結果

問題 No.2507 Yet Another Subgraph Counting
コンテスト
ユーザー emthrm
提出日時 2023-08-22 11:55:12
言語 C++23
(gcc 13.3.0 + boost 1.87.0)
結果
TLE  
実行時間 -
コード長 5,518 bytes
コンパイル時間 2,265 ms
コンパイル使用メモリ 118,196 KB
実行使用メモリ 10,496 KB
最終ジャッジ日時 2024-12-26 09:22:11
合計ジャッジ時間 22,884 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge5
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ファイルパターン 結果
other AC * 47 TLE * 5
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 <algorithm>
#include <array>
#include <bit>
#include <cassert>
#include <concepts>
#include <cstdint>
#include <iostream>
#include <iterator>
#include <utility>
#include <vector>

namespace emthrm {

template <int MaxN, typename T>
std::vector<T> subset_convolution(
    const std::vector<T>& f, const std::vector<T>& g) {
  using Polynomial = std::array<T, MaxN + 1>;
  assert(std::has_single_bit(f.size()) && f.size() == g.size());
  const int n = std::countr_zero(f.size());
  assert(n <= MaxN);
  const int domain_size = 1 << n;
  const auto ranked_zeta_transform =
      [n, domain_size](const std::vector<T>& f) -> std::vector<Polynomial> {
    std::vector a(domain_size, Polynomial{});
    for (int i = 0; i < domain_size; ++i) {
      a[i][std::popcount(static_cast<unsigned int>(i))] = f[i];
    }
    for (int bit = 1; bit < domain_size; bit <<= 1) {
      for (int i = 0; i < domain_size; ++i) {
        if ((i & bit) == 0) {
          for (int degree = 0; degree <= n; ++degree) {
            a[i | bit][degree] += a[i][degree];
          }
        }
      }
    }
    return a;
  };
  std::vector<Polynomial> a = ranked_zeta_transform(f);
  const std::vector<Polynomial> b = ranked_zeta_transform(g);
  for (int i = 0; i < domain_size; ++i) {
    // Hadamard product
    for (int degree_of_a = n; degree_of_a >= 0; --degree_of_a) {
      const T tmp = std::exchange(a[i][degree_of_a], T{});
      for (int degree_of_b = 0; degree_of_a + degree_of_b <= n; ++degree_of_b) {
        a[i][degree_of_a + degree_of_b] += tmp * b[i][degree_of_b];
      }
    }
  }
  for (int bit = 1; bit < domain_size; bit <<= 1) {
    for (int i = 0; i < domain_size; ++i) {
      if ((i & bit) == 0) {
        for (int degree = 0; degree <= n; ++degree) {
          a[i | bit][degree] -= a[i][degree];
        }
      }
    }
  }
  std::vector<T> c(domain_size);
  for (int i = 0; i < domain_size; ++i) {
    c[i] = a[i][std::popcount(static_cast<unsigned int>(i))];
  }
  return c;
}

template <int MaxN, typename T>
std::vector<T> exp_of_set_power_series(const std::vector<T>& f) {
  assert(std::has_single_bit(f.size()) && f[0] == 0);
  const int n = std::countr_zero(f.size());
  assert(n <= MaxN);
  std::vector<T> exponential{1};
  exponential.reserve(1 << n);
  for (int i = 0; i < n; ++i) {
    std::ranges::copy(subset_convolution<MaxN>(
                          exponential,
                          std::vector(std::next(f.begin(), 1 << i),
                                      std::next(f.begin(), 1 << (i + 1)))),
                      std::back_inserter(exponential));
  }
  return exponential;
}

}  // namespace emthrm

bool KthBit(const std::unsigned_integral auto bit_field, const int k) {
  return std::cmp_equal(bit_field >> k & 1, 1);
}

// <TLE?> #906824 ベース
// O(4^n n^2) 時間
int main() {
  constexpr int kMaxN = 13;

  int n, m;
  std::cin >> n >> m;
  assert(2 <= n && n <= kMaxN && 1 <= m && m <= n * (n - 1) / 2);
  std::vector<std::uint32_t> graph(n);
  while (m--) {
    int u, v;
    std::cin >> u >> v;
    assert(1 <= u && u < v && v <= n);
    --u; --v;
    graph[u] |= UINT32_C(1) << v;
    graph[v] |= UINT32_C(1) << u;
  }

  std::vector num_of_paths(1 << n, std::vector(n, INT64_C(0)));
  for (int start = 0; start < n; ++start) {
    num_of_paths[1 << start][start] = 1;
  }
  for (std::uint32_t bit = 1; bit < (UINT32_C(1) << n); ++bit) {
    const int start = std::countr_zero(bit);
    for (int current_vertex = start; current_vertex < n; ++current_vertex) {
      for (int next_vertex = start + 1; next_vertex < n; ++next_vertex) {
        if (!KthBit(bit, next_vertex) &&
            KthBit(graph[current_vertex], next_vertex)) {
          num_of_paths[bit | (1 << next_vertex)][next_vertex] +=
              num_of_paths[bit][current_vertex];
        }
      }
    }
  }

  std::vector<std::int64_t> num_of_cycles(1 << n, 0);
  for (int vertex = 0; vertex < n; ++vertex) {
    num_of_cycles[1 << vertex] = 1;
  }
  for (std::uint32_t bit = 7; bit < (UINT32_C(1) << n); ++bit) {
    if (std::popcount(bit) < 3) continue;
    const int start = std::countr_zero(bit);
    for (int last = start + 1; last < n; ++last) {
      if (KthBit(bit, last) && KthBit(graph[last], start)) {
        num_of_cycles[bit] += num_of_paths[bit][last];
      }
    }
    num_of_cycles[bit] /= 2;
  }

  std::vector<std::uint64_t> dp(1 << n, 0);
  dp[1] = 1;
  for (int vertex = 1; vertex < n; ++vertex) {
    // O(4^k k^2) 時間
    for (std::uint32_t cycle = UINT32_C(1) << vertex;
         cycle < (UINT32_C(1) << (vertex + 1)); ++cycle) {
      if (num_of_cycles[cycle] == 0) continue;
      std::vector<int> on_cycle;
      on_cycle.reserve(std::popcount(cycle));
      for (int i = 0; i <= vertex; ++i) {
        if (KthBit(cycle, i)) on_cycle.emplace_back(i);
      }
      std::vector<std::uint64_t> tmp(
          dp.begin(), std::next(dp.begin(), 1 << vertex));
      for (std::uint32_t i = 1; i < (UINT32_C(1) << vertex); ++i) {
        if ((cycle & i) == UINT32_C(0)) {
          int degree = 0;
          for (const int v : on_cycle) degree += std::popcount(i & graph[v]);
          tmp[i] *= degree;
        }
      }
      tmp = emthrm::exp_of_set_power_series<kMaxN>(tmp);
      for (std::uint32_t i = 0; i < (UINT32_C(1) << vertex); ++i) {
        if ((cycle & i) == UINT32_C(0)) {
          dp[cycle | i] += tmp[i] * num_of_cycles[cycle];
        }
      }
    }
  }

  std::cout << emthrm::exp_of_set_power_series<kMaxN>(dp)[(1 << n) - 1] << '\n';
  return 0;
}
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