HDU1150(最小顶点覆盖)

Machine Schedule

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 7362    Accepted Submission(s): 3677

Problem Description

As we all know, machine scheduling is a very classical problem in computer science and has been studied for a very long history. Scheduling problems differ widely in the nature of the constraints that must be satisfied and the type of schedule desired. Here we consider a 2-machine scheduling problem.

There are two machines A and B. Machine A has n kinds of working modes, which is called mode_0, mode_1, …, mode_n-1, likewise machine B has m kinds of working modes, mode_0, mode_1, … , mode_m-1. At the beginning they are both work at mode_0.

For k jobs given, each of them can be processed in either one of the two machines in particular mode. For example, job 0 can either be processed in machine A at mode_3 or in machine B at mode_4, job 1 can either be processed in machine A at mode_2 or in machine B at mode_4, and so on. Thus, for job i, the constraint can be represent as a triple (i, x, y), which means it can be processed either in machine A at mode_x, or in machine B at mode_y.

Obviously, to accomplish all the jobs, we need to change the machine's working mode from time to time, but unfortunately, the machine's working mode can only be changed by restarting it manually. By changing the sequence of the jobs and assigning each job to a suitable machine, please write a program to minimize the times of restarting machines.

 

Input

The input file for this program consists of several configurations. The first line of one configuration contains three positive integers: n, m (n, m < 100) and k (k < 1000). The following k lines give the constrains of the k jobs, each line is a triple: i, x, y.

The input will be terminated by a line containing a single zero.

 

Output

The output should be one integer per line, which means the minimal times of restarting machine.

 

Sample Input

5 5 10

0 1 1

1 1 2

2 1 3

3 1 4

4 2 1

5 2 2

6 2 3

7 2 4

8 3 3

9 4 3

0

 

Sample Output

3

题意：机器A有n种工作方式，B有m中工作方式，有k个工作。给定一个三元组(i,x,y)工作i可以用机器A的x工作方式完成也可以用机器B的y工作方式完成。不过，两个机器没转换一次工作方式均需要重启机器一次。问安排合适的工作次序，最少需要需要重启机器几次？

思路：将机器A的工作方式作为点独立集U,B的工作方式作为点独立集V。工作方式x到y的无向边表示工作i，则问题 转化为求二分图中最小顶点覆盖问题。

#include"cstdio"
#include"cstring"
#include"vector"
using namespace std;
const int MAXN=;
vector<int> G[MAXN];
int V,E;
void add_edge(int u,int  v)
{
    G[u].push_back(v);
    G[v].push_back(u);
}
int match[MAXN];
int vis[MAXN];
bool dfs(int u)
{
    vis[u]=;
    for(int i=;i<G[u].size();i++)
    {
        int v=G[u][i],w=match[v];
        if(w==||(!vis[w]&&dfs(w)))
        {
            match[u]=v;
            match[v]=u;
            return true;
        }
    }
    return false;
}

int binpartite_matching()
{
    int ans=;
    memset(match,,sizeof(match));
    for(int i=;i<=V;i++)
    {
        if(!match[i])
        {
            memset(vis,,sizeof(vis));
            if(dfs(i))    ans++;
        }
    }
    return ans;
}

int main()
{
    while(scanf("%d",&V)!=EOF&&V)
    {
        scanf("%*d%d",&E);
        for(int i=;i<MAXN;i++)    G[i].clear();
        for(int i=;i<E;i++)
        {
            int u,v;
            scanf("%*d%d%d",&u,&v);
            add_edge(u,+v);
            add_edge(+v,u);
        }
        int ans=binpartite_matching();
        printf("%d\n",ans);
    }

    return ;
}