【UOJ#79】一般图最大匹配（带花树）

题面

题解

#include<iostream>
#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<cmath>
#include<algorithm>
#include<set>
#include<map>
#include<vector>
#include<queue>
using namespace std;
#define ll long long
#define RG register
#define MAX 555
#define MAXL 255555
inline int read()
{
    RG int x=0,t=1;RG char ch=getchar();
    while((ch<'0'||ch>'9')&&ch!='-')ch=getchar();
    if(ch=='-')t=-1,ch=getchar();
    while(ch<='9'&&ch>='0')x=x*10+ch-48,ch=getchar();
    return x*t;
}
struct Line{int v,next;}e[MAXL];
int h[MAX],cnt=1;
inline void Add(int u,int v){e[cnt]=(Line){v,h[u]};h[u]=cnt++;}
int match[MAX],pre[MAX],f[MAX],vis[MAX],tim,dfn[MAX];
int n,m,ans;
int getf(int x){return x==f[x]?x:f[x]=getf(f[x]);}
int lca(int u,int v)
{
	++tim;u=getf(u);v=getf(v);
	while(dfn[u]!=tim)
	{
		dfn[u]=tim;
		u=getf(pre[match[u]]);
		if(v)swap(u,v);
	}
	return u;
}
queue<int> Q;
void Blossom(int x,int y,int w)
{
	while(getf(x)!=w)
	{
		pre[x]=y,y=match[x];
		if(vis[y]==2)vis[y]=1,Q.push(y);
		if(getf(x)==x)f[x]=w;
		if(getf(y)==y)f[y]=w;
		x=pre[y];
	}
}
bool Aug(int S)
{
	for(int i=1;i<=n;++i)f[i]=i,vis[i]=pre[i]=0;
	while(!Q.empty())Q.pop();Q.push(S);vis[S]=1;
	while(!Q.empty())
	{
		int u=Q.front();Q.pop();
		for(int i=h[u];i;i=e[i].next)
		{
			int v=e[i].v;
			if(getf(u)==getf(v)||vis[v]==2)continue;
			if(!vis[v])
			{
				vis[v]=2;pre[v]=u;
				if(!match[v])
				{
					for(int x=v,lst;x;x=lst)
						lst=match[pre[x]],match[x]=pre[x],match[pre[x]]=x;
					return true;
				}
				vis[match[v]]=1,Q.push(match[v]);
			}
			else
			{
				int w=lca(u,v);
				Blossom(u,v,w);
				Blossom(v,u,w);
			}
		}
	}
	return false;
}
int main()
{
	n=read();m=read();
	for(int i=1;i<=m;++i)
	{
		int u=read(),v=read();
		Add(u,v);Add(v,u);
	}
	for(int i=1;i<=n;++i)if(!match[i])ans+=Aug(i);
	printf("%d
",ans);
	for(int i=1;i<=n;++i)printf("%d ",match[i]);puts("");
	return 0;
}