POJ 1325 Machine Schedule (binary map minimum point set overlay Hungarian algorithm)

Machine Schedule

Time Limit: 1000MS		Memory Limit: 10000K
Total Submissions: 12621		Accepted: 5399

Description

As we all know, machine scheduling are a very classical problem in computer science and have been studied for a very long hi Story. 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 was machines a and B. Machine A have n kinds of working modes, which is called Mode_0, Mode_1, ..., mode_n-1, lik Ewise machine B has m kinds of working modes, MODE_0, Mode_1, ..., mode_m-1. At the beginning they is both work at Mode_0.

For k jobs given, each of the them can is processed in either one of the one of the both machines in particular mode. For example, job 0 can either is processed in machine A at mode_3 or in machine B at Mode_4, Job 1 can either be processed In machine A is mode_2 or in machine B at Mode_4, and so on. Thus, for Job I, the constraint can is represent as a triple (I, X, y), which means it can be processed either 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 is 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 <) and K (K < 1000). The following k lines give the constrains of the K jobs, each of which is a triple:i, X, Y.

The input would be terminated to a line containing a single zero.

Output

the output should is 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

Beijing 2002

Title Link: http://poj.org/problem?id=1325

Main topic: Two machines, each job can work in different modes of different machines, a x y indicates that job a can be done by machine 1 x mode or machine 2 y mode, to complete all jobs, must constantly switch machine mode, try to find a suitable distribution relationship so that the minimum number of switches, Note that machine 1 and Machine 2 start working in 0 mode for minimum number of times

Topic Analysis: The minimum point set coverage problem, 1 and 22 machines as two sides of the graph, according to each work corresponding to the machine model to build the edge, and then is to find the smallest point of the dichotomy, that is, the smallest point set, so that it contains all the edges, according to the minimum number of points in the binary map coverage = Maximum match, So directly with the Hungarian algorithm to solve the maximum match, note that the 0 mode does not connect the edge can

#include <cstdio> #include <cstring>int const MAX = 105;bool G[max][max];int Cx[max], Cy[max];bool Vis[max];            int n, M, k;int DFS (int x) {for (int y = 0; y < m; y++) {if (!vis[y] && G[x][y]) {            Vis[y] = true; if (cy[y] = =-1 | |                DFS (Cy[y])) {cx[x] = y;                Cy[y] = x;            return 1; }}} return 0;}    int Maxmatch () {int res = 0;    memset (CX,-1, sizeof (CX));    memset (CY,-1, sizeof (CY));            for (int i = 0; i < n; i++) {if (cx[i] = = 1) {memset (Vis, false, sizeof (VIS));        Res + = DFS (i); }} return res;}        int main () {while (scanf ("%d", &n)! = EOF && N) {memset (g, false, sizeof (g));        scanf ("%d%d", &m, &k);            for (int i = 0; i < K; i++) {int tmp, x, y;            scanf ("%d%d%d", &tmp, &x, &y); if (x * y) g[X][y] = true;        } int ans = Maxmatch ();    printf ("%d\n", ans); }}

POJ 1325 Machine Schedule (binary map minimum point set overlay Hungarian algorithm)