結果

問題 No.1207 グラフX
ユーザー m_tsubasa
提出日時 2020-08-30 13:26:04
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 432 ms / 2,000 ms
コード長 3,248 bytes
コンパイル時間 2,608 ms
コンパイル使用メモリ 203,652 KB
最終ジャッジ日時 2025-01-13 21:09:39
ジャッジサーバーID
（参考情報） 		judge3 / judge4
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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

ソースコード

diff # 

#include <bits/stdc++.h>
using namespace std;

struct Unionfind {
  // tree number
  vector<int> par;
  // constructor
  Unionfind(int n = 1) : par(n, -1) {}
  // search root
  int root(int x) {
    if (par[x] < 0) return x;
    return par[x] = root(par[x]);
  }
  // is same?
  bool issame(int x, int y) { return root(x) == root(y); }

  // add
  // already added, return 0
  bool uni(int x, int y) {
    x = root(x);
    y = root(y);
    if (x == y) return 0;
    if (par[x] > par[y]) swap(x, y);
    par[x] += par[y];
    par[y] = x;
    return 1;
  }
  int size(int x) { return -par[root(x)]; }
};

template <int mod = (int)(1e9 + 7)>
struct ModInt {
  int x;
  constexpr ModInt() : x(0) {}
  constexpr ModInt(int64_t y)
      : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}
  constexpr ModInt &operator+=(const ModInt &p) noexcept {
    if ((x += p.x) >= mod) x -= mod;
    return *this;
  }
  constexpr ModInt &operator-=(const ModInt &p) noexcept {
    if ((x += mod - p.x) >= mod) x -= mod;
    return *this;
  }
  constexpr ModInt &operator*=(const ModInt &p) noexcept {
    x = (int)(1LL * x * p.x % mod);
    return *this;
  }
  constexpr ModInt &operator/=(const ModInt &p) noexcept {
    *this *= p.inverse();
    return *this;
  }
  constexpr ModInt operator-() const { return ModInt(-x); }
  constexpr ModInt operator+(const ModInt &p) const noexcept {
    return ModInt(*this) += p;
  }
  constexpr ModInt operator-(const ModInt &p) const noexcept {
    return ModInt(*this) -= p;
  }
  constexpr ModInt operator*(const ModInt &p) const noexcept {
    return ModInt(*this) *= p;
  }
  constexpr ModInt operator/(const ModInt &p) const noexcept {
    return ModInt(*this) /= p;
  }
  constexpr bool operator==(const ModInt &p) const noexcept { return x == p.x; }
  constexpr bool operator!=(const ModInt &p) const noexcept { return x != p.x; }
  constexpr ModInt inverse() const noexcept {
    int a = x, b = mod, u = 1, v = 0, t = 0;
    while (b > 0) {
      t = a / b;
      swap(a -= t * b, b);
      swap(u -= t * v, v);
    }
    return ModInt(u);
  }
  constexpr ModInt pow(int64_t n) const {
    ModInt res(1), mul(x);
    while (n) {
      if (n & 1) res *= mul;
      mul *= mul;
      n >>= 1;
    }
    return res;
  }
  friend constexpr ostream &operator<<(ostream &os, const ModInt &p) noexcept {
    return os << p.x;
  }
  friend constexpr istream &operator>>(istream &is, ModInt &a) noexcept {
    int64_t t = 0;
    is >> t;
    a = ModInt<mod>(t);
    return (is);
  }
  constexpr int get_mod() { return mod; }
};

using P = pair<int, int>;

int n, m, x;
Unionfind uf;
vector<int> dp;
vector<vector<P>> g;

ModInt<> solve(int now, int par);

int main() {
  cin >> n >> m >> x;
  uf = Unionfind(n);
  g.resize(n);
  for (int i = 0; i < m; ++i) {
    int a, b, c;
    cin >> a >> b >> c;
    if (!uf.issame(--a, --b)) {
      g[a].push_back(P(b, c));
      g[b].push_back(P(a, c));
      uf.uni(a, b);
    }
  }
  dp.assign(n, 1);
  cout << solve(0, -1) << endl;
  return 0;
}

ModInt<> solve(int now, int par) {
  ModInt<> res;
  for (auto [to, z] : g[now])
    if (to != par) {
      res += solve(to, now);
      res += ModInt<>(x).pow(z) * dp[to] * (n - dp[to]);
      dp[now] += dp[to];
    }
  return res;
}
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