Codeforces 348E 树的中心点的性质 / 树形DP / 点分治

#include <bits/stdc++.h>
#define pii pair<int, int>
using namespace std;
const int maxn = 100010;
int f[maxn];
int d[maxn];
vector<pii> G[maxn];
int mx[maxn], mx_pos[maxn], dye[maxn], sum[maxn];
int v[maxn];
int ans, ans_cnt, root, pos, n, m;
void add(int x, int y, int z) {
	G[x].push_back(make_pair(y, z));
	G[y].push_back(make_pair(x, z));
}
bool dfs(int x, int fa, int now) {
	int flag = (v[x] == 1);
	d[x] = now;
	for (auto y : G[x]) {
		if(y.first == fa) continue;
		int tmp = dfs(y.first, x, now + y.second);
		flag |= tmp;
		f[y.first] = x;
	}
	if(flag && d[x] > ans) {
		ans = d[x];
		pos = x;
	}
	return flag;
}
void get_root() {
	dfs(1, -1, 0);
	memset(d, 0, sizeof(d));
	ans = 0;
	root = pos;
	dfs(root, -1, 0);
	int Sum = d[pos], tmp = pos;
	while(d[tmp] > d[pos] / 2) {
		tmp = f[tmp];
	}
	root = tmp;
}
void update(int pos, int ch, int val) {
	if(mx[pos] < mx[ch] + val) {
		mx[pos] = mx[ch] + val;
		mx_pos[pos] = mx_pos[ch];
	} else if(mx[pos] == mx[ch] + val) {
		mx_pos[pos] = pos;
	}
}
bool dfs1(int x, int fa, int color) {
	dye[x] = color;
	int flag = (v[x] == 1);
	if(flag == 1) mx_pos[x] = x;
	for (auto y : G[x]) {
		if(y.first == fa) continue;
		int tmp;
		tmp = dfs1(y.first, x, color);
		f[y.first] = x;
		if(tmp) {
			update(x, y.first, y.second);
		}
		flag |= tmp;
	}
	return flag;
}
void dfs2(int x, int fa) {
	for (auto y : G[x]) {
		if(y.first == fa) continue;
		dfs2(y.first, x);
		sum[x] += sum[y.first];
	}
	if(sum[x] > ans && v[x] == 0) {
		ans = sum[x];
		ans_cnt = 1;
	} else if(sum[x] == ans && v[x] == 0) {
		ans_cnt++;
	}
}
vector<pii> res;
map<int, int> mp;
set<int> s;
int tot;
void solve() {
	for (auto y : G[root]) {
		int tmp = dfs1(y.first, root, ++tot);
		if(tmp) {
			res.push_back(make_pair(mx[y.first] + y.second, mx_pos[y.first]));
		}
	}
	if(v[root] == 1) {
		res.push_back(make_pair(0, root));
	}
	sort(res.begin(), res.end());
	s.insert(dye[res[res.size() - 1].second]);
	for (int i = res.size() - 1; i >= 1; i--) {
		if(res[i].first == res[i - 1].first) {
			s.insert(dye[res[i].second]);
			s.insert(dye[res[i - 1].second]);
		} else {
			break;
		}
	}
	for (int i = 0; i < res.size(); i++) {
		mp[res[i].first]++;
	}
	for (int i = 1; i <= n; i++) {
		if(v[i] == 1) {
			if(s.count(dye[i]) && s.size() > 1) {
				if(s.size() > 2) {
					sum[i]++;
				} else {
					for (int j = res.size() - 1; j >= 0; j--) {
						if(dye[i] != dye[res[j].second]) {
							sum[i]++;
							sum[res[j].second]++;
							sum[root]--;
							break;
						}
					}
				}
			} else {
				if(s.size() > 1) {
					sum[i]++;
					continue;
				}
				if(dye[i] != dye[res[res.size() - 1].second]) {
					sum[i]++;
					sum[res[res.size() - 1].second]++;
					sum[root]--;
				}
				else {
					sum[i]++;
					if(mp[res[res.size() - 2].first] == 1) {
						sum[res[res.size() - 2].second]++;
						sum[root]--;
					}
				}
			}
		}
	}
	ans = ans_cnt = 0;
	dfs2(root, -1);
}

int main() {
	int x, y, z;
	scanf("%d%d", &n, &m);
	for (int i = 1; i <= m ;i++) {
		scanf("%d", &x);
		v[x] = 1;
	}
	for (int i = 1; i < n; i++) {
		scanf("%d%d%d", &x, &y, &z);
		add(x, y, z);
	}
	get_root();
	solve();
	printf("%d %d\n", ans, ans_cnt);
}