#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #define EPS 1e-9 #define PI acos(-1.0) #define INF 0x3f3f3f3f #define LL long long #define Pair pair const int MOD = 1073741824; const int N = 3000+5; const int dx[] = {-1,1,0,0,-1,-1,1,1}; const int dy[] = {0,0,-1,1,-1,1,-1,1}; using namespace std; struct Edge { int to,next; } edge[N*N*2]; int head[N],tot; int n;//n个点 int father[N],pre[N];//father记录一个点属于哪个一个点为根的花 int Q[N*N*2],first,tail;//bfs队列 int match[N];//匹配 bool odd[N],vis[N];//odd记录一个点为奇点/偶点，1为奇，0为偶 int timeBlock;//LCA时间戳 int top[N],rinedge[N]; void addEdge(int x,int y) {//添边 edge[tot].to=y; edge[tot].next=head[x]; head[x]=tot++; } int Find(int x){//并查集寻找根节点 if(father[x]!=x) return father[x]=Find(father[x]); return x; } int lca(int x, int y){//求解最近公共祖先 timeBlock++; while(x){ rinedge[x]=timeBlock; x=Find(top[x]); } x=y; while(rinedge[x]!=timeBlock) x=Find(top[x]); return x; } void blossom(int x, int y, int k) {//将奇环缩成一个点并将原来是奇点的点变为偶点并加入队列 while(Find(x)!=Find(k)){ pre[x]=y; y=match[x]; odd[y]=false; Q[tail++]=y; father[Find(x)]=k; father[Find(y)]=k; x=pre[y]; } } bool bfs(int s) { memset(top,0,sizeof(top)); memset(pre,0,sizeof(pre)); memset(odd,false,sizeof(odd)); memset(vis,false,sizeof(vis)); for(int i=1;i<=n;i++) father[i]=i; vis[s]=true; first=tail=0; Q[tail++]=s; while(first!=tail){ int now=Q[first++]; for(int i=head[now];i!=-1;i=edge[i].next){ int to=edge[i].to; if(!vis[to]){ top[to]=now; pre[to]=now; odd[to]=true; vis[to]=true; if(!match[to]){ int j=to; while(j){ int x=pre[j]; int y=match[x]; match[j]=x; match[x]=j; j=y; } return true; } vis[match[to]]=true; top[match[to]]=to; Q[tail++]=match[to]; } else if(Find(now)!=Find(to) && odd[to]==false) { int k=lca(now,to); blossom(now,to,k); blossom(to,now,k); } } } return false; } int main() { memset(head,-1,sizeof(head)); memset(match,0,sizeof(match)); tot=0; int m; scanf("%d%d",&n,&m); for(int i=1;i<=m;i++){ int x,y; scanf("%d%d",&x,&y); addEdge(x,y); addEdge(y,x); } int res=0; for(int i=1;i<=n;i++) if(!match[i]) res+=bfs(i); printf("%d\n",res); for(int i=1;i<=n;i++) printf("%d ",match[i]); printf("\n"); return 0; }
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