Edmonds`s_matching_algorithem.cpp

#include<bits/stdc++.h>
using namespace std;
const int maxn=505;
const int maxm=maxn*maxn*2;
int n,m,que[maxm],ql,qr,pre[maxn],tim=0;
struct edge {
    int v,nex;
}edge[maxm];
int head[maxn],ecnt=0;
int match[maxn],f[maxn],tp[maxn],tic[maxn];
int find(int x) {
    return f[x]==x?f[x]:f[x]=find(f[x]);
}
void add_edge(int u,int v) {
    edge[++ecnt]={v,head[u]};head[u]=ecnt;
    edge[++ecnt]={u,head[v]};head[v]=ecnt;
}
int lca(int x,int y) {
    for (++tim;;swap(x,y)) if (x) {
        x=find(x);
        if (tic[x]==tim) return x; else tic[x]=tim,x=pre[match[x]];
    }
}
void shrink(int x,int y,int p) {
    while (find(x)!=p) {
        pre[x]=y,y=match[x];
        if (tp[y]==2) tp[y]=1,que[++qr]=y;
        if (find(x)==x) f[x]=p;
        if (find(y)==y) f[y]=p;
        x=pre[y];
    }
}
bool aug(int s) {
    for (int i=1;i<=n;++i) f[i]=i;
    memset(tp,0,sizeof tp),memset(pre,0,sizeof pre);
    tp[que[ql=qr=1]=s]=1;
    int t=0;
    while (ql<=qr) {
        int x=que[ql++];
        for (int i=head[x],v=edge[i].v;i;i=edge[i].nex,v=edge[i].v) {
            if (find(v)==find(x) || tp[v]==2) continue; 
            if (!tp[v]) {
                tp[v]=2,pre[v]=x;
                if (!match[v]) {
                    for (int now=v,last,tmp;now;now=last) {
                        last=match[tmp=pre[now]];
                        match[now]=tmp,match[tmp]=now;
                    }
                    return true;
                } 
                tp[match[v]]=1,que[++qr]=match[v];
            } else if (tp[v]==1) {
                int l=lca(x,v);
                shrink(x,v,l);
                shrink(v,x,l);
            }
        }
    }   
    return false;
}
int main() {
	scanf("%d%d",&n,&m);//  点数和边数
	for(int i=1;i<=m;i++) {
		int u,v;scanf("%d%d",&u,&v);
		add_edge(u,v);
	}
    int ans=0; // 最大匹配数
    for (int i=1;i<=n;++i) ans+=(!match[i] && aug(i));
    printf("%d\n",ans);
    for (int i=1;i<=n;++i) printf("%d ",match[i]); // 每个点的匹配，0为没有匹配
    puts("");
    return 0;
}