// A DFS based recursive function
// that returns true if a matching
// for vertex u is possible
bool bpm(BipartieGraph bg, int u,
bool[] seen, int[] matchR)
{
// Try every job one by one
for (int v = 0; v < bg.PartBVertices.Length; v++)
{
// If applicant u is interested
// in job v and v is not visited
if (bg.ContainsEdgeAtoB(u, v) && !seen[v])
{
// Mark v as visited
seen[v] = true;
// If job 'v' is not assigned to
// an applicant OR previously assigned
// applicant for job v (which is matchR[v])
// has an alternate job available.
// Since v is marked as visited in the above
// line, matchR[v] in the following recursive
// call will not get job 'v' again
if (matchR[v] < 0 || bpm(bg, matchR[v],
seen, matchR))
{
matchR[v] = u;
return(true);
}
}
}
return(false);
}
// Returns maximum number of
// matching from M to N
public int[] FindMaxMatching(BipartieGraph bg)
{
// An array to keep track of the
// applicants assigned to jobs.
// The value of matchR[i] is the
// applicant number assigned to job i,
// the value -1 indicates nobody is assigned.
// matchR[B] = A
int[] matchR = new int[bg.PartBVertices.Length];
// Initially all jobs are available
for (int i = 0; i < bg.PartBVertices.Length; ++i)
{
matchR[i] = -1;
}
// Count of jobs assigned to applicants
int result = 0;
for (int u = 0; u < bg.PartAVertices.Length; u++)
{
// Mark all jobs as not
// seen for next applicant.
bool[] seen = new bool[bg.PartAVertices.Length];
//for(int i = 0; i < bg.PartAVertices.Length; ++i)
// seen[i] = false;
// Find if the applicant
// 'u' can get a job
if (bpm(bg, u, seen, matchR))
{
result++;
}
}
return(matchR);
}
public void Test(BipartieGraph bg)
{
var matching = new BipartieGraphMaxMatching().FindMaxMatching(bg);
IsMatching(matching);
}
