HDU 1150 Machine Schedule（二分匹配+匈牙利算法）

深藏阁楼爱情的钟 2022-06-10 05:18 177阅读 0赞

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

题解：

题意：

有两台机器A和B以及N个需要运行的任务。每台机器有M种不同的模式，而每个任务都恰好在一台机器上运行。如果它在机器A上运行，则机器A需要设置为模式xi,如果它在机器B上运行，则机器A需要设置为模式yi。每台机器上的任务可以按照任意顺序执行，但是每台机器每转换一次模式需要重启一次。请合理为每个任务安排一台机器并合理安排顺序，使得机器重启次数尽量少。

思路：

把两个机器需要不同的模式匹配一下就是需要重启的次数，匈牙利算法模板题

代码：

#include<algorithm>
    #include<iostream>
    #include<cstring>
    #include<stdio.h>
    #include<math.h>
    #include<string>
    #include<stdio.h>
    #include<queue>
    #include<stack>
    #include<map>
    #include<deque>
    #define M (t[k].l+t[k].r)/2
    #define lson k*2
    #define rson k*2+1
    #define ll long long
    #define INF 100861111;
    using namespace std;
    int n,m;
    int vis[105];
    int p[105][105];
    int used[105];
    int find(int u)//匈牙利算法
    {
        int i;
        for(i=1;i<=m;i++)
        {
            if(!vis[i]&&p[u][i])
            {
                vis[i]=1;
                if(!used[i]||find(used[i]))
                {
                    used[i]=u;
                    return 1;
                }
            }
        }
        return 0;
    }
    int main()
    {
        int i,j,k,ans,q,x,y,d;
        while(scanf("%d",&n)!=EOF&&n)
        {
            scanf("%d%d",&m,&q);
            memset(p,0,sizeof(p));
            for(i=0;i<q;i++)
            {
                scanf("%d%d%d",&d,&x,&y);
                p[x][y]=1;
            }
            memset(used,0,sizeof(used));
            ans=0;
            for(i=1;i<=n;i++)
            {
                memset(vis,0,sizeof(vis));
                if(find(i))
                    ans++;
            }
            printf("%d\n",ans);
        }
        return 0;
    }