POJ 1325 Machine Schedule

最新推荐文章于 2018-12-02 19:17:44 发布

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最新推荐文章于 2018-12-02 19:17:44 发布

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本文探讨了一个经典的计算机科学问题——两机调度问题。该问题涉及如何通过改变作业序列和分配每项作业到合适的机器来最小化重启机器的次数，以完成所有作业任务。文章提供了一种解决方案，并使用了匈牙利算法求解最大匹配。

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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
Source

Beijing 2002

这样如果我们要把所有的作业做完，是不是找出最小的点覆盖将所有的边都覆盖掉即可
匈牙利算法求最大匹配。

#include<iostream>
#include<cstring>
#include<cstdio>
using namespace std;
const int N=105;
int n,m,k,ans,lft[N];
bool vis[N],d[N][N];
bool dfs(int u)
{
    for(int i=1;i<=m;++i)
        if(d[u][i]&&!vis[i])
        {
            vis[i]=1;
            if(lft[i]==-1||dfs(lft[i]))
            {
                lft[i]=u;
                return 1;
            }
        }
    return 0;
}
int main()
{
    while(scanf("%d",&n)&&n)
    {
        ans=0;
        memset(d,0,sizeof(d));
        scanf("%d%d",&m,&k);
        while(k--)
        {
            int x,y,z;
            scanf("%d%d%d",&x,&y,&z);
            if(y==0||z==0)
                continue;
            d[++y][++z]=1;
        }
        memset(lft,-1,sizeof(lft));
        for(int i=1;i<=n;++i)
        {
            memset(vis,0,sizeof(vis));
            if(dfs(i))
                ++ans;
        }
        printf("%d\n",ans);
    }
    return 0;
}