結果
問題 | No.2507 Yet Another Subgraph Counting |
ユーザー |
|
提出日時 | 2023-08-22 16:27:55 |
言語 | C++17(gcc12) (gcc 12.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 238 ms / 2,000 ms |
コード長 | 8,738 bytes |
コンパイル時間 | 1,868 ms |
コンパイル使用メモリ | 188,920 KB |
実行使用メモリ | 5,376 KB |
最終ジャッジ日時 | 2024-09-15 14:16:17 |
合計ジャッジ時間 | 6,118 ms |
ジャッジサーバーID (参考情報) |
judge1 / judge4 |
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ファイルパターン | 結果 |
---|---|
other | AC * 52 |
ソースコード
#include <cassert>#include <iostream>#include <limits>#include <utility>#include <vector>#include <immintrin.h>namespace library {namespace bits {template <typename T, std::enable_if_t<std::is_integral_v<T>, std::nullptr_t> = nullptr>T kth_bit(T v, size_t k) { return (v >> k) & 1; }template <typename T, std::enable_if_t<std::is_integral_v<T>, std::nullptr_t> = nullptr>size_t bit_length(const T v) {if constexpr (std::numeric_limits<std::make_unsigned_t<T>>::digits <= 32) {return 32 - __builtin_clz(v);} else {return 64 - __builtin_clzll(v);}}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);}}// See https://www.intel.com/content/www/us/en/docs/intrinsics-guide/index.html#text=_pdep&ig_expand=4939template <typename T, std::enable_if_t<std::is_integral_v<T>, std::nullptr_t> = nullptr>__attribute__((target("bmi2"))) T pdep(const T src, const T mask) {/*T dst = 0;for (size_t i = 0, j = 0; i < BIT_NUM; ++i) {if (kth_bit(mask, i)) dst |= kth_bit(src, j) << i, ++j;}return dst;*/if constexpr (std::numeric_limits<std::make_unsigned_t<T>>::digits <= 32) {return _pdep_u32(src, mask);} else {return _pdep_u64(src, mask);}}}namespace subset_transform {template <typename T> void zeta(std::vector<T>& x) {const size_t n = x.size();for (size_t b = 1; b < n; b *= 2) for (size_t l = 0; l < n; l += 2 * b) for (size_t i = l; i < l + b; ++i) {x[i + 1 * b] += x[i + 0 * b];}}template <typename T> void mobius(std::vector<T>& x) {const size_t n = x.size();for (size_t b = 1; b < n; b *= 2) for (size_t l = 0; l < n; l += 2 * b) for (size_t i = l; i < l + b; ++i) {x[i + 1 * b] -= x[i + 0 * b];}}}namespace set_power_series {namespace details {template <typename T> struct polynomial : std::vector<T> {using std::vector<T>::vector;polynomial& operator+=(const polynomial& q) {for (size_t i = 0; i < q.size(); ++i) (*this)[i] += q[i];return *this;}polynomial& operator-=(const polynomial& q) {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();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_length(f.size()) - 1;std::vector<T> g{ 1 };for (size_t i = 0; i < n; ++i) {std::vector<T> h = subset_convolution(g, std::vector<T>(f.begin() + (1 << i), f.begin() + (1 << (i + 1))));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>;using Int = uint64_t;using set_power_series = std::vector<Int>;std::vector<Int> count_cycles(const size_t n, const size_t, const std::vector<edge>& edges) {// adjacency liststd::vector adj(n, std::vector<vertex>{});for (const auto& [u, v] : edges) adj[u].push_back(v), adj[v].push_back(u);// "c" mentioned in the editorialstd::vector<Int> c(1u << n);// dp[S: vertex set][v: vertex] := # simple paths from min S to v passing vertices in S (but not passing vertices not in S)std::vector dp(1u << n, std::vector<Int>(n));// base casesfor (vertex v = 0; v < n; ++v) {dp[1u << v][v] = 1;}for (vertex_set S = 1; S < 1u << n; ++S) {// min Sconst vertex start = library::bits::count_tz(S);for (vertex cur = 0; cur < n; ++cur) for (const vertex nxt : adj[cur]) {if (start == nxt) {c[S] += dp[S][cur];} else if (start < nxt and not library::bits::kth_bit(S, nxt)) {const vertex_set T = S | (1u << nxt);dp[T][nxt] += dp[S][cur];}}}for (vertex_set S = 1; S < 1u << n; ++S) {const size_t card = library::bits::popcount(S);if (card == 1) c[S] = 1;if (card == 2) c[S] = 0;if (card >= 3) c[S] /= 2;}return c;}Int solve(const size_t n, const size_t m, const std::vector<edge>& edges) {// E[S: vertex set] := # edges connecting vertices in S.std::vector<Int> E(1u << n);for (const auto& [u, v] : edges) ++E[(1u << u) | (1u << v)];library::subset_transform::zeta(E);// "c" mentioned in the editorialconst set_power_series c = count_cycles(n, m, edges);// "f" mentioned in the editorialset_power_series f(1u << n);for (vertex_set C = 1; C < 1u << n; ++C) {// max Cconst vertex t = library::bits::bit_length(C) - 1;// {0, ..., t} - Cconst vertex_set S = ((1u << (t + 1)) - 1) ^ C;const size_t k = library::bits::popcount(S);// "g_C" mentioned in the editorialset_power_series g(1u << k);for (vertex_set A = 0; A < 1u << k; ++A) {// For more information about pdep, see https://www.intel.com/content/www/us/en/docs/intrinsics-guide/index.html#text=_pdep&ig_expand=4939.const vertex_set T = library::bits::pdep(A, S);g[A] = f[T] * (E[T | C] - E[T] - E[C]);}// "h_C" mentioned in the editorialconst set_power_series h = library::set_power_series::subset_exp(g);for (vertex_set A = 0; A < 1u << k; ++A) {const vertex_set X = library::bits::pdep(A, S) | C;f[X] += c[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';}