最终代码：

#include <bits/stdc++.h>
using namespace std;
const int maxn = 2e5 + 5;
int n;
long long ans;
bool vis[maxn];
vector<int> g[maxn];

int get_size(int u, int p) { // 求连通块大小 
	if (vis[u]) return 0;
	int sum = 1;
	for (auto v : g[u])
		if (v != p)
			sum += get_size(v, u);
	return sum;
}
// weight center 更新重心 
int cal_wc(int u, int p, int tot, int &wc) {
	if (vis[u])
		return 0;
	int sum = 1, ms = 0;
	for (auto v : g[u]) {
		if (v != p) {
			int tmp = cal_wc(v, u, tot, wc);
			sum += tmp;
			ms = max(ms, tmp);
		}
	}
	ms = max(ms, tot - sum);
	if (ms <= tot/2) wc = u;
	return sum;
}

void dfs2(int u, int p, int d, long long c[2]) {
	if (vis[u]) return;
	c[d]++;
	for (auto v : g[u])
		if (v != p)
			dfs2(v, u, d^1, c);
}

void dfs(int u) {
	if (vis[u])
		return;
	cal_wc(u, -1, get_size(u, -1), u);
	// 处理
	long long cnt[2] = {1}; // cnt[0] = 1, cnt[1] = 0
	for (auto v : g[u]) {
		long long c[2] = {}; // c[0] = c[1] = 0
		dfs2(v, u, 1, c);
		ans += (long long) cnt[0] * c[0] + (long long) cnt[1] * c[1];
		cnt[0] += c[0];
		cnt[1] += c[1];
	}
	vis[u] = true;
	for (auto v : g[u])
		dfs(v);
}

int main() {
	scanf("%d", &n);
	for (int i = 1; i < n; i++) {
		int u, v;
		scanf("%d%d", &u, &v);
		g[u].push_back(v);
		g[v].push_back(u);
	}
	dfs(1);
	printf("%lld\n", ans);
	return 0;
}

#include <bits/stdc++.h>
using namespace std;
const int maxn = 2e5 + 5;
int n;
long long ans;
bool vis[maxn];
vector<int> g[maxn];

int get_size(int u, int p) {
	if (vis[u]) return 0;
	int sum = 1;
	for (auto v : g[u])
		if (v != p)
			sum += get_size(v, u);
	return sum;
}
// weight center
int cal_wc(int u, int p, int tot, int &wc) {
	if (vis[u])
		return 0;
	int sum = 1, ms = 0;
	for (auto v : g[u]) {
		if (v != p) {
			int tmp = cal_wc(v, u, tot, wc);
			sum += tmp;
			ms = max(ms, tmp);
		}
	}
	ms = max(ms, tot - sum);
	if (ms <= tot/2) wc = u;
	return sum;
}

void dfs(int u) {
	if (vis[u])
		return;
	cal_wc(u, -1, get_size(u, -1), u);
	// u 变成重心了
	cout << u << " .." << endl;
	vis[u] = true;
	for (auto v : g[u])
		dfs(v);
}

int main() {
	scanf("%d", &n);
	for (int i = 1; i < n; i++) {
		int u, v;
		scanf("%d%d", &u, &v);
		g[u].push_back(v);
		g[v].push_back(u);
	}
	dfs(1);
	return 0;
}