結果

問題 No.1333 Squared Sum
ユーザー KoDKoD
提出日時 2021-01-08 22:20:55
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 418 ms / 2,000 ms
コード長 8,143 bytes
コンパイル時間 1,249 ms
コンパイル使用メモリ 85,320 KB
実行使用メモリ 43,392 KB
最終ジャッジ日時 2024-11-16 12:59:15
合計ジャッジ時間 12,434 ms
ジャッジサーバーID
（参考情報） 		judge5 / judge4
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テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 2 ms
5,248 KB
testcase_01 AC 2 ms
5,248 KB
testcase_02 AC 2 ms
5,248 KB
testcase_03 AC 374 ms
21,248 KB
testcase_04 AC 368 ms
21,248 KB
testcase_05 AC 376 ms
21,248 KB
testcase_06 AC 363 ms
21,248 KB
testcase_07 AC 363 ms
21,248 KB
testcase_08 AC 362 ms
21,248 KB
testcase_09 AC 362 ms
21,248 KB
testcase_10 AC 364 ms
21,248 KB
testcase_11 AC 361 ms
21,376 KB
testcase_12 AC 361 ms
21,120 KB
testcase_13 AC 360 ms
43,264 KB
testcase_14 AC 401 ms
32,512 KB
testcase_15 AC 418 ms
40,704 KB
testcase_16 AC 2 ms
5,248 KB
testcase_17 AC 2 ms
5,248 KB
testcase_18 AC 2 ms
5,248 KB
testcase_19 AC 2 ms
5,248 KB
testcase_20 AC 2 ms
5,248 KB
testcase_21 AC 3 ms
5,248 KB
testcase_22 AC 2 ms
5,248 KB
testcase_23 AC 2 ms
5,248 KB
testcase_24 AC 2 ms
5,248 KB
testcase_25 AC 2 ms
5,248 KB
testcase_26 AC 397 ms
42,752 KB
testcase_27 AC 394 ms
33,152 KB
testcase_28 AC 397 ms
42,752 KB
testcase_29 AC 358 ms
43,392 KB
testcase_30 AC 137 ms
10,752 KB
testcase_31 AC 74 ms
7,552 KB
testcase_32 AC 205 ms
14,080 KB
testcase_33 AC 160 ms
11,904 KB
testcase_34 AC 283 ms
17,664 KB
testcase_35 AC 206 ms
14,080 KB
testcase_36 AC 131 ms
9,728 KB
testcase_37 AC 122 ms
9,984 KB
testcase_38 AC 143 ms
11,264 KB
testcase_39 AC 236 ms
15,616 KB
testcase_40 AC 297 ms
20,384 KB
testcase_41 AC 293 ms
20,384 KB
testcase_42 AC 300 ms
20,384 KB
testcase_43 AC 269 ms
20,384 KB
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 # 

#line 1 "main.cpp"

/**
 * @title Template
 */

#include <iostream>
#include <algorithm>
#include <utility>
#include <numeric>
#include <vector>
#include <array>
#include <cassert>

#line 2 "/Users/kodamankod/Desktop/cpp_programming/Library/other/range.cpp"

#line 4 "/Users/kodamankod/Desktop/cpp_programming/Library/other/range.cpp"

class range {
  struct iter {
    std::size_t itr;
    constexpr iter(std::size_t pos) noexcept: itr(pos) { }
    constexpr void operator ++ () noexcept { ++itr; }
    constexpr bool operator != (iter other) const noexcept { return itr != other.itr; }
    constexpr std::size_t operator * () const noexcept { return itr; }
  };

  struct reviter {
    std::size_t itr;
    constexpr reviter(std::size_t pos) noexcept: itr(pos) { }
    constexpr void operator ++ () noexcept { --itr; }
    constexpr bool operator != (reviter other) const noexcept { return itr != other.itr; }
    constexpr std::size_t operator * () const noexcept { return itr; }
  };

  const iter first, last;

public:
  constexpr range(std::size_t first, std::size_t last) noexcept: first(first), last(std::max(first, last)) { }
  constexpr iter begin() const noexcept { return first; }
  constexpr iter end() const noexcept { return last; }
  constexpr reviter rbegin() const noexcept { return reviter(*last - 1); } 
  constexpr reviter rend() const noexcept { return reviter(*first - 1); } 
};

/**
 * @title Range
 */
#line 2 "/Users/kodamankod/Desktop/cpp_programming/Library/algebraic/modular.cpp"

#line 2 "/Users/kodamankod/Desktop/cpp_programming/Library/algebraic/mod_inv.cpp"

#line 4 "/Users/kodamankod/Desktop/cpp_programming/Library/algebraic/mod_inv.cpp"
#include <cstdint>

constexpr std::pair<int64_t, int64_t> mod_inv(int64_t a, int64_t b) {
  if ((a %= b) == 0) return { b, 0 };
  int64_t s = b, t = (a < 0 ? a + b : a);
  int64_t m0 = 0, m1 = 1, tmp = 0;
  while (t > 0) {
    const auto u = s / t;
    s -= t * u; m0 -= m1 * u;
    tmp = s; s = t; t = tmp; tmp = m0; m0 = m1; m1 = tmp;
  }
  return { s, (m0 < 0 ? m0 + b / s : m0) };
}

/**
 * @title Extended GCD
 */
#line 4 "/Users/kodamankod/Desktop/cpp_programming/Library/algebraic/modular.cpp"

#line 8 "/Users/kodamankod/Desktop/cpp_programming/Library/algebraic/modular.cpp"
#include <type_traits>

template <class Modulus>
class modular {
public:
  using value_type = uint32_t;
  using cover_type = uint64_t;
 
  static constexpr uint32_t mod() { return Modulus::mod(); }
  template <class T>
  static constexpr value_type normalize(T value_) noexcept {
    if (value_ < 0) {
      value_ = -value_;
      value_ %= mod();
      if (value_ == 0) return 0;
      return mod() - value_;
    }
    return value_ % mod();
  }

private:
  value_type value;

  template <bool IsPrime, std::enable_if_t<IsPrime>* = nullptr>
  constexpr modular inverse_helper() const noexcept { return power(*this, mod() - 2); }
  template <bool IsPrime, std::enable_if_t<!IsPrime>* = nullptr>
  constexpr modular inverse_helper() const noexcept {
    const auto tmp = mod_inv(value, mod());
    assert(tmp.first == 1);
    return modular(tmp.second);
  }

public:
  constexpr modular() noexcept : value(0) { }
  template <class T>
  explicit constexpr modular(T value_) noexcept : value(normalize(value_)) { }
  template <class T>
  explicit constexpr operator T() const noexcept { return static_cast<T>(value); }
 
  constexpr value_type get() const noexcept { return value; }
  constexpr value_type &extract() noexcept { return value; }
  constexpr modular operator - () const noexcept { return modular(mod() - value); }
  constexpr modular operator ~ () const noexcept { return inverse(*this); }
 
  constexpr modular operator + (const modular &rhs) const noexcept { return modular(*this) += rhs; }
  constexpr modular& operator += (const modular &rhs) noexcept { 
    if ((value += rhs.value) >= mod()) value -= mod(); 
    return *this; 
  }
 
  constexpr modular operator - (const modular &rhs) const noexcept { return modular(*this) -= rhs; }
  constexpr modular& operator -= (const modular &rhs) noexcept { 
    if ((value += mod() - rhs.value) >= mod()) value -= mod(); 
    return *this; 
  }
 
  constexpr modular operator * (const modular &rhs) const noexcept { return modular(*this) *= rhs; }
  constexpr modular& operator *= (const modular &rhs) noexcept { 
    value = (cover_type) value * rhs.value % mod();
    return *this;
  }
 
  constexpr modular operator / (const modular &rhs) const noexcept { return modular(*this) /= rhs; }
  constexpr modular& operator /= (const modular &rhs) noexcept { return (*this) *= inverse(rhs); }
 
  constexpr bool zero() const noexcept { return value == 0; }
  constexpr bool operator == (const modular &rhs) const noexcept { return value == rhs.value; }
  constexpr bool operator != (const modular &rhs) const noexcept { return value != rhs.value; }
 
  friend std::ostream& operator << (std::ostream &stream, const modular &rhs) { return stream << rhs.value; }
  friend constexpr modular inverse(const modular &val) noexcept { return val.inverse_helper<Modulus::is_prime>(); }
  friend constexpr modular power(modular val, cover_type exp) noexcept { 
    modular res(1);
    for (; exp > 0; exp >>= 1, val *= val) if (exp & 1) res *= val;
    return res;
  }
 
};
 
template <uint32_t Mod, bool IsPrime = true>
struct static_modulus { 
  static constexpr uint32_t mod() noexcept { return Mod; } 
  static constexpr bool is_prime = IsPrime;
};

template <uint32_t Id = 0, bool IsPrime = false>
struct dynamic_modulus {
  static uint32_t &mod() noexcept { static uint32_t val = 0; return val; }
  static constexpr bool is_prime = IsPrime;
};

template <uint32_t Mod, bool IsPrime = true>
using mint32_t = modular<static_modulus<Mod, IsPrime>>;
using rmint32_t = modular<dynamic_modulus<>>;

/*
 * @title Modint
 */
#line 2 "/Users/kodamankod/Desktop/cpp_programming/Library/other/fix_point.cpp"

#line 4 "/Users/kodamankod/Desktop/cpp_programming/Library/other/fix_point.cpp"

template <class Func>
struct fix_point_impl: private Func {
  explicit constexpr fix_point_impl(Func &&func): Func(std::forward<Func>(func)) { }
  template <class... Args>
  constexpr decltype(auto) operator () (Args &&... args) const {
    return Func::operator()(*this, std::forward<Args>(args)...);
  }
};

template <class Func>
constexpr decltype(auto) fix_point(Func &&func) {
  return fix_point_impl<Func>(std::forward<Func>(func));
}

/**
 * @title Lambda Recursion
 */
#line 17 "main.cpp"

using i32 = std::int32_t;
using i64 = std::int64_t;
using u32 = std::uint32_t;
using u64 = std::uint64_t;
using isize = std::ptrdiff_t;
using usize = std::size_t;

constexpr i32 inf32 = (u32) ~0 >> 2;
constexpr i64 inf64 = (u64) ~0 >> 2;

template <class T>
using Vec = std::vector<T>;

using Fp = mint32_t<1000000007>;

struct Data {
  Fp sq_sum;
  Fp sq_sum_path;
  Fp sum_path;
  Fp cnt_path;
};

int main() {
  usize N;
  std::cin >> N;
  Vec<Vec<std::pair<usize, u32>>> graph(N);
  for (auto i: range(1, N)) {
    usize a, b;
    u32 w;
    std::cin >> a >> b >> w;
    a -= 1;
    b -= 1;
    graph[a].emplace_back(b, w);
    graph[b].emplace_back(a, w);
  }
  Vec<Data> dp(N, Data { });
  fix_point([&](auto dfs, const usize u, const usize p) -> void {
    for (const auto [v, w]: graph[u]) {
      if (v != p) {
        dfs(v, u);
        Data merge { };
        merge.sq_sum_path = Fp(w) * Fp(w) + Fp(w) * Fp(w) * dp[v].cnt_path + dp[v].sq_sum_path + Fp(2) * Fp(w) * dp[v].sum_path; 
        merge.sq_sum = merge.sq_sum_path + dp[v].sq_sum;
        merge.sum_path = Fp(w) + Fp(w) * dp[v].cnt_path + dp[v].sum_path;
        merge.cnt_path = dp[v].cnt_path + Fp(1);
        Data next { };
        next.sq_sum = dp[u].sq_sum + merge.sq_sum + dp[u].sq_sum_path * merge.cnt_path + merge.sq_sum_path * dp[u].cnt_path + Fp(2) * dp[u].sum_path * merge.sum_path;
        next.sq_sum_path = dp[u].sq_sum_path + merge.sq_sum_path;
        next.sum_path = dp[u].sum_path + merge.sum_path;
        next.cnt_path = dp[u].cnt_path + merge.cnt_path;
        dp[u] = std::move(next);
      }
    }
  })(0, 0);
  std::cout << dp[0].sq_sum << '\n';
  return 0;
}
0