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Machine Schedule

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 9000    Accepted Submission(s): 4518

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)

 

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题目大意：n个任务都可以在A机器上也可以在B机器上操作，每个机器有多种操作模式，当改变操作方式时机器会重启一次。对于给出的n个任务，计算出最小的机器重启数。

思路：每个任务建立x->y的边，求最少得点可以连接所有边，即求最小点覆盖。最小点覆盖=最大二分匹配数。

匈牙利算法。

附上AC代码：

#include<iostream>#include<algorithm>#include<cstring>using namespace std;const int maxn=100+5;int G[maxn][maxn];int used[maxn];int result[maxn];int u,v,T;int t,x,y;int cnt;//从左边开始找增广路int find(int x){    for(int i=0;i<v;i++)    {        if(G[x][i]==1&&!used[i])        {            used[i]=1;            if(result[i]==-1||find(result[i]))            {                result[i]=x;                return 1;            }        }    }    return 0;}int main(){    ios::sync_with_stdio(false);        while(cin>>u,u)    {        cnt=0;        memset(result,-1,sizeof(result));        memset(G,0,sizeof(G));        cin>>v>>T;                for(int i=0;i<T;i++)        {            cin>>t>>x>>y;            if(x>0&&y>0)//初始态为0，所以0边不添加            G[x][y]=1;        }                for(int i=0;i<u;i++)        {            memset(used,0,sizeof(used));//每次都要初始化标记            if(find(i))cnt++;        }        cout<<cnt<<endl;    }    return 0;}