边分治+虚树+直径合并：P4220通道

本文搬运自本人高中时期CSDN博客，若图片加载不出来，可到原文查看：https://blog.csdn.net/zhangtingxiqwq/article/details/135266426

https://www.luogu.com.cn/problem/P4220

第一棵树可以直接边分治，然后黑白染色，弄到第二棵树上建虚树

第三棵树很难搞。需要回到题目本身，发现题目没叫我们求奇奇怪怪的东西，而是求距离，肯定有啥性质，而且还是最大距离，就是一个点集的直径。

直径显然支持合并性，我们直接在虚树上树形dp进行合并即可

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pre coding at 8:14
st coding at 9:00
fn coding at 10:35
st bugging at 11:30
passing at 12:32
fn blogging at 12:45
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//7.2k
#include<bits/stdc++.h>
using namespace std;
#ifdef LOCAL
 #define debug(...) fprintf(stdout, ##__VA_ARGS__)
#else
 #define debug(...) void(0)
#endif
#define int long long
inline int read(){int x=0,f=1;char ch=getchar(); while(ch<'0'||
ch>'9'){if(ch=='-')f=-1;ch=getchar();}while(ch>='0'&&ch<='9'){
x=(x<<1)+(x<<3)+(ch^48);ch=getchar();}return x*f;}
#define Z(x) (x)*(x)
#define pb push_back
#define fi first
#define se second
//srand(time(0));
#define N 200010
//#define M
//#define mo
struct Point { int x, w, o; };
int n, m, i, j, k, T, c;
int Log2[N<<1], ans; 

struct Tree {
	int i, j, k; 
	int tot, m, dfn[N], oula[N<<1], oula_xu[N], dep[N], h[N]; 
	struct node { int y, z; };
	vector<node>G[N<<1]; 
	void add_edge(int u, int v, int w) {
		debug("%lld %lld %lld\n", u, v, w); 
		G[u].pb({v, w}); G[v].pb({u, w}); 
	}
	void dfs1(int x, int fa) {
		dfn[x]=++tot; h[x] = h[fa]+1; 
		oula[++m]=x; oula_xu[x]=m; 
		for(auto t : G[x]) if(t.y != fa) {
			int y = t.y, z = t.z; dep[y] = dep[x] + z; 
			dfs1(y, x); oula[++m]=x; 
		}
	}
//	struct ST {
		struct Node { int x, dep; };
		Node min(Node A, Node B) { return (A.dep < B.dep) ? A : B; }
		int min(int a, int b) { return a < b ? a : b; }
		Node f[N][22]; 
		int l, r; 
		void Pre_Lca() {
			for(i=2; i<=m; ++i) Log2[i]=Log2[i>>1]+1; 
			for(i=1; i<=m; ++i) f[i][0]={oula[i], h[oula[i]]}; 
			for(k=1; k<=20; ++k)
				for(l=1, r=(1<<k); r<=m; ++l, ++r) 
					f[l][k]=min(f[l][k-1], f[l+(1<<(k-1))][k-1]); 
		}
		int qry(int a, int b) {
			int k = Log2[b-a+1]; 
			return min(f[a][k], f[b-(1<<k)+1][k]).x; 
		}
//	}Lca; 
	int lca(int x, int y) {
		int a = oula_xu[x], b = oula_xu[y]; 
//		debug("qry[%d %d] => %d %d\n", x, y, min(a, b), max(a, b)); 
		return qry(min(a, b), max(a, b)); 
	}
	int dis(int x, int y) {
		int z = lca(x, y); 
		return dep[x] + dep[y] - 2 * dep[z]; 
	}
}T1, T2, T3;

namespace Tree1 {
	int u, v, w, tot, i, b[N]; 
	vector<pair<int, int> >G[N]; 
	void dfs(int x, int fa) {
		for(auto t : G[x]) if(t.fi != fa) {
			int y = t.fi, z = t.se; 
			if(!b[x]) b[x]=++tot, T1.add_edge(x, tot, 0); 
			else T1.add_edge(b[x], tot+1, 0), b[x]=++tot; 
			T1.add_edge(b[x], y, z); 
			dfs(y, x); 
		}
	}
	void Main() {
		tot=n; 
		for(i=1; i<n; ++i) {
			u=read(); v=read(); w=read(); 
			G[u].pb({v, w}); G[v].pb({u, w}); 
		}
		dfs(1, 0); 
		T1.dfs1(1, 0); 
		for(i=1; i<=tot; ++i) debug("%lld ", T1.h[i]); debug("\n"); 
		debug("---\n"); 
//		T1.Lca.Pre_Lca(); 
	}
}

namespace Tree2 {
	int i, u, v, w; 
	void Main() {
		for(i=1; i<n; ++i) {
			u=read(); v=read(); w=read(); 
			T2.add_edge(u, v, w); 
		}
		T2.dfs1(1, 0); T2.Pre_Lca(); 
		for(i=1; i<=T2.m; ++i) debug("%lld ", T2.oula[i]); debug("\n"); 
		for(i=1; i<=n; ++i) debug("%lld ", T2.oula_xu[i]); debug("\n"); 
	}
}

namespace Tree3 {
	int u, v, w; 
	void Main() {
		for(i=1; i<n; ++i) {
			u=read(); v=read(); w=read(); 
			T3.add_edge(u, v, w); 
		}
		T3.dfs1(1, 0); T3.Pre_Lca(); 
	}
}

namespace XuTree_part {
	int sta[N], top, o[N], w[N], l; 
	vector<pair<int, int> >E;
	pair<int, int> dp[N][2]; 
	vector<int>G[N]; 
	void build(vector<Point> h) {
		sort(h.begin(), h.end(), [] (Point x, Point y) { return T2.dfn[x.x] < T2.dfn[y.x]; }); 
		sta[top = 1] = 1; E.clear(); 
		for(auto t : h) 
			if(t.x != 1) {
				l = T2.lca(t.x, sta[top]); 
//				debug("LCA (%lld %lld) = %lld\n", t.x, sta[top], l); 
				if(l != sta[top]) {
					while(T2.dfn[l] < T2.dfn[sta[top-1]]) 
						E.pb({sta[top-1], sta[top]}), --top; 
					if(l != sta[top-1])	E.pb({l, sta[top]}), sta[top]=l; 
					else E.pb({l, sta[top]}), --top; 
				}
				sta[++top]=t.x; 
			}
		while(top>1) E.pb({sta[top-1], sta[top]}), --top; 
		for(auto t : E) G[t.fi].clear(), G[t.se].clear(), o[t.fi]=o[t.se]=0; 
		for(auto t : E) G[t.fi].pb(t.se), debug("%lld -> %lld\n", t.fi, t.se); 
		for(auto  t : h) o[t.x]=t.o, w[t.x]=t.w+T2.dep[t.x]; 
		for(auto t : h) debug("%lld : %lld\n", t.x, w[t.x]); debug("\n"); 
	}
	int Len(int x, int y) { return T3.dis(x, y) + w[x] + w[y]; }
	int calc(int x, int y, int z) {
		if(!x || !y) return 0; 
		debug("(%lld %lld) %lld\n", x, y, z); 
		return Len(x, y) - 2*T2.dep[z] + c; 
	}
	pair<int, int> merge(pair<int, int>A, pair<int, int>B) {
		int s=-1e18, x=0, y=0; 
		if(A.fi && A.se && Len(A.fi, A.se) > s) s=Len(A.fi, A.se), x=A.fi, y=A.se; 
		if(B.fi && B.se && Len(B.fi, B.se) > s) s=Len(B.fi, B.se), x=B.fi, y=B.se; 
		if(A.fi && B.fi && Len(A.fi, B.fi) > s) s=Len(A.fi, B.fi), x=A.fi, y=B.fi; 
		if(A.fi && B.se && Len(A.fi, B.se) > s) s=Len(A.fi, B.se), x=A.fi, y=B.se; 
		if(A.se && B.fi && Len(A.se, B.fi) > s) s=Len(A.se, B.fi), x=A.se, y=B.fi; 
		if(A.se && B.se && Len(A.se, B.se) > s) s=Len(A.se, B.se), x=A.se, y=B.se; 
		if(s < 0 && A.fi) x = A.fi; if(s < 0 && B.fi) x = B.fi; 
		return {x, y}; 
	}
	void dfs(int x) {
		dp[x][0] = dp[x][1] = {0, 0}; 
		if(o[x] == 1) dp[x][0] = {x, 0}; 
		if(o[x] == 2) dp[x][1] = {x, 0}; 
		for(int y : G[x]) {
			dfs(y); 
			ans = max(ans, calc(dp[x][0].fi, dp[y][1].fi, x)); 
			ans = max(ans, calc(dp[x][0].fi, dp[y][1].se, x)); 
			ans = max(ans, calc(dp[x][0].se, dp[y][1].fi, x)); 
			ans = max(ans, calc(dp[x][0].se, dp[y][1].se, x)); 
			ans = max(ans, calc(dp[x][1].fi, dp[y][0].fi, x)); 
			ans = max(ans, calc(dp[x][1].fi, dp[y][0].se, x)); 
			ans = max(ans, calc(dp[x][1].se, dp[y][0].fi, x)); 
			ans = max(ans, calc(dp[x][1].se, dp[y][0].se, x)); 
			dp[x][0] = merge(dp[x][0], dp[y][0]); 
			dp[x][1] = merge(dp[x][1], dp[y][1]); 
		}
	}
	void Main(vector<Point> h) {
		if(h.size() <= 1) return ; 
		build(h); 
		dfs(1); 
	}
}

namespace Edge_part {
	int w[N], rt, sum, i, j, dis[N], b[N]; 
	int mx[N], ST, ED; 
	map<pair<int, int>, int>mp; 
	void map_edge() {
		for(i=1; i<=Tree1::tot; ++i) 
			for(auto t : T1.G[i]) mp[{i, t.y}]=t.z, debug("%d =? %d %d\n", i, t.y, t.z); 
	}
	void dfs(int x, int fa) {
//		debug("\t %d -> %d\n", fa, x); 
		w[x]=1; 
		for(auto t : T1.G[x]) if(t.y!=fa && !b[t.y]) {
			int y = t.y, z = t.z; 
			dfs(y, x); w[x]+=w[y]; 
		}
		mx[x]=max(w[x], sum-w[x]); 
		if(mx[x] < mx[rt]) rt=x, ST=x, ED=fa; 
	}
	vector<Point> h; 
	void dfs2(int x, int fa, int o) {
		if(x<=n) h.pb({x, dis[x], o}); 
		if(x<=n) debug("[x %lld] %lld %lld\n", x, dis[x], o); 
		for(auto t : T1.G[x]) if(t.y!=fa && !b[t.y]) {
			int y = t.y, z = t.z; 
			dis[y] = dis[x] + z; 
			dfs2(y, x, o); 
		}
	}
	void solve(int x) {
		dfs(x, 0); sum=w[x]; rt=0; dfs(x, 0); 
		if(sum == 1) return ; 
		int st = ST, ed = ED;
		b[st]=1; solve(ed); b[st]=0; 
		b[ed]=1; solve(st); b[ed]=0; 
//		debug("\t[%d] <-> [%d] %d\n", st, ed, c); 
		h.clear(); 
		c = mp[{st, ed}]; 
		debug("{%lld} [%lld] <-> [%lld] %lld\n", x, st, ed, c); 
		dis[st]=0; dfs2(st, ed, 1); 
		dis[ed]=0; dfs2(ed, st, 2); 
		XuTree_part::Main(h); 
	}
	void Main() {
		mx[0]=1e18; 
		map_edge(); 
		solve(1); 
	}
}

signed main()
{
	#ifdef LOCAL
	  freopen("in.txt", "r", stdin);
	  freopen("out.txt", "w", stdout);
	#endif
//	T=read();
//	while(T--) {
//
//	}
	n=read(); 	
	Tree1::Main(); Tree2::Main(); Tree3::Main(); 
	Edge_part::Main(); 
	printf("%lld", ans); 
	return 0;
}