Machine Schedule hdu 1150 二分图的最小点覆盖

Machine Schedule

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 4982    Accepted Submission(s): 2465

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 5 100 1 11 1 22 1 33 1 44 2 15 2 26 2 37 2 48 3 39 4 30

 

Sample Output

3

 

Source

Asia 2002, Beijing (Mainland China)

 

Recommend

Ignatius.L

这个题目应该讲是最小点覆盖的好题目，最小顶点覆盖是值取顶点集[x,y],使的有边e1和至少一个顶点V1等相关联，这就是二分图的最小顶点覆盖问题。在题目中

是指有k个任务，每个任务可以由a,b机器完成，每个机器如果换成别的方式需要重启，求最小重启的个数，也就是把a,b的某个模式看成是顶点，把任务看成是边，那么问题就是是否存在一个最小规模的点击，使得所有的边都至少和该点集中的一个点相关联。

最小点覆盖=最大匹配数

#include<stdio.h>#include<string.h>using namespace std;#define M 2000int n,m;int link[M],g[M][M];//g[][]是算地图，link代表联系bool vis[M];bool find(int i){    for(int j=1;j<=n;j++)    if(g[i][j]&&!vis[j])    {        vis[j]=true;        if(link[j]==0||find(link[j]))        {            link[j]=i;            return true;        }    }    return false;}int main(){     int k;     while(scanf("%d",&n),n)    {        scanf("%d%d",&m,&k);        memset(g,0,sizeof(g));        memset(link,0,sizeof(link));        int a,b,c;        while(k--)        {            scanf("%d%d%d",&a,&b,&c);            g[b][c]=1;        }        int num=0;        for(int i=1;i<=n;i++)        {            memset(vis,false,sizeof(vis));            if(find(i))            {                //printf("fdsjklfsd");                num++;            }        }        printf("%d\n",num);    }    return 0;}