[洛谷P4178]Tree

题目大意：给一棵树，问有多少条路径长度小于等于$k$

题解：点分治

卡点：无

C++ Code：

#include <cstdio>
#include <algorithm>
#define maxn 40010
const int inf = 0x3f3f3f3f;
inline int max(int a, int b) {return a > b ? a : b;}

int head[maxn], cnt;
struct Edge {
	int to, nxt, w;
} e[maxn << 1];
inline void add(int a, int b, int c) {
	e[++cnt] = (Edge) {b, head[a], c}; head[a] = cnt;
	e[++cnt] = (Edge) {a, head[b], c}; head[b] = cnt;
}

bool vis[maxn];
namespace Center_of_Gravity {
	int sz[maxn], __nodenum;
	int root, MIN;
	#define n __nodenum
	void __getroot(int u, int fa) {
		sz[u] = 1;
		int MAX = 0;
		for (int i = head[u]; i; i = e[i].nxt) {
			int v = e[i].to;
			if (v != fa && !vis[v]) {
				__getroot(v, u);
				sz[u] += sz[v];
				MAX = max(MAX, sz[v]);
			}
		}
		MAX = max(MAX, n - sz[u]);
		if (MAX < MIN) MIN = MAX, root = u;
	}
	int getroot(int u, int nodenum = 0) {
		n = nodenum ? nodenum : sz[u];
		MIN = inf;
		__getroot(u, 0);
		return root;
	}
	#undef n
}
using Center_of_Gravity::getroot;

int n, k, ans;
int S[maxn], tot;
void getlist(int u, int fa, int val) {
	if (val <= k) S[++tot] = val;
	for (int i = head[u]; i; i = e[i].nxt) {
		int v = e[i].to;
		if (v != fa && !vis[v]) getlist(v, u, val + e[i].w);
	}
}
int calc(int u, int val) {
	tot = 0;
	getlist(u, 0, val);
	std::sort(S + 1, S + tot + 1);
	int l = 1, r = tot, res = 0;
	while (l <= r) {
		if (S[l] + S[r] <= k) res += r - l, l++;
		else r--;
	}
	return res;
}
void solve(int u) {
	vis[u] = true;
	ans += calc(u, 0);
	for (int i = head[u]; i; i = e[i].nxt) {
		int v = e[i].to;
		if (!vis[v]) {
			ans -= calc(v, e[i].w);
			solve(getroot(v));
		}
	}
}

int main() {
	scanf("%d", &n);
	for (int i = 1, a, b, c; i < n; i++) {
		scanf("%d%d%d", &a, &b, &c);
		add(a, b, c);
	}
	scanf("%d", &k);
	solve(getroot(1, n));
	printf("%d
", ans);
	return 0;
}