有一个节点有士兵，求达到要求的方案里放士兵最 小数量。

思路：建树，每个child有唯一的father,用每个点有两种状态有士兵跟没有 士兵，dp[i][1]表示有士兵，dp[i][0]表示没有士兵。

则状态转移方程为：dp[father][1]=sum(max(dp[child][0],dp[child][1])+1;

                 dp[father][0]=sum(dp[child][1]);

源代码：

#include <iostream>
#include <cstdio>
#include <cstring>
using namespace std;
const int MAXN=1500;
int f[MAXN+10];
bool visit[MAXN+10];
int n;
int result[MAXN+10][2];
void tree_dp(int node)
{
  int i;
  for(i=1;i<=n;i++)
    {
      if(visit[i]==false&&f[i]==node)
	{
	  visit[i]=true;
	  tree_dp(i);
	    result[node][1]+=min(result[i][1],result[i][0]);
	          result[node][0]+=result[i][1];
	}
      
    

      
    }
  //result[node][1]++;
}
int main()
{
  int j;
  int father,child;
  int t;
  int i;
  int root;
  while(scanf("%d",&n)!=EOF)
    {
      memset(f,0,sizeof(f));
      memset(visit,false,sizeof(visit));
        memset(result,0,sizeof(result));
      for(i=1;i<=n;i++)
	{
	  result[i][1]=1;
	}
    

      
      root=0;
      for(i=1;i<=n;i++)
	{
	  scanf("%d:(%d)",&father,&t);
	        father++;
	  for(j=1;j<=t;j++)
	    {
	      scanf("%d",&child);
	      child++;
	  
	      f[child]=father;
	      if(child==root)
		{
		  root=father;
		}
	    }
	  
	  
	}
      tree_dp(root);
      
      printf("%d/n",min(result[root][0],result[root][1]));      
      
      
      
    }
  return 0;
}
 


}


附题目：

Strategic game

Time Limit: 2000MS		Memory Limit: 10000K
Total Submissions: 2808		Accepted: 1225

Description

Bob enjoys playing computer games, especially strategic games, but sometimes he cannot find the solution fast enough and then he is very sad. Now he has the following problem. He must defend a medieval city, the roads of which form a tree. He has to put the minimum number of soldiers on the nodes so that they can observe all the edges. Can you help him?

Your program should find the minimum number of soldiers that Bob has to put for a given tree.

For example for the tree:

the solution is one soldier ( at the node 1).

Input

The input contains several data sets in text format. Each data set represents a tree with the following description:

• 
  
• the number of nodes
• the description of each node in the following format
  node_identifier:(number_of_roads) node_identifier₁ node_identifier₂ ... node_identifier_{number_of_roads}
  or
  node_identifier:(0)

The node identifiers are integer numbers between 0 and n-1, for n nodes (0 < n <= 1500);the number_of_roads in each line of input will no more than 10. Every edge appears only once in the input data.

Output

The output should be printed on the standard output. For each given input data set, print one integer number in a single line that gives the result (the minimum number of soldiers). An example is given in the following:

Sample Input

4

0:(1) 1

1:(2) 2 3

2:(0)

3:(0)

5

3:(3) 1 4 2

1:(1) 0

2:(0)

0:(0)

4:(0)

Sample Output

1

2