結果

問題 No.2507 Yet Another Subgraph Counting
ユーザー suisensuisen
提出日時 2023-08-21 23:21:31
言語 C++17(gcc12)
(gcc 12.3.0 + boost 1.87.0)
結果
AC  
実行時間 270 ms / 2,000 ms
コード長 8,768 bytes
コンパイル時間 1,475 ms
コンパイル使用メモリ 90,296 KB
実行使用メモリ 5,376 KB
最終ジャッジ日時 2024-09-15 14:15:39
合計ジャッジ時間 6,296 ms
ジャッジサーバーID
(参考情報)
judge5 / judge2
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
other AC * 52
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 #
プレゼンテーションモードにする

#include <cassert>
#include <iostream>
#include <limits>
#include <utility>
#include <vector>
namespace library {
namespace bits {
template <typename T, std::enable_if_t<std::is_integral_v<T>, std::nullptr_t> = nullptr>
size_t bit_width(const T v) {
size_t res = 0;
while (T{1} << res <= v) ++res;
return res;
}
template <typename T, std::enable_if_t<std::is_integral_v<T>, std::nullptr_t> = nullptr>
T bit_deposite(const T src, const T mask, const size_t bitwidth) {
T dst = 0;
size_t j = 0;
for (size_t i = 0; i < bitwidth; ++i) {
if ((mask >> i) & 1) dst |= ((src >> j) & 1) << i, ++j;
}
return dst;
}
template <typename T, std::enable_if_t<std::is_integral_v<T>, std::nullptr_t> = nullptr>
size_t popcount(const T v) {
if constexpr (std::numeric_limits<std::make_unsigned_t<T>>::digits <= 32) {
return __builtin_popcount(v);
} else {
return __builtin_popcountll(v);
}
}
template <typename T, std::enable_if_t<std::is_integral_v<T>, std::nullptr_t> = nullptr>
size_t count_tz(const T v) {
if constexpr (std::numeric_limits<std::make_unsigned_t<T>>::digits <= 32) {
return __builtin_ctz(v);
} else {
return __builtin_ctzll(v);
}
}
}
namespace kronecker_power_transform {
namespace details {
template <auto transform, typename RefGettter, size_t... I>
void unit_transform(RefGettter ref, std::index_sequence<I...>) {
transform(ref(I)...);
}
}
template <typename T, size_t D, auto unit_transform>
void kronecker_power_transform(std::vector<T> &x) {
const size_t n = x.size();
for (size_t block = 1; block < n; block *= D) {
for (size_t l = 0; l < n; l += D * block) {
for (size_t offset = l; offset < l + block; ++offset) {
const auto ref = [&](size_t i) -> T& { return x[offset + i * block]; };
details::unit_transform<unit_transform>(ref, std::make_index_sequence<D>{});
}
}
}
}
}
namespace subset_transform {
namespace details {
template <typename T> void zeta_unit(T &x0, T &x1) { x1 += x0; }
template <typename T> void mobius_unit(T &x0, T &x1) { x1 -= x0; }
}
template <typename T>
void zeta(std::vector<T> &a) {
kronecker_power_transform::kronecker_power_transform<T, 2, details::zeta_unit<T>>(a);
}
template <typename T>
void mobius(std::vector<T> &a) {
kronecker_power_transform::kronecker_power_transform<T, 2, details::mobius_unit<T>>(a);
}
}
namespace set_power_series {
namespace details {
template <typename T>
struct polynomial : std::vector<T> {
using std::vector<T>::vector;
polynomial& operator+=(const polynomial &q) {
assert(this->size() == q.size());
for (size_t i = 0; i < q.size(); ++i) (*this)[i] += q[i];
return *this;
}
polynomial& operator-=(const polynomial &q) {
assert(this->size() == q.size());
for (size_t i = 0; i < q.size(); ++i) (*this)[i] -= q[i];
return *this;
}
polynomial& operator*=(const polynomial &q) {
const size_t n = this->size();
assert(n == q.size());
polynomial r(n);
for (size_t i = 0; i < n; ++i) for (size_t j = 0; i + j < n; ++j) r[i + j] += (*this)[i] * q[j];
return *this = std::move(r);
}
polynomial operator+(const polynomial &q) { polynomial p = *this; p += q; return p; }
polynomial operator-(const polynomial &q) { polynomial p = *this; p -= q; return p; }
polynomial operator*(const polynomial &q) { polynomial p = *this; p *= q; return p; }
};
template <typename T>
std::vector<polynomial<T>> add_rank(const std::vector<T>& a) {
const size_t n = a.size();
std::vector fs(n, polynomial<T>(bits::count_tz(n) + 1, T{0}));
for (size_t i = 0; i < n; ++i) fs[i][bits::popcount(i)] = a[i];
return fs;
}
template <typename T>
std::vector<T> remove_rank(const std::vector<polynomial<T>>& polys) {
const size_t n = polys.size();
std::vector<T> a(n);
for (size_t i = 0; i < n; ++i) a[i] = polys[i][bits::popcount(i)];
return a;
}
}
template <typename T>
std::vector<T> subset_convolution(const std::vector<T>& a, const std::vector<T>& b) {
const size_t n = a.size();
auto ra = details::add_rank(a);
auto rb = details::add_rank(b);
subset_transform::zeta(ra);
subset_transform::zeta(rb);
for (size_t i = 0; i < n; ++i) ra[i] *= rb[i];
subset_transform::mobius(ra);
return details::remove_rank(ra);
}
template <typename T>
std::vector<T> subset_exp(const std::vector<T>& f) {
assert(f[0] == 0);
const size_t n = bits::bit_width(f.size()) - 1;
std::vector<T> g{1};
for (size_t i = 0; i < n; ++i) {
std::vector<T> p(f.begin() + (1 << i), f.begin() + (1 << (i + 1)));
std::vector<T> h = subset_convolution(std::move(p), g);
std::move(h.begin(), h.end(), std::back_inserter(g));
}
return g;
}
}
}
using vertex = size_t;
using vertex_set = size_t;
using edge = std::pair<vertex, vertex>;
std::vector<uint64_t> count_cycles(const size_t n, const size_t, const std::vector<edge> &edges) {
std::vector adj(n, std::vector<vertex>{});
for (const auto &[u, v] : edges) adj[u].push_back(v), adj[v].push_back(u);
std::vector cycle_dp(1u << n, std::vector<uint64_t>(n));
for (size_t v = 0; v < n; ++v) {
cycle_dp[1u << v][v] = 1;
}
std::vector<uint64_t> cycle(1u << n);
for (vertex_set s = 1; s < 1u << n; ++s) {
const vertex start = library::bits::count_tz(s);
for (vertex cur = 0; cur < n; ++cur) if (cycle_dp[s][cur]) {
for (const vertex nxt : adj[cur]) {
if (start == nxt) {
cycle[s] += cycle_dp[s][cur];
} else if (start < nxt and not ((s >> nxt) & 1)) {
const vertex_set nxt_s = s | (1u << nxt);
cycle_dp[nxt_s][nxt] += cycle_dp[s][cur];
}
}
}
}
for (vertex_set s = 1; s < 1u << n; ++s) {
const size_t popcnt = library::bits::popcount(s);
if (popcnt == 1) cycle[s] = 1;
else if (popcnt == 2) cycle[s] = 0;
else cycle[s] /= 2;
}
return cycle;
}
uint64_t solve(const size_t n, const size_t m, const std::vector<edge> &edges) {
// e[S] := # edges connecting vertices in S.
std::vector<uint64_t> e(1u << n);
for (const auto &[u, v] : edges) {
++e[(1u << u) | (1u << v)];
}
library::subset_transform::zeta(e);
using sps = std::vector<uint64_t>;
const sps cycle = count_cycles(n, m, edges);
sps f(1u << n);
for (vertex_set C = 1; C < 1u << n; ++C) {
// max C
const vertex t = library::bits::bit_width(C) - 1;
// { 0, ..., t } - C
const vertex_set S = ((1u << (t + 1)) - 1) ^ C;
const size_t k = library::bits::popcount(S);
sps g(1u << k);
for (vertex_set A = 0; A < 1u << k; ++A) {
const vertex_set T = library::bits::bit_deposite(A, S, t);
g[A] = f[T] * (e[T | C] - e[T] - e[C]);
}
const sps h = library::set_power_series::subset_exp(g);
for (vertex_set A = 0; A < 1u << k; ++A) {
const vertex_set X = library::bits::bit_deposite(A, S, t) | C;
f[X] += cycle[C] * h[A];
}
}
return library::set_power_series::subset_exp(f).back();
}
int main() {
size_t n, m;
std::cin >> n >> m;
std::vector<edge> edges(m);
for (auto &[u, v] : edges) {
std::cin >> u >> v;
--u, --v;
}
std::cout << solve(n, m, edges) << '\n';
}
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