Machine Schedule

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 9438    Accepted Submission(s): 4745

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 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

Asia 2002, Beijing (Mainland China)

Recommend

Ignatius.L

题目大意：有A、B两台机器，分别有n,m种工作状态，编号为0~n-1，0~m-1。现在有k个任务，可以在A机器上以xi或B机器上yi状态下完成。每次更换状态都要重启一次。问完成这些任务要重启多少次。（任务完成没有顺序）

解题思路：二分图，把A机器的n种当成左边，B机器的m种状态当成右边，（xi,yi）构成一条边，匈牙利求出最大匹配数即可。

#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;
const int maxn=105;
int line[maxn][maxn];
bool used[maxn];
int n,m,k,match[maxn];

bool dfs(int x)
{
    for(int i=1;i<m;i++)//状态为0的任务在初始时直接完成，不用计算
    {
        if(line[x][i]==1 && used[i]==false)
        {
            used[i] = true;
            if(match[i]==-1 || dfs(match[i]))
            {
                match[i] = x;
                return true;
            }
        }
    }
    return false;
}

int main()
{
    while(scanf("%d",&n)!=EOF)
    {
        if(n==0)
            break;
        memset(line,0,sizeof(line));
        scanf("%d %d",&m,&k);
        int i,x,y;
        while(k--)
        {
            scanf("%d %d %d",&i,&x,&y);
            line[x][y]=1;
        }
        memset(match,-1,sizeof(match));
        int ans=0;
        for(i=1;i<n;i++)//状态为0的任务在初始时直接完成，不用计算
        {
            memset(used,false,sizeof(used));
            if(dfs(i))
                ans++;
        }
        printf("%d\n",ans);
    }
}