Machine Schedule - POJ 1325 二分图匹配-优快云博客

本文链接：https://blog.youkuaiyun.com/u014733623/article/details/40544571

探讨一个经典的计算机科学问题——两机调度。目标是最小化在完成所有任务过程中机器重启的次数。通过建立约束条件并利用二分图匹配算法解决此问题。

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Machine Schedule

Time Limit: 1000MS		Memory Limit: 10000K
Total Submissions: 11997		Accepted: 5108

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

Sample Output

题意：一项工作需要A机器在某种状态或B机器在某种状态，问至少转变机器多少次。

思路：将每项工作的AB两种状态连接起来，然后二分图匹配。可以这样理解，匹配过后，对于一项工作需要a和b状态的话，要么a和b相连，要么a与别的相连或b与别的相连，不会存在a,b既不相连也不和别的相连的情况。

AC代码如下：

#include<cstdio>
#include<cstring>
using namespace std;
int n,m,g[110][110],match[110],vis[110],VIS;
bool dfs(int u)
{
    int i,j,k;
    for(i=1;i<=n;i++)
       if(g[i][u] && vis[i]!=VIS)
       {
           vis[i]=VIS;
           if(match[i]==0 || dfs(match[i]))
           {
               match[i]=u;
               return true;
           }
       }
    return false;
}
int main()
{
    int i,j,k,p,u,v,ans;
    while(~scanf("%d",&n) && n>0)
    {
        scanf("%d%d",&m,&k);
        memset(g,0,sizeof(g));
        memset(match,0,sizeof(match));
        for(i=1;i<=k;i++)
        {
            scanf("%d%d%d",&p,&u,&v);
            g[u][v]=1;
        }
        ans=0;
        for(i=1;i<=m;i++)
        {
            VIS++;
            if(dfs(i))
              ans++;
        }
        printf("%d\n",ans);
    }
}