POJ1325Machine Schedule（匈牙利算法）

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.

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.

The output should be one integer per line, which means the minimal times of restarting machine.

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

3
【分析】本题要求二部图的最小点覆盖集问题，即求最小的顶点集合，覆盖住所有的点。转换成求二部图的最大匹配问题，因为：二部图的点覆盖数==匹配数。

#include <iostream>
#include <cstdio>
#include <cstdlib>
#include <cmath>
#include <algorithm>
#include <climits>
#include <cstring>
#include <string>
#include <set>
#include <map>
#include <queue>
#include <stack>
#include <vector>
#include <list>
#include<functional>
#define mod 1000000007
#define inf 0x3f3f3f3f
#define pi acos(-1.0)
using namespace std;
typedef long long ll;
const int N=105;
const int M=15005;
int nx,ny;
int job;
int edg[N][N];
int ans=0;
int visx[N],visy[N];
int cx[N],cy[N];
int dfs(int u)
{
    visx[u]=1;
    for(int v=1;v<=ny;v++){
        if(edg[u][v]&&!visy[v]){
            visy[v]=1;
            if(!cy[v]||dfs(cy[v])){
                cx[u]=v;cy[v]=u;
                return 1;
            }
        }
    }
    return 0;
}
int solve()
{
    memset(cx,0,sizeof(cx));memset(cy,0,sizeof(cy));
    for(int i=1;i<=nx;i++){
        if(!cx[i]){
            memset(visx,0,sizeof(visx));memset(visy,0,sizeof(visy));
            ans+=dfs(i);
        }
    }
}
int main() {
    int x,y,m;
    scanf("%d%d%d",&nx,&ny,&job);
    memset(edg,0,sizeof(edg));
    for(int i=0;i<job;i++){
        scanf("%d%d%d",&m,&x,&y);
        edg[x][y]=1;
    }
    solve();
    printf("%d\n",ans);
    return 0;
}