带花树(一般图最大匹配)
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#define N 45#define SET(a,b) memset(a,b,sizeof(a))deque<int> Q;//g[i][j]存放关系图:i,j是否有边,match[i]存放i所匹配的点//建图开始初始化g//最终匹配方案为match//复杂度O(n^3)//点是从1到n的 bool g[N][N],inque[N],inblossom[N];int match[N],pre[N],base[N];//找公共祖先int findancestor(int u,int v){ bool inpath[N]={false}; while(1) { u=base[u]; inpath[u]=true; if(match[u]==-1)break; u=pre[match[u]]; } while(1) { v=base[v]; if(inpath[v])return v; v=pre[match[v]]; }}//压缩花void reset(int u,int anc){ while(u!=anc) { int v=match[u]; inblossom[base[u]]=1; inblossom[base[v]]=1; v=pre[v]; if(base[v]!=anc)pre[v]=match[u]; u=v; }}void contract(int u,int v,int n){ int anc=findancestor(u,v); SET(inblossom,0); reset(u,anc);reset(v,anc); if(base[u]!=anc)pre[u]=v; if(base[v]!=anc)pre[v]=u; for(int i=1;i<=n;i++) if(inblossom[base[i]]) { base[i]=anc; if(!inque[i]) { Q.push_back(i); inque[i]=1; } }}bool dfs(int S,int n){ for(int i=0;i<=n;i++)pre[i]=-1,inque[i]=0,base[i]=i; Q.clear();Q.push_back(S);inque[S]=1; while(!Q.empty()) { int u=Q.front();Q.pop_front(); for(int v=1;v<=n;v++) { if(g[u][v]&&base[v]!=base[u]&&match[u]!=v) { if(v==S||(match[v]!=-1&&pre[match[v]]!=-1))contract(u,v,n); else if(pre[v]==-1) { pre[v]=u; if(match[v]!=-1)Q.push_back(match[v]),inque[match[v]]=1; else { u=v; while(u!=-1) { v=pre[u]; int w=match[v]; match[u]=v; match[v]=u; u=w; } return true; } } } } } return false;}int solve(int n){ SET(match,-1); int ans=0; for(int i=1;i<=n;i++) if(match[i]==-1&&dfs(i,n)) ans++; return ans;}