一般图最大匹配带花树

 1 #include<cstdio>
 2 #include<cctype>
 3 #include<cstring>
 4 #include<algorithm>
 5 using namespace std;
 6 int read() {
 7     int x=0,f=1;
 8     char c=getchar();
 9     for (;!isdigit(c);c=getchar()) if (c==‘-‘) f=-1;
10     for (;isdigit(c);c=getchar()) x=x*10+c-‘0‘;
11     return x*f;
12 }
13 const int maxn=505;
14 const int maxm=maxn*maxn*2;
15 int n,m,que[maxm],ql,qr,pre[maxn],tim=0;
16 struct edge {
17     int v,nxt;
18 } e[maxm];
19 int h[maxn],tot=0;
20 int match[maxn],f[maxn],tp[maxn],tic[maxn];
21 int find(int x) {
22     return f[x]==x?f[x]:f[x]=find(f[x]);
23 }
24 void add(int u,int v) {
25     e[++tot]=(edge){v,h[u]};
26     h[u]=tot;
27 }
28 int lca(int x,int y) {
29     for (++tim;;swap(x,y)) if (x) {
30         x=find(x);
31         if (tic[x]==tim) return x; else tic[x]=tim,x=pre[match[x]];
32     }
33 }
34 void shrink(int x,int y,int p) {
35     while (find(x)!=p) {
36         pre[x]=y,y=match[x];
37         if (tp[y]==2) tp[y]=1,que[++qr]=y;
38         if (find(x)==x) f[x]=p;
39         if (find(y)==y) f[y]=p;
40         x=pre[y];
41     }
42 }
43 bool aug(int s) {
44     for (int i=1;i<=n;++i) f[i]=i;
45     memset(tp,0,sizeof tp),memset(pre,0,sizeof pre);
46     tp[que[ql=qr=1]=s]=1; // 1: type A ; 2: type B
47     int t=0;
48     while (ql<=qr) {
49         int x=que[ql++];
50         for (int i=h[x],v=e[i].v;i;i=e[i].nxt,v=e[i].v) {
51             if (find(v)==find(x) || tp[v]==2) continue; 
52             if (!tp[v]) {
53                 tp[v]=2,pre[v]=x;
54                 if (!match[v]) {
55                     for (int now=v,last,tmp;now;now=last) {
56                         last=match[tmp=pre[now]];
57                         match[now]=tmp,match[tmp]=now;
58                     }
59                     return true;
60                 } 
61                 tp[match[v]]=1,que[++qr]=match[v];
62             } else if (tp[v]==1) {
63                 int l=lca(x,v);
64                 shrink(x,v,l);
65                 shrink(v,x,l);
66             }
67         }
68     }   
69     return false;
70 }
71 int main() {
72 #ifndef ONLINE_JUDGE
73     freopen("test.in","r",stdin);
74     freopen("my.out","w",stdout);
75 #endif
76     n=read(),m=read();
77     for (int i=1;i<=m;++i) {
78         int x=read(),y=read();
79         add(x,y),add(y,x);
80     }
81     int ans=0;
82     for (int i=1;i<=n;++i) ans+=(!match[i] && aug(i));
83     printf("%d\n",ans);
84     for (int i=1;i<=n;++i) printf("%d ",match[i]);
85     puts("");
86     return 0;
87 }