hdoj--1150--Machine Schedule（最小点覆盖）

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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

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
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

# 思路： 
这很明显是有张二分图。              
点：A模式，B模式；                  
边：job_k可由机器A的模式i转化成机器B的模式j（可以理解是任务）                   
那么问题就转化成是否存在一个最小点集，使得所有的边都至少和该点集的一个点相联系。                    
这就是最小顶点覆盖数                

最小点覆盖=最大匹配

匈牙利算法

```cpp
#include<stdio.h>  
#include<string.h>  
#include<vector>  
#include<algorithm>  
using namespace std;  
vector<int>map[1010];  
int used[1010],pipei[1010];  
int find(int x)  
{  
    for(int i=0;i<map[x].size();i++)  
    {  
        int y=map[x][i];  
        if(!used[y])  
        {  
            used[y]=1;  
            if(!pipei[y]||find(pipei[y]))  
            {  
                pipei[y]=x;  
                return 1;  
            }  
        }  
    }  
    return 0;  
}  
int main()  
{  
    int n;  
    while(scanf("%d",&n),n)  
    {  
        int a,b,c;  
        int m,k;  
        memset(pipei,0,sizeof(pipei));  
        scanf("%d%d",&m,&k);  
        for(int i=0;i<=n;i++)  
        map[i].clear();  
        while(k--)  
        {  
            scanf("%d%d%d",&a,&b,&c);  
            if(b&&c)  
            map[b].push_back(c);  
        }  
        int sum=0;  
        for(int i=0;i<n;i++)  
        {  
            memset(used,0,sizeof(used));  
            sum+=find(i);  
        }  
        printf("%d\n",sum);  
    }  
    return 0;  
}
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