Edmond's blossom C++ Implementation

Revision en1, by Kerpoo, 2016-12-30 00:52:28

I love this implementation of Edmond's Blossoms :-)

Edmond's Blossoms algorithm give a maximum matching in general graphs (non-bipartite)

/*
GETS:
V->number of vertices
E->number of edges
pair of vertices as edges (vertices are 1..n)

GIVES:
output of edmonds() is the maximum matching
match[i] if matched pair of i (-1 if there isn't a matched pair)
 */

#include <bits/stdc++.h>
using namespace std;
const int M=500;
struct struct_edge{int v;struct_edge* n;};
typedef struct_edge* edge;
struct_edge pool[M*M*2];
edge top=pool,adj[M];
int V,E,match[M],qh,qt,q[M],father[M],base[M];
bool inq[M],inb[M],ed[M][M];
void add_edge(int u,int v)
{
  top->v=v,top->n=adj[u],adj[u]=top++;
  top->v=u,top->n=adj[v],adj[v]=top++;
}
int LCA(int root,int u,int v)
{
  static bool inp[M];
  memset(inp,0,sizeof(inp));
  while(1)
    {
      inp[u=base[u]]=true;
      if (u==root) break;
      u=father[match[u]];
    }
  while(1)
    {
      if (inp[v=base[v]]) return v;
      else v=father[match[v]];
    }
}
void mark_blossom(int lca,int u)
{
  while (base[u]!=lca)
    {
      int v=match[u];
      inb[base[u]]=inb[base[v]]=true;
      u=father[v];
      if (base[u]!=lca) father[u]=v;
    }
}
void blossom_contraction(int s,int u,int v)
{
  int lca=LCA(s,u,v);
  memset(inb,0,sizeof(inb));
  mark_blossom(lca,u);
  mark_blossom(lca,v);
  if (base[u]!=lca)
    father[u]=v;
  if (base[v]!=lca)
    father[v]=u;
  for (int u=0;u<V;u++)
    if (inb[base[u]])
      {
	base[u]=lca;
	if (!inq[u])
	  inq[q[++qt]=u]=true;
      }
}
int find_augmenting_path(int s)
{
  memset(inq,0,sizeof(inq));
  memset(father,-1,sizeof(father));
  for (int i=0;i<V;i++) base[i]=i;
  inq[q[qh=qt=0]=s]=true;
  while (qh<=qt)
    {
      int u=q[qh++];
      for (edge e=adj[u];e;e=e->n)
        {
	  int v=e->v;
	  if (base[u]!=base[v]&&match[u]!=v)
	    if ((v==s)||(match[v]!=-1 && father[match[v]]!=-1))
	      blossom_contraction(s,u,v);
	    else if (father[v]==-1)
	      {
		father[v]=u;
		if (match[v]==-1)
		  return v;
		else if (!inq[match[v]])
		  inq[q[++qt]=match[v]]=true;
	      }
        }
    }
  return -1;
}
int augment_path(int s,int t)
{
  int u=t,v,w;
  while (u!=-1)
    {
      v=father[u];
      w=match[v];
      match[v]=u;
      match[u]=v;
      u=w;
    }
  return t!=-1;
}
int edmonds()
{
  int matchc=0;
  memset(match,-1,sizeof(match));
  for (int u=0;u<V;u++)
    if (match[u]==-1)
      matchc+=augment_path(u,find_augmenting_path(u));
  return matchc;
}
int main()
{
  int u,v;
  cin>>V>>E;
  while(E--)
    {
      cin>>u>>v;
      if (!ed[u-1][v-1])
	{
	  add_edge(u-1,v-1);
	  ed[u-1][v-1]=ed[v-1][u-1]=true;
	}
    }
  cout<<edmonds()<<endl;
  for (int i=0;i<V;i++)
    if (i<match[i])
      cout<<i+1<<" "<<match[i]+1<<endl;
}

thanks a lot to boleyn.su

Tags graphs, matchings, implementation, c++

History

 
 
 
 
Revisions
 
 
  Rev. Lang. By When Δ Comment
en3 English Kerpoo 2016-12-30 15:24:13 4
en2 English Kerpoo 2016-12-30 01:04:38 40
en1 English Kerpoo 2016-12-30 00:52:28 2976 Initial revision (published)