BZOJ 3197 [Sdoi2013]assassin

题解：

树上Hash

首先重心在边上就把边分裂

以重心为根建树，这样两个根一定对应

然后f[i][j]表示i匹配另一棵的j节点的最小代价

把他们的儿子摘出来做最小权匹配即可

#include<iostream>
#include<cstdio>
#include<cstring>
#include<vector>
#include<queue>
#include<algorithm>
using namespace std;
const int maxn=1500;
typedef unsigned long long uLint;
const int oo=100000000;//

int n;
int rx[maxn],ry[maxn];
int mi[maxn],ming[maxn];

int cntedge=0;
int head[maxn]={0};
int to[maxn<<1],nex[maxn<<1];
void Addedge(int x,int y){
	nex[++cntedge]=head[x];
	to[cntedge]=y;
	head[x]=cntedge;
}

int root1=0,root2=0;
int siz[maxn]={0},g[maxn]={0};
void Dfs(int x,int fa){
	siz[x]=1;g[x]=0;
	for(int i=head[x];i;i=nex[i]){
		if(to[i]==fa)continue;
		Dfs(to[i],x);
		siz[x]+=siz[to[i]];
		g[x]=max(g[x],siz[to[i]]);
	}
	g[x]=max(g[x],n-siz[x]);
	
	if(g[x]<=g[root1]){
		root2=root1;root1=x;
	}else if(g[x]<=g[root2]){
		root2=x;
	}
}

uLint hh[maxn];
int dep[maxn];
int father[maxn];
void Gethash(int x,int fa){
	hh[x]=666;
	father[x]=fa;
	dep[x]=dep[fa]+1;
	for(int i=head[x];i;i=nex[i]){
		if(to[i]==fa)continue;
		Gethash(to[i],x);
		hh[x]+=hh[to[i]];
	}
	hh[x]=hh[x]*hh[x];
}

int a[maxn];
bool cmp(const int &rhs1,const int &rhs2){
	if(dep[rhs1]==dep[rhs2])return hh[rhs1]<hh[rhs2];
	else return dep[rhs1]>dep[rhs2];
}

struct NetworkFlow{
	int totn,s,t;
	
	struct Edge{
		int from,to,cap,flow,cost;
	};
	vector<int>G[maxn];
	vector<Edge>edges;
	void Addedge(int x,int y,int z,int w){
		Edge e;
		e.from=x;e.to=y;e.cap=z;e.flow=0;e.cost=w;
		edges.push_back(e);
		e.from=y;e.to=x;e.cap=0;e.flow=0;e.cost=-w;
		edges.push_back(e);
		int c=edges.size();
		G[x].push_back(c-2);
		G[y].push_back(c-1);
	}
	
	int inq[maxn];
	int d[maxn];
	int p[maxn];
	queue<int>q;
	int Spfa(int &nowflow,int &nowcost){
		for(int i=1;i<=totn;++i){
			d[i]=oo;inq[i]=0;
		}
		d[s]=0;inq[s]=1;q.push(s);
		while(!q.empty()){
			int x=q.front();q.pop();inq[x]=0;
			for(int i=0;i<G[x].size();++i){
				Edge e=edges[G[x][i]];
				if((e.cap>e.flow)&&(d[x]+e.cost<d[e.to])){
					d[e.to]=d[x]+e.cost;
					p[e.to]=G[x][i];
					if(!inq[e.to]){
						q.push(e.to);
						inq[e.to]=1;
					}
				}
			}
		}
		
		if(d[t]==oo)return 0;
		
		int f=oo,x=t;
		while(x!=s){
			Edge e=edges[p[x]];
			f=min(f,e.cap-e.flow);
			x=e.from;
		}
		nowflow+=f;nowcost+=f*d[t];
		x=t;
		while(x!=s){
			edges[p[x]].flow+=f;
			edges[p[x]^1].flow-=f;
			x=edges[p[x]].from;
		}
		return 1;
	}
	
	int Mincost(){
		int flow=0,cost=0;
		while(Spfa(flow,cost)){
		}
		return cost;
	}
	void MCMFinit(){
		totn=n+n+2;s=n+n+1;t=s+1;
		edges.clear();
		G[s].clear();G[t].clear();
	}
}W;

int f[maxn][maxn];
int main(){
	scanf("%d",&n);
	for(int i=1;i<=n-1;++i){
		int x,y;
		scanf("%d%d",&x,&y);
		Addedge(x,y);
		Addedge(y,x);
		rx[i]=x;ry[i]=y;
	}
	for(int i=1;i<=n;++i)scanf("%d",&ming[i]);
	for(int i=1;i<=n;++i)scanf("%d",&mi[i]);
	mi[n+1]=ming[n+1]=0;
	
	g[0]=0x7fffffff;
	Dfs(1,0);
	if(g[root1]!=g[root2])root2=0;
	if(root1&&root2){
		cntedge=0;
		memset(head,0,sizeof(head));
		for(int i=0;i<n;++i){
			if((rx[i]==root1&&ry[i]==root2)||(rx[i]==root2&&ry[i]==root1))continue;
			Addedge(rx[i],ry[i]);
			Addedge(ry[i],rx[i]);
		}
		Addedge(root1,n+1);
		Addedge(n+1,root1);
		Addedge(root2,n+1);
		Addedge(n+1,root2);
		root1=++n;
	}
	Gethash(root1,0);
	
	for(int i=1;i<=n;++i)a[i]=i;
	sort(a+1,a+1+n,cmp);
	
	for(int i=1;i<=n;++i){
		for(int j=1;j<=n;++j){
			int x=a[i];
			int y=a[j];
			if(hh[x]!=hh[y]){
				f[x][y]=oo;
				continue;
			}
			W.MCMFinit();
			for(int ii=head[x];ii;ii=nex[ii]){
				if(to[ii]==father[x])continue;
				W.G[to[ii]].clear();
			}
			for(int ii=head[y];ii;ii=nex[ii]){
				if(to[ii]==father[y])continue;
				W.G[to[ii]+n].clear();
			}
			for(int ii=head[x];ii;ii=nex[ii]){
				if(to[ii]==father[x])continue;
				for(int jj=head[y];jj;jj=nex[jj]){
					if(to[jj]==father[y])continue;
					if(hh[to[ii]]!=hh[to[jj]])continue;
					W.Addedge(to[ii],to[jj]+n,1,f[to[ii]][to[jj]]);
				}
			}
			for(int ii=head[x];ii;ii=nex[ii]){
				if(to[ii]==father[x])continue;
				W.Addedge(W.s,to[ii],1,0);
			}
			for(int ii=head[y];ii;ii=nex[ii]){
				if(to[ii]==father[y])continue;
				W.Addedge(to[ii]+n,W.t,1,0);
			}
			f[x][y]=(ming[x]^mi[y])+W.Mincost();
		}
	}
	
//	for(int i=1;i<=n;++i){
//		for(int j=1;j<=n;++j){
//			cout<<f[i][j]<<' ';
//		}
//		cout<<endl;
//	}
	printf("%d\n",f[root1][root1]);
	return 0;
}