Submission #969625

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Source Code Expand

#include <bits/stdc++.h>

using namespace std;
#define FOR(i,n) for(int i = 0; i < (n); i++)
#define sz(c) ((int)c.size())
#define ten(n) ((int)1e##n)
using ll = long long;

template<typename ...> static inline int getchar_unlocked(void) { return getchar(); }
template<typename ...> static inline void putchar_unlocked(int c) { putchar(c); }
#define mygc(c) (c)=getchar_unlocked()
#define mypc(c) putchar_unlocked(c)
void reader(int& x) { int k, m = 0; x = 0; for (;;) { mygc(k); if (k == '-') { m = 1; break; }if ('0' <= k&&k <= '9') { x = k - '0'; break; } }for (;;) { mygc(k); if (k<'0' || k>'9')break; x = x * 10 + k - '0'; }if (m) x = -x; }
void reader(ll& x) { int k, m = 0; x = 0; for (;;) { mygc(k); if (k == '-') { m = 1; break; }if ('0' <= k&&k <= '9') { x = k - '0'; break; } }for (;;) { mygc(k); if (k<'0' || k>'9')break; x = x * 10 + k - '0'; }if (m) x = -x; }
int reader(char c[]) { int i, s = 0; for (;;) { mygc(i); if (i != ' '&&i != '\n'&&i != '\r'&&i != '\t'&&i != EOF) break; }c[s++] = i; for (;;) { mygc(i); if (i == ' ' || i == '\n' || i == '\r' || i == '\t' || i == EOF) break; c[s++] = i; }c[s] = '\0'; return s; }
int reader(string& c) { int i; for (;;) { mygc(i); if (i != ' '&&i != '\n'&&i != '\r'&&i != '\t'&&i != EOF) break; }c.push_back(i); for (;;) { mygc(i); if (i == ' ' || i == '\n' || i == '\r' || i == '\t' || i == EOF) break; c.push_back(i); }; return sz(c); }
template <class T, class S> void reader(T& x, S& y) { reader(x); reader(y); }
template <class T, class S, class U> void reader(T& x, S& y, U& z) { reader(x); reader(y); reader(z); }
template <class T, class S, class U, class V> void reader(T& x, S& y, U& z, V & w) { reader(x); reader(y); reader(z); reader(w); }
void writer(int x, char c) { int s = 0, m = 0; char f[10]; if (x<0)m = 1, x = -x; while (x)f[s++] = x % 10, x /= 10; if (!s)f[s++] = 0; if (m)mypc('-'); while (s--)mypc(f[s] + '0'); mypc(c); }
void writer(ll x, char c) { int s = 0, m = 0; char f[20]; if (x<0)m = 1, x = -x; while (x)f[s++] = x % 10, x /= 10; if (!s)f[s++] = 0; if (m)mypc('-'); while (s--)mypc(f[s] + '0'); mypc(c); }
void writer(const char c[]) { int i; for (i = 0; c[i] != '\0'; i++)mypc(c[i]); }
void writer(const char x[], char c) { int i; for (i = 0; x[i] != '\0'; i++)mypc(x[i]); mypc(c); }
template<class T> void writerLn(T x) { writer(x, '\n'); }
template<class T, class S> void writerLn(T x, S y) { writer(x, ' '); writer(y, '\n'); }
template<class T, class S, class U> void writerLn(T x, S y, U z) { writer(x, ' '); writer(y, ' '); writer(z, '\n'); }
template<class T> void writerArr(T x[], int n) { if (!n) { mypc('\n'); return; }FOR(i, n - 1)writer(x[i], ' '); writer(x[n - 1], '\n'); }
template<class T> void writerArr(vector<T>& x) { writerArr(x.data(), (int)x.size()); }

template<class T> T gcd(T a, T b) { return b ? gcd(b, a % b) : a; }
template<class T> T lcm(T a, T b) { return a / gcd(a, b) * b; }
ll mod_pow(ll a, ll n, ll mod) {
	ll ret = 1;
	ll p = a % mod;
	while (n) {
		if (n & 1) ret = ret * p % mod;
		p = p * p % mod;
		n >>= 1;
	}
	return ret;
}
template<class T> T extgcd(T a, T b, T& x, T& y) { for (T u = y = 1, v = x = 0; a;) { T q = b / a; swap(x -= q * u, u); swap(y -= q * v, v); swap(b -= q * a, a); } return b; }
template<class T> T mod_inv(T a, T m) { T x, y; extgcd(a, m, x, y); return (m + x % m) % m; }

using Pii = pair<int, int>;
using Pll = pair<ll, ll>;

class CentroidDecomposition {
private:
	using edge_t = Pii;
	int g_to(const Pii& edge) { return edge.first; }

	vector<vector<int>> e;
	const int n;
	vector<int> subtree_size; // buffer for compute_subtree_size
	vector<int> depth, rank, parent;

	int compute_subtree_size(int v, int par) {
		int c = 1;
		for (auto w : e[v]) {
			if (w == par || rank[w] != -1) continue;
			c += compute_subtree_size(w, v);
		}
		return subtree_size[v] = c;
	}

	Pii search_centroid(int v, int par, int sub_size) {
		Pii ret(ten(9), -1);
		int s = 1, m = 0;
		for (auto w : e[v]) {
			if (w == par || rank[w] != -1) continue;
			ret = min(ret, search_centroid(w, v, sub_size));
			m = max(m, subtree_size[w]);
			s += subtree_size[w];
		}
		m = max(m, sub_size - s);
		ret = min(ret, Pii(m, v));
		return ret;
	}

	int build_centroid_decomposition_tree(int v, int par, int rnk, vector<vector<int>>& childs) {
		compute_subtree_size(v, -1);
		int s = search_centroid(v, -1, subtree_size[v]).second;

		parent[s] = par;
		rank[s] = rnk;
		if (par != -1) childs[par].push_back(s);

		for (auto w : e[s]) {
			if (rank[w] != -1) continue;
			build_centroid_decomposition_tree(w, s, rnk + 1, childs);
		}
		return s;
	}

public:
	template<int ARRAY_BUF>
	CentroidDecomposition(vector<edge_t>(&e)[ARRAY_BUF], int n) :
		n(n),
		e(n),
		subtree_size(n),
		depth(n), rank(n, -1), parent(n) {
		FOR(i, n) {
			for (const edge_t& ed : e[i]) {
				this->e[i].push_back(g_to(ed));
			}
		}
	}

	CentroidDecomposition(vector<vector<edge_t>>& e) :
		n(sz(e)),
		e(n),
		subtree_size(n),
		depth(n), rank(n, -1), parent(n) {
		FOR(i, n) {
			this->e[i].resize(sz(e[i]));
			for (const edge_t& ed : e[i]) {
				this->e[i].push_back(g_to(ed));
			}
		}
	}

	// pair<centroid_decomposition_tree, root_vertex>
	// centroid_decomposition_tree = vector<vector<int>> directed graph
	pair<vector<vector<int>>,int> build() {
		vector<vector<int>> childs(n);
		int root = build_centroid_decomposition_tree(0, -1, 0, childs);

		return make_pair(childs, root);
	}
};

Pll add(Pll& l, Pll& r) { return Pll(l.first + r.first, l.second + r.second); }
Pll sub(Pll& l, Pll& r) { return Pll(l.first - r.first, l.second - r.second); }

int min_cost[ten(5)];
vector<Pii> e[ten(5)];

bool centroid_used[ten(5)];
void enm(int v, int p, int len, vector <int>& ret, int cc_len) {
	if (len > cc_len) return;
	ret.push_back(len);
	for (auto& kv : e[v]) {
		if (centroid_used[kv.first]) continue;
		if (kv.first == p) continue;
		enm(kv.first, v, len + kv.second, ret, cc_len);
	}
}

Pll cnt(vector<int>& ds, int len) {
	static ll sm[ten(5) + 1];
	sort(ds.begin(), ds.end());
	sm[0] = 0;
	FOR(i, sz(ds)) sm[i + 1] = sm[i] + ds[i];
	int j = sz(ds);

	Pll ret(0, 0);
	FOR(i, sz(ds)) {
		while (j > 0 && ds[i] + ds[j - 1] > len) j--;
		ret.first += j;
		ret.second += sm[j] + ll(ds[i]) * j;
		if (j > i) {
			// de-dup
			ret.first--;
			ret.second -= ds[i] * 2;
		}
	}

	return Pll(ret.first / 2, ret.second / 2);
}

// 頂点sを重心とする部分木Sについての計算
// u-v-path (****uとvのpathに必ずsが含まれる****) ものについて、全て計算する
// e.x) u-v-pathの中で、距離がcc_len以下のpathを数え上げる, cc_len以下のpathのsumを計算する
Pll solve_dfs(int s, int cc_len, vector<vector<int>>& centroid_childs) {
	centroid_used[s] = true; // 部分木を区切るのに使用

	// phase 1
	// 部分木に再帰的に適用する
	Pll ret(0, 0);
	for (auto& ch : centroid_childs[s]) {
		if (centroid_used[ch]) continue;
		//再帰的に小さい部分木に適用
		Pll atmp = solve_dfs(ch, cc_len, centroid_childs);
		ret = add(ret, atmp);
	}

	// phase 2
	//頂点sからの距離を保存
	vector<int> ds;
	ds.push_back(0);
	for (auto& kv : e[s]) {
		if (centroid_used[kv.first]) continue;
		
		// phase 2.1
		//  sと隣接する頂点が属する部分木について、sからの距離を計算
		vector<int> tmp;
		enm(kv.first, -1, kv.second, tmp, cc_len);

		//phase 2.2
		//  phase 3で無駄に計算されるものを、あらかじめ引き算する。
		Pll atmp = cnt(tmp, cc_len);
		ret = sub(ret, atmp);

		// phase 2.3
		//  sからの距離に追加
		for (auto& x : tmp) ds.push_back(x);
	}

	// phase 3
	// この部分木についての計算をする
	// dsには、sからの距離が入っているので、u-v-pathの距離がcc_len以下となるような(u,v)の個数が計算出来る
	// ただしここで計算した結果には u-v-pathに****sが含まれない****ものも含まれているので、
	// phase2.3で事前に引き算をしておく
	Pll btmp = cnt(ds, cc_len);
	ret = add(ret, btmp);

	centroid_used[s] = false;

	return ret;
}

ll solve(int n, int x) {
	CentroidDecomposition cd(e, n);

	vector<vector<int>> centroid_childs;
	int root;
	tie(centroid_childs,root) = cd.build();

	Pll cnt = solve_dfs(root, x, centroid_childs);
	ll origin_path_count = cnt.first;
	ll sum = cnt.second;

	FOR(i, n) {
		min_cost[i] = ten(9);
		for (auto& kv : e[i]) min_cost[i] = min(min_cost[i], kv.second);
	}

	FOR(u, n) {
		for (auto& kv : e[u]) {
			int t, c; tie(t, c) = kv;
			if (u > t) continue;
			if (c <= x) continue; // already counted

			int cost = c;
			if (sz(e[u]) != n - 1) {
				cost = min(cost, x + min_cost[t]);
			}
			if (sz(e[t]) != n - 1) {
				cost = min(cost, x + min_cost[u]);
			}
			if (sz(e[u]) + sz(e[t]) != n) {
				cost = min(cost, x + x);
			}
			if (sz(e[u]) != 1 && sz(e[t]) != 1) {
				cost = min(cost, x + x + x);
			}

			origin_path_count++;
			sum += cost;
		}
	}

	ll black = ll(n) * (n - 1) / 2 - origin_path_count;
	sum += black * x;

	return sum;
}


int main() {
	int n, x; reader(n, x);
	FOR(i, n - 1) {
		int u, v, c; reader(u, v, c);
		u--; v--;
		e[u].emplace_back(v, c);
		e[v].emplace_back(u, c);
	}

	ll ans = 0;
	ll c = solve(n, x);
	writerLn(c);

	return 0;
}

Submission Info

Judge Result