Bipartite-Matching

/*First METHOD 
Solved Using kuhn's Algorithm 
Kho-Kho algorithm ~ Take a free vertex and find a augmentation which increase the match atleast by one.
Berge's Theorem ~ A matching M in a Bipartite graph is maximum if and only if there doesn exist any augmenting path.
Run in O(N*M+N*N) */ 
class PointyWizardHats {
 public:
 int parent[55],visited[55],rnode,lnode;
 vector<int> graph[55];
 bool can_be_kept(int bh,int br,int th,int tr) // General Constraint for the problem
 {
  if(br>tr and (th*br>bh*tr))
    return true;
  return false; 
 }
 bool dfs(int u)
 {
   if(visited[u])
      return false;
   visited[u]=true;
   for(int i=0;i<(int)graph[u].size();i++)
   {
     int v=graph[u][i];
     if(parent[v]==-1 or dfs(parent[v]))
     {
       parent[v]=u;
       return true;
     }
   }
   return false;
 }
 int kuhn_salgo()
 {
   SET(parent);  
   for(int i=0;i<lnode;i++)  
   { 
    CLR(visited);  
    dfs(i);
   }
   return rnode-count(parent,parent+rnode,-1);   
 }
 int getNumHats(vector <int> topHeight, vector <int> topRadius, vector <int> bottomHeight, vector <int> bottomRadius) 
 {
  lnode=bottomHeight.size();rnode=topHeight.size();
  LOOP(j,rnode)
   LOOP(i,lnode)
     if(can_be_kept(bottomHeight[i],bottomRadius[i],topHeight[j],topRadius[j]))
        graph[i].push_back(j);
  
  return kuhn_salgo(); 
 }
};