結果

問題 No.1207 グラフX
コンテスト
ユーザー tkmst201
提出日時 2021-02-05 10:59:56
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 310 ms / 2,000 ms
コード長 5,043 bytes
コンパイル時間 2,510 ms
コンパイル使用メモリ 201,908 KB
最終ジャッジ日時 2025-01-18 11:43:39
ジャッジサーバーID
（参考情報） 		judge2 / judge3
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 46
権限があれば一括ダウンロードができます
コンパイルメッセージ
main.cpp: In function ‘int main()’:
main.cpp:119:22: warning: ignoring return value of ‘int scanf(const char*, ...)’ declared with attribute ‘warn_unused_result’ [-Wunused-result]
  119 |                 scanf("%d %d %d", &x, &y, &z);
      |                 ~~~~~^~~~~~~~~~~~~~~~~~~~~~~~

ソースコード

diff # 

#include <bits/stdc++.h>
using namespace std;
#define FOR(i,a,b) for(int i=(a);i<(b);++i)
#define REP(i,n) FOR(i,0,n)
#define ALL(v) begin(v),end(v)
template<typename A, typename B> inline bool chmax(A & a, const B & b) { if (a < b) { a = b; return true; } return false; }
template<typename A, typename B> inline bool chmin(A & a, const B & b) { if (a > b) { a = b; return true; } return false; }
using ll = long long;
using pii = pair<int, int>;
constexpr ll INF = 1ll<<30;
constexpr ll longINF = 1ll<<60;
constexpr ll MOD = 1000000007;
constexpr bool debug = false;
//---------------------------------//

struct UnionFind {
public:
	using size_type = int;
	
	UnionFind(size_type n) : n(n), size_(n, 1) {
		par.resize(n);
		std::iota(par.begin(), par.end(), 0);
	}
	
	size_type size(size_type x) { return size_[find(x)]; }
	
	size_type find(size_type x) {
		assert(x < n);
		while (par[x] != x) {
			par[x] = par[par[x]];
			x = par[x];
		}
		return x;
	}
	
	void unite(size_type x, size_type y) {
		x = find(x);
		y = find(y);
		if (x == y) return;
		if (size(x) > size(y)) std::swap(x, y);
		par[x] = y;
		size_[y] += size_[x];
	}
	
	bool issame(size_type x, size_type y) { return find(x) == find(y); }
	
private:
	size_type n;
	std::vector<size_type> size_, par;
};

template<int M>
struct ModInt {
	static_assert(M > 0);
	
public:
	using value_type = int;
	using calc_type = std::int_fast64_t;
	
private:
	value_type val_;
	
public:
	constexpr ModInt(calc_type val = 0) : val_(val < 0 ? (val % M + M) % M : val % M) {}
	constexpr const value_type & val() const noexcept { return val_; }
	constexpr static decltype(M) mod() noexcept { return M; }
	
	explicit constexpr operator bool() const noexcept { return val_; }
	constexpr bool operator !() const noexcept { return !static_cast<bool>(*this); }
	constexpr ModInt operator +() const noexcept { return ModInt(*this); }
	constexpr ModInt operator -() const noexcept { return ModInt(-val_); }
	constexpr ModInt operator ++(int) noexcept { ModInt res = *this; ++*this; return res; }
	constexpr ModInt operator --(int) noexcept { ModInt res = *this; --*this; return res; }
	constexpr ModInt & operator ++() noexcept { val_ = val_ + 1 == M ? 0 : val_ + 1; return *this; }
	constexpr ModInt & operator --() noexcept { val_ = val_ == 0 ? M - 1 : val_ - 1; return *this; }
	constexpr ModInt & operator +=(const ModInt & rhs) noexcept { val_ += val_ < M - rhs.val_ ? rhs.val_ : rhs.val_ - M; return *this; }
	constexpr ModInt & operator -=(const ModInt & rhs) noexcept { val_ += val_ >= rhs.val_ ? -rhs.val_ : M - rhs.val_; return *this; }
	constexpr ModInt & operator *=(const ModInt & rhs) noexcept { val_ = static_cast<calc_type>(val_) * rhs.val_ % M; return *this; }
	constexpr ModInt & operator /=(const ModInt & rhs) noexcept { return *this *= rhs.inv(); }
	friend constexpr ModInt operator +(const ModInt & lhs, const ModInt & rhs) noexcept { return ModInt(lhs) += rhs; }
	friend constexpr ModInt operator -(const ModInt & lhs, const ModInt & rhs) noexcept { return ModInt(lhs) -= rhs; }
	friend constexpr ModInt operator *(const ModInt & lhs, const ModInt & rhs) noexcept { return ModInt(lhs) *= rhs; }
	friend constexpr ModInt operator /(const ModInt & lhs, const ModInt & rhs) noexcept { return ModInt(lhs) /= rhs; }
	friend constexpr bool operator ==(const ModInt & lhs, const ModInt & rhs) noexcept { return lhs.val_ == rhs.val_; }
	friend constexpr bool operator !=(const ModInt & lhs, const ModInt & rhs) noexcept { return !(lhs == rhs); }
	friend std::ostream & operator <<(std::ostream & os, const ModInt & rhs) { return os << rhs.val_; }
	friend std::istream & operator >>(std::istream & is, ModInt & rhs) { calc_type x; is >> x; rhs = ModInt(x); return is; }
	
	constexpr ModInt pow(calc_type n) const noexcept {
		ModInt res = 1, x = val_;
		if (n < 0) { x = x.inv(); n = -n; }
		while (n) { if (n & 1) res *= x; x *= x; n >>= 1; }
		return res;
	}
	
	constexpr ModInt inv() const noexcept {
		value_type a = val_, a1 = 1, a2 = 0, b = M, b1 = 0, b2 = 1;
		while (b > 0) {
			value_type q = a / b, r = a % b;
			value_type nb1 = a1 - q * b1, nb2 = a2 - q * b2;
			a = b; b = r;
			a1 = b1; b1 = nb1;
			a2 = b2; b2 = nb2;
		}
		assert(a == 1);
		return a1;
	}
};
using mint = ModInt<MOD>;

int main() {
	int N, M, X;
	cin >> N >> M >> X;
	vector<vector<int>> g(N);
	UnionFind uf(N);
	vector<int> U, V, W;
	REP(i, M) {
		int x, y, z;
		scanf("%d %d %d", &x, &y, &z);
		--x; --y;
		if (uf.issame(x, y)) continue;
		uf.unite(x, y);
		g[x].emplace_back(y);
		g[y].emplace_back(x);
		U.emplace_back(x);
		V.emplace_back(y);
		W.emplace_back(z);
	}
	
	vector<int> child(N);
	auto dfs = [&](auto self, int u, int p) -> int {
		child[u] = 1;
		for (int v : g[u]) {
			if (v == p) continue;
			child[u] += self(self, v, u);
		}
		return child[u];
	};
	dfs(dfs, 0, -1);
	
	mint ans = 0;
	REP(i, U.size()) {
		if (child[U[i]] < child[V[i]]) swap(U[i], V[i]);
		// U[i] -> V[i]
		mint pat = (mint)child[V[i]] * (N - child[V[i]]);
		ans += pat * mint(X).pow(W[i]);
	}
	cout << ans << endl;
}
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