Strategic Game

Time Limit: 20000/10000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 2925    Accepted Submission(s): 1222

Problem 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.

The input file 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

or

node_identifier:(0)

The node identifiers are integer numbers between 0 and n-1, for n nodes (0 < n <= 1500). Every edge appears only once in the input data.

For example for the tree:

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

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 table:  

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  

Source
Southeastern Europe 2000  

Recommend JGShining     这题用树形DP，速度很快 154MS. 相比于二分匹配的做法快很多。 二分匹配做法见：
http://www.cnblogs.com/kuangbin/archive/2012/08/19/2646713.html  

/*
HDU 1054

G++ 312ms 560K
*/

#include<stdio.h>
#include<string.h>
#include<iostream>
#include<algorithm>
using namespace std;
const int MAXN=1510;
struct Node
{
    int father,brother,child;
    int yes;//该结点放置
    int no;//该结点不放置
}t[MAXN];
void DFS(int x)
{
    int child=t[x].child;
    while(child)
    {
        DFS(child);
        t[x].yes+=min(t[child].yes,t[child].no);
        //父亲结点放置了，儿子结点可以放置也可以不放置
        t[x].no+=t[child].yes;
        //父亲结点没有放置，儿子结点必须放置
        child=t[child].brother;
    }
}
bool used[MAXN];
int main()
{
    //freopen("in.txt","r",stdin);
    //freopen("out.txt","w",stdout);
    int n;
    int root,k,v;
    while(scanf("%d",&n)!=EOF)
    {
        memset(used,false,sizeof(used));
        int Root;//根结点
        for(int i=0;i<n;i++)
        {
            scanf("%d:(%d)",&root,&k);
            root++;//编号从1开始
            if(i==0)Root=root;
            if(!used[root])
            {
                used[root]=true;
                t[root].brother=t[root].father=t[root].child=0;
                t[root].yes=1;
                t[root].no=0;
            }
            while(k--)
            {
                scanf("%d",&v);
                v++;
                if(!used[v])
                {
                    used[v]=true;
                    t[v].brother=t[v].father=t[v].child=0;
                    t[v].yes=1;
                    t[v].no=0;
                }
                t[v].brother=t[root].child;
                t[v].father=root;
                t[root].child=v;
            }

        }
        DFS(Root);
        printf("%d\n",min(t[Root].yes,t[Root].no));

    }
    return 0;
}