Bzoj3197: [Sdoi2013]assassin

题面

传送门

Sol

套路：找出重心，如果有两个就新建一个点

然后把这棵树hash一下

设\(f[i][j]\)表示第一颗树到\(i\)第二棵树到\(j\)，子树\(i,j\)同构的付出的最小代价

转移：每次把这一层hash值相同的点做一边二分图权匹配(KM/费用流)就好了

一遍AC

# include <bits/stdc++.h>
# define IL inline
# define RG register
# define Fill(a, b) memset(a, b, sizeof(a))
using namespace std;
typedef long long ll;
IL int Input(){
	RG int x = 0, z = 1; RG char c = getchar();
	for(; c < '0' || c > '9'; c = getchar()) z = c == '-' ? -1 : 1;
	for(; c >= '0' && c <= '9'; c = getchar()) x = (x << 1) + (x << 3) + (c ^ 48);
	return x * z;
}
const int maxn(1005);
const int inf(1e9);
const ll seed1(9377);
const ll seed2(10007);
namespace MCMF{
	int dis[maxn], pre1[maxn], pre2[maxn], vis[maxn], first[maxn], cnt, ans, s, t;
	queue <int> q;
	struct Edge{
		int to, next, f, w;
	} edge[maxn * maxn * 2];
	IL void Init(RG int a, RG int b){
		s = a, t = b, ans = cnt = 0;
		for(RG int i = a; i <= b; ++i) first[i] = -1;
	}
	IL void Add(RG int u, RG int v, RG int f, RG int w){
		edge[cnt] = (Edge){v, first[u], f, w}, first[u] = cnt++;
		edge[cnt] = (Edge){u, first[v], 0, -w}, first[v] = cnt++;
	}
	IL int Aug(){
		for(RG int i = s; i <= t; ++i) dis[i] = inf;
		q.push(s), dis[s] = 0, vis[s] = 1;
		while(!q.empty()){
			RG int u = q.front(); q.pop();
			for(RG int e = first[u]; e != -1; e = edge[e].next){
				RG int v = edge[e].to;
				if(edge[e].f && dis[v] > dis[u] + edge[e].w){
					dis[v] = dis[u] + edge[e].w;
					pre1[v] = e, pre2[v] = u;
					if(!vis[v]) q.push(v), vis[v] = 1;
				}
			}
			vis[u] = 0;
		}
		if(dis[t] == inf) return 0;
		RG int ret = inf;
		for(RG int p = t; p; p = pre2[p]) ret = min(ret, edge[pre1[p]].f);
		ans += ret * dis[t];
		for(RG int p = t; p; p = pre2[p])
			edge[pre1[p]].f -= ret, edge[pre1[p] ^ 1].f += ret;
		return 1;
	}
	IL int Calc(){
		for(ans = 0; Aug(); );
		return ans;
	}
}
int cnt, first[maxn];
struct Edge{
	int to, next;
} edge[maxn << 1];
namespace Hash{
	struct Val{
		unsigned long long f1, f2;
		IL int operator ==(RG Val b) const{
			return f1 == b.f1 && f2 == b.f2;
		}
	} v[maxn];
	IL int Cmp(RG int a, RG int b){
		return v[a].f1 != v[b].f1 ? v[a].f1 < v[b].f1 : v[a].f2 < v[b].f2;
	}
	int size[maxn];
	IL void GetHash(RG int u, RG int ff){
		vector <int> son; son.clear(), size[u] = 1;
		for(RG int e = first[u]; e != -1; e = edge[e].next){
			RG int v = edge[e].to;
			if(v != ff){
				GetHash(v, u);
				size[u] += size[v], son.push_back(v);
			}
		}
		sort(son.begin(), son.end(), Cmp);
		for(RG int i = 0, l = son.size(); i < l; ++i){
			v[u].f1 = v[u].f1 * seed1 + v[son[i]].f1 * seed1 + v[son[i]].f2 * seed2;
			v[u].f2 = v[u].f2 * seed2 + v[son[i]].f1 * seed2 + v[son[i]].f2 * seed1;
		}
		v[u].f1 = v[u].f1 * seed1 + size[u];
		v[u].f2 = v[u].f2 * seed2 + size[u];
	}
};
int n, size[maxn], c1[maxn], c2[maxn], rt, tmp;
int f[maxn][maxn];
IL void Add(RG int u, RG int v){
	edge[cnt] = (Edge){v, first[u]}, first[u] = cnt++;
}
IL void GetRoot(RG int u){
	size[u] = 1; RG int mx = 0;
	for(RG int e = first[u]; e != -1; e = edge[e].next){
		RG int v = edge[e].to;
		if(!size[v]){
			GetRoot(v);
			size[u] += size[v];
			mx = max(mx, size[v]);
		}
	}
	mx = max(mx, n - size[u]);
	if((mx << 1) <= n){
		if(!rt) rt = u;
		else tmp = u;
	}
}
IL void Solve(RG int u1, RG int u2, RG int ff1, RG int ff2){
	f[u1][u2] = c1[u1] != c2[u2];
	vector <int> son1, son2; son1.clear(), son2.clear();
	for(RG int e = first[u1]; e != -1; e = edge[e].next)
		if(edge[e].to != ff1) son1.push_back(edge[e].to);
	for(RG int e = first[u2]; e != -1; e = edge[e].next)
		if(edge[e].to != ff2) son2.push_back(edge[e].to);
	RG int l1 = son1.size(), l2 = son2.size(), s = 0, t = l1 + l2 + 1;
	for(RG int i = 0; i < l1; ++i)
		for(RG int j = 0; j < l2; ++j)
			if(Hash::v[son1[i]] == Hash::v[son2[j]]) Solve(son1[i], son2[j], u1, u2);
	MCMF::Init(0, t);
	for(RG int i = 0; i < l1; ++i)
		for(RG int j = 0; j < l2; ++j)
			if(Hash::v[son1[i]] == Hash::v[son2[j]]) MCMF::Add(i + 1, j + 1 + l1, 1, f[son1[i]][son2[j]]);
	for(RG int i = 0; i < l1; ++i) MCMF::Add(s, i + 1, 1, 0);
	for(RG int i = 0; i < l2; ++i) MCMF::Add(i + 1 + l1, t, 1, 0);
	RG int ret = MCMF::Calc();
	f[u1][u2] += ret;
}
int main(){
	n = Input();
	for(RG int i = 1; i <= n + 1; ++i) first[i] = -1;
	for(RG int i = 1; i < n; ++i){
		RG int u = Input(), v = Input();
		Add(u, v), Add(v, u);
	}
	for(RG int i = 1; i <= n; ++i) c1[i] = Input();
	for(RG int i = 1; i <= n; ++i) c2[i] = Input();
	GetRoot(1);
	if(tmp){
		for(RG int e = first[rt]; e != -1; e = edge[e].next)
			if(edge[e].to == tmp) edge[e].to = n + 1;
		for(RG int e = first[tmp]; e != -1; e = edge[e].next)
			if(edge[e].to == rt) edge[e].to = n + 1;
		Add(n + 1, rt), Add(n + 1, tmp), rt = n + 1;
	}
	Hash::GetHash(rt, 0);
	Solve(rt, rt, 0, 0);
	printf("%d\n", f[rt][rt]);
	return 0;
}