I love this implementation of Edmond's Blossoms :-)
Edmond's Blossoms algorithm give a maximum matching in general graphs (non-bipartite)
CODE
/*
GETS:
V->number of vertices
E->number of edges
pair of vertices as edges (vertices are 1..V)
GIVES:
output of edmonds() is the maximum matching
match[i] is 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