結果
| 問題 |
No.2507 Yet Another Subgraph Counting
|
| ユーザー |
 suisen
|
| 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 | 234 ms / 2,000 ms |
| コード長 | 8,738 bytes |
| コンパイル時間 | 6,490 ms |
| コンパイル使用メモリ | 221,568 KB |
| 最終ジャッジ日時 | 2025-02-16 12:18:54 |
|
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 |
|---|---|
| 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=4939
template <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 list
std::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 editorial
std::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 cases
for (vertex v = 0; v < n; ++v) {
dp[1u << v][v] = 1;
}
for (vertex_set S = 1; S < 1u << n; ++S) {
// min S
const 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 editorial
const set_power_series c = count_cycles(n, m, edges);
// "f" mentioned in the editorial
set_power_series f(1u << n);
for (vertex_set C = 1; C < 1u << n; ++C) {
// max C
const vertex t = library::bits::bit_length(C) - 1;
// {0, ..., t} - C
const vertex_set S = ((1u << (t + 1)) - 1) ^ C;
const size_t k = library::bits::popcount(S);
// "g_C" mentioned in the editorial
set_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 editorial
const 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';
}