题解 c（留坑）

传送门

这题卡常……而且目前还没有卡过去

首先以原树重心为根，向所有子树重心连边，可以建立一棵点分树

点分树有两个性质：

一个是树高只有log层

另一个是两点在点分树上的lca一定在原树上两点间的树上路径上

所以在原树上不断删点，并统计当前子树中的信息就好

至于如何统计，令 \(dp[i][j][k][l]\) 表示分治中心为 \(i\) ，到点 \(j\) ，第一条边颜色为 \(k\) ，最后一条边颜色为 \(j\) 的最大得分

转移挺好写的，询问时暴力枚举相关连边的颜色

留个坑，纯点分治还不会写呢

Code:

#include <bits/stdc++.h>
using namespace std;
#define INF 0x3f3f3f3f
#define N 100010
#define ll long long
#define reg register int
#define fir first
#define sec second
#define make make_pair
#define pb push_back
#define min2(a, b) ((a)<(b)?(a):(b))
#define max2(a, b) ((a)>(b)?(a):(b))
//#define int long long 
char buf[1<<21], *p1=buf, *p2=buf;
#define getchar() (p1==p2&&(p2=(p1=buf)+fread(buf, 1, 1<<21, stdin)), p1==p2?EOF:*p1++)
inline int read() {
	int ans=0, f=1; char c=getchar();
	while (!isdigit(c)) {if (c=='-') f=-f; c=getchar();}
	while (isdigit(c)) {ans=(ans<<3)+(ans<<1)+(c^48); c=getchar();}
	return ans*f;
}
int n, m, q;
int head[N], size;
struct edge{int to, next, val;}e[N*3];
inline void add(int s, int t, int w) {e[++size].to=t; e[size].val=w; e[size].next=head[s]; head[s]=size;}
namespace force{
	bool none[N];
	int dfs(int u, int to, int fa, int now, int sum) {
		//cout<<"dfs "<<u<<' '<<to<<' '<<fa<<' '<<now<<' '<<sum<<endl;
		if (u==to) return sum;
		int ans=0;
		for (int i=head[u],v; ~i; i=e[i].next) {
			v = e[i].to;
			if (v==fa || none[v]) continue;
			ans=max(ans, dfs(v, to, u, e[i].val, sum+(now!=e[i].val)));
		}
		if (!ans) none[u]=1;
		return ans;
	}
	void solve() {
		for (int i=1,u,v,w; i<=m; ++i) {
			u=read(); v=read(); w=read();
			add(u, v, w); add(v, u, w);
		}
		q=read();
		if (!q) exit(0);
		for (int i=1,x,y; i<=q; ++i) {
			x=read(); y=read();
			memset(none, 0, sizeof(bool)*(n+5));
			printf("%d\n", dfs(x, y, 0, 0, 0));
		}
		exit(0);
	}
}
namespace task1{
	bool none[N];
	int dfs(int u, int to, int fa, int now, int sum, int dis) {
		//cout<<"dfs "<<u<<' '<<to<<' '<<fa<<' '<<now<<' '<<sum<<endl;
		if (dis>60) {none[u]=1; return 0;}
		if (u==to) return sum;
		int ans=0;
		for (int i=head[u],v; ~i; i=e[i].next) {
			v = e[i].to;
			if (v==fa || none[v]) continue;
			ans=max(ans, dfs(v, to, u, e[i].val, sum+(now!=e[i].val), dis+1));
		}
		if (!ans) none[u]=1;
		return ans;
	}
	void solve() {
		for (int i=1,u,v,w; i<=m; ++i) {
			u=read(); v=read(); w=read();
			add(u, v, w); add(v, u, w);
		}
		q=read();
		if (!q) exit(0);
		for (int i=1,x,y; i<=q; ++i) {
			x=read(); y=read();
			memset(none, 0, sizeof(bool)*(n+5));
			printf("%d\n", dfs(x, y, 0, 0, 0, 0));
		}
		exit(0);
	}
}
namespace task{
	int fa[N][25], dep[N], lg[N], rot, siz[N], msiz[N], sumsiz;
	bool rm[N];
	struct st{int i, j, k; st() {} st(int a, int b, int c):i(a),j(b),k(c){}};
	inline bool operator == (st a, st b) {return a.i==b.i&&a.j==b.j&&a.k==b.k;}
	inline bool operator < (st a, st b) {return a.k<b.k;}
	struct pair_hash{inline size_t operator () (pair<int, int> p) const {return hash<int>()(p.fir*p.sec+p.fir);}};
	unordered_map<pair<int, int>, vector<int>*, pair_hash> mp{5000, pair_hash()};
	unordered_map<pair<int, int>, vector<st>*, pair_hash> dp{20000, pair_hash()};
	unordered_map<pair<int, int>, int, pair_hash> tem{50, pair_hash()};
	struct edge{int to, next;}e2[N<<1];
	inline void add(int s, int t) {e2[++size].to=t; e2[size].next=head[s]; head[s]=size;}
	vector<int> e[N];
	void getrt(int u, int fa) {
		//cout<<"getrt"<<u<<' '<<fa<<endl;
		siz[u]=1; msiz[u]=0;
		for (register auto v:e[u]) {
			if (!rm[v] && v!=fa) {
				getrt(v, u);
				siz[u]+=siz[v];
				msiz[u]=max(msiz[u], siz[v]);
			}
		}
		//cout<<"sumsiz: "<<sumsiz<<' '<<sumsiz-siz[u]<<' '<<msiz[u]<<' '<<msiz[rot]<<' '<<rot<<endl;
		msiz[u]=max(msiz[u], sumsiz-siz[u]);
		if (msiz[u]<msiz[rot]) rot=u;
	}
	void info(int u, int fa) {
		//cout<<"info "<<u<<' '<<fa<<endl;
		for (register auto v:e[u]) {
			if (v==fa || rm[v]) continue;
			if (rot==u) {
				if (dp.find(make(u, v))==dp.end()) dp[make(u, v)]=new vector<st>;
				auto t1=mp[make(u, v)]; auto t2=dp[make(u, v)];
				for (register auto it:*t1)
					t2->pb(st(it, it, 1));
			}
			else {
				if (dp.find(make(rot, v))==dp.end()) dp[make(rot, v)]=new vector<st>;
				for (register auto it:*dp[make(rot, u)])
					for (register auto t:*mp[make(u, v)])
						tem[make(it.i, t)] = max(tem[make(it.i, t)], it.k+(it.j!=t));
				register auto t1=dp[make(rot, v)];
				for (register auto it:tem) t1->pb(st(it.fir.fir, it.fir.sec, it.sec));
				//assert(tem.size()<=9);
				tem.clear();
			}
			info(v, u);
			//cout<<"size: "<<dp.size()<<endl;
		}
	}
	void build(int u) {
		//cout<<"build "<<u<<endl;
		rm[u]=1;
		info(u, 0);
		for (register auto v:e[u]) {
			rot=0;
			if (!rm[v]) {
				sumsiz=siz[v];
				getrt(v, u);
				add(u, rot), add(rot, u);
				//info(rot, u, t);
				build(rot);
			}
		}
	}
	void dfs(int u, int pa) {
		//cout<<"dfs "<<u<<' '<<pa<<endl;
		for (reg i=1; i<25; ++i)
			if (dep[u]>=(1<<i)) fa[u][i] = fa[fa[u][i-1]][i-1];
			else break;
		for (reg i=head[u],v; ~i; i=e2[i].next) {
			v = e2[i].to;
			if (v!=pa) dep[v]=dep[u]+1, fa[v][0]=u, dfs(v, u);
		}
	}
	int lca(int a, int b) {
		if (dep[a]<dep[b]) swap(a, b);
		while (dep[a]>dep[b]) a=fa[a][lg[dep[a]-dep[b]]-1];
		if (a==b) return a;
		for (reg i=lg[dep[a]]-1; ~i; --i)
			if (fa[a][i]!=fa[b][i])
				a=fa[a][i], b=fa[b][i];
		return fa[a][0];
	}
	void solve() {
		for (reg i=1; i<=n; ++i) lg[i]=lg[i-1]+(1<<lg[i-1]==i);
		pair<int, int> t1, t2;
		for (reg i=1,u,v,w; i<=m; ++i) {
			u=read(); v=read(); w=read();
			e[u].pb(v); e[v].pb(u);
			t1=make(u, v), t2=make(v, u);
			if (mp.find(t1)==mp.end()) mp[t1]=new vector<int>;
			mp[t1]->pb(w);
			if (mp.find(t2)==mp.end()) mp[t2]=new vector<int>;
			mp[t2]->pb(w);
		}
		for (reg i=1,siz; i<=n; ++i) {
			sort(e[i].begin(), e[i].end());
			siz=unique(e[i].begin(), e[i].end())-e[i].begin();
			e[i].resize(siz);
		}
		for (register auto it:mp) {
			sort(it.sec->begin(), it.sec->end());
			int siz=unique(it.sec->begin(), it.sec->end())-it.sec->begin();
			it.sec->resize(min2(siz, 3));
		}
		msiz[0]=sumsiz=n;
		getrt(1, 0);
		int root=rot;
		//cout<<"root: "<<root<<endl;
		build(rot);
		dep[root]=1;
		dfs(root, 0);
		//for (auto it:dp) cout<<it.fir.i<<' '<<it.fir.j<<' '<<it.fir.k<<' '<<it.fir.h<<' '<<it.sec<<endl;
		q=read(); if (!q) exit(0);
		for (reg i=1,x,y,t,ans; i<=q; ++i) {
			x=read(); y=read();
			if (x==y) {puts("0"); continue;}
			t=lca(x, y); ans=0;
			//cout<<"lca: "<<x<<' '<<y<<' '<<t<<endl;
			if (t==x || t==y) {
				//puts("pos1");
				if (t!=x) swap(x, y);
				for (register auto it:*dp[make(t, y)]) ans=max(ans, it.k);
				printf("%d\n", ans);
				continue;
			}
			for (register auto i:*dp[make(t, x)])
				for (register auto j:*dp[make(t, y)])
					ans = max(ans, i.k+j.k-(i.i==j.i));
			printf("%d\n", ans);
		}
		//cout<<"size: "<<dp.size()<<endl;
		exit(0);
	}
}
signed main()
{
	memset(head, -1, sizeof(head));
	n=read(); m=read();
	//if (n<100000) force::solve();
	//else task1::solve();
	task::solve();
	return 0;
}