MATCHING - Fast Maximum Matching.cpp

#include<bits/stdc++.h>
using namespace std;
#define MAX 100001
#define NIL 0
#define INF (1<<28)
 
vector< int > G[MAX];
int n, m, match[MAX], dist[MAX];
/// n: number of nodes on left side, nodes are numbered 1 to n
/// m: number of nodes on right side, nodes are numbered n+1 to n+m
/// G = NIL[0] u G1[G[1---n]] u G2[G[n+1---n+m]]
 
bool bfs()
{
    int i, u, v, len;
    queue< int > Q;
    for(i=1; i<=n; i++)
    {
        if(match[i]==NIL)
        {
            dist[i] = 0;
            Q.push(i);
        }
        else
            dist[i] = INF;
    }
    dist[NIL] = INF;
    while(!Q.empty())
    {
        u = Q.front();
        Q.pop();
        if(u!=NIL)
        {
            len = G[u].size();
            for(i=0; i<len; i++)
            {
                v = G[u][i];
                if(dist[match[v]]==INF)
                {
                    dist[match[v]] = dist[u] + 1;
                    Q.push(match[v]);
                }
            }
        }
    }
    return (dist[NIL]!=INF);
}
 
bool dfs(int u)
{
    int i, v, len;
    if(u!=NIL)
    {
        len = G[u].size();
        for(i=0; i<len; i++)
        {
            v = G[u][i];
            if(dist[match[v]]==dist[u]+1)
            {
                if(dfs(match[v]))
                {
                    match[v] = u;
                    match[u] = v;
                    return true;
                }
            }
        }
        dist[u] = INF;
        return false;
    }
    return true;
}
 
int hopcroft_karp()
{
    int matching = 0, i;
    /// match[] is assumed NIL for all vertex in G
    while(bfs())
        for(i=1; i<=n; i++)
            if(match[i]==NIL && dfs(i))
                matching++;
    return matching;
}
int main()
{
    int i, u, v,p;
    scanf("%d%d%d", &n, &m, &p);
    for(i=0; i<p; i++)
    {
        scanf("%d%d", &u, &v);
// u in G1, v in G2
        v += n;
        G[u].push_back(v);
        G[v].push_back(u);
    }
    printf("%d\n", hopcroft_karp());
    return 0;
}