結果

問題 No.2507 Yet Another Subgraph Counting
ユーザー rniyarniya
提出日時 2023-10-09 21:22:49
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 286 ms / 2,000 ms
コード長 7,493 bytes
コンパイル時間 2,536 ms
コンパイル使用メモリ 210,204 KB
最終ジャッジ日時 2025-02-17 06:30:39
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 * 52
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ソースコード

diff #
プレゼンテーションモードにする

#include <bits/stdc++.h>
#ifdef LOCAL
#include <debug.hpp>
#else
#define debug(...) void(0)
#endif
namespace internal {
template <typename T, int LIM> std::vector<std::array<T, LIM + 1>> ranked_zeta(const std::vector<T>& a) {
int n = a.size(), len = __builtin_ctz(n);
assert((n & (n - 1)) == 0);
std::vector<std::array<T, LIM + 1>> res(n);
for (int i = 0; i < n; i++) res[i][__builtin_popcount(i)] = a[i];
for (int step = 1; step < n; step <<= 1) {
for (int start = 0; start < n; start += 2 * step) {
for (int i = start; i < start + step; i++) {
for (int j = 0; j <= len; j++) {
res[i | step][j] += res[i][j];
}
}
}
}
return res;
}
template <typename T, int LIM> std::vector<T> ranked_mobius(std::vector<std::array<T, LIM + 1>>& ranked) {
int n = ranked.size(), len = __builtin_ctz(n);
assert((n & (n - 1)) == 0);
for (int step = 1; step < n; step <<= 1) {
for (int start = 0; start < n; start += 2 * step) {
for (int i = start; i < start + step; i++) {
for (int j = 0; j <= len; j++) {
ranked[i | step][j] -= ranked[i][j];
}
}
}
}
std::vector<T> res(n);
for (int i = 0; i < n; i++) res[i] = ranked[i][__builtin_popcount(i)];
return res;
}
} // namespace internal
template <typename T, int LIM = 20>
std::vector<T> subset_convolution(const std::vector<T>& a, const std::vector<T>& b) {
auto ra = internal::ranked_zeta<T, LIM>(a);
auto rb = internal::ranked_zeta<T, LIM>(b);
int n = ra.size(), len = __builtin_ctz(n);
for (int i = 0; i < n; i++) {
auto &f = ra[i], &g = rb[i];
for (int j = len; j >= 0; j--) {
T sum = 0;
for (int k = 0; k <= j; k++) sum += f[k] * g[j - k];
f[j] = sum;
}
}
return internal::ranked_mobius<T, LIM>(ra);
}
template <typename T, int LIM = 20> std::vector<T> exp_of_set_power_series(std::vector<T>& a) {
int n = __builtin_ctz(a.size());
assert(int(a.size()) == 1 << n and a[0] == T(0));
std::vector<T> res(1 << n);
res[0] = T(1);
for (int i = 0; i < n; i++) {
std::vector<T> f(begin(a) + (1 << i), begin(a) + (2 << i));
std::vector<T> g(begin(res), begin(res) + (1 << i));
auto h = subset_convolution<T, LIM>(f, g);
std::copy(begin(h), end(h), begin(res) + (1 << i));
}
return res;
}
using namespace std;
typedef long long ll;
#define all(x) begin(x), end(x)
constexpr int INF = (1 << 30) - 1;
constexpr long long IINF = (1LL << 60) - 1;
constexpr int dx[4] = {1, 0, -1, 0}, dy[4] = {0, 1, 0, -1};
template <class T> istream& operator>>(istream& is, vector<T>& v) {
for (auto& x : v) is >> x;
return is;
}
template <class T> ostream& operator<<(ostream& os, const vector<T>& v) {
auto sep = "";
for (const auto& x : v) os << exchange(sep, " ") << x;
return os;
}
template <class T, class U = T> bool chmin(T& x, U&& y) { return y < x and (x = forward<U>(y), true); }
template <class T, class U = T> bool chmax(T& x, U&& y) { return x < y and (x = forward<U>(y), true); }
template <class T> void mkuni(vector<T>& v) {
sort(begin(v), end(v));
v.erase(unique(begin(v), end(v)), end(v));
}
template <class T> int lwb(const vector<T>& v, const T& x) { return lower_bound(begin(v), end(v), x) - begin(v); }
int topbit(signed t) { return t == 0 ? -1 : 31 - __builtin_clz(t); }
int topbit(long long t) { return t == 0 ? -1 : 63 - __builtin_clzll(t); }
int botbit(signed a) { return a == 0 ? 32 : __builtin_ctz(a); }
int botbit(long long a) { return a == 0 ? 64 : __builtin_ctzll(a); }
int popcount(signed t) { return __builtin_popcount(t); }
int popcount(long long t) { return __builtin_popcountll(t); }
bool ispow2(int i) { return i && (i & -i) == i; }
long long MSK(int n) { return (1LL << n) - 1; }
/*
f(S) = S S
exp f (V)
f(S)
1
2
c(S) = S
bit dp
*/
int main() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
int n, m;
cin >> n >> m;
vector<int> G(n, 0);
for (; m--;) {
int u, v;
cin >> u >> v;
u--, v--;
G[u] |= 1 << v;
G[v] |= 1 << u;
}
vector<ll> c(1 << n, 0); // S S
{
vector dp(1 << n, vector(n, vector<ll>(n, 0)));
for (int i = 0; i < n; i++) {
dp[1 << i][i][i] = 1;
c[1 << i] += 1;
}
for (int mask = 0; mask < 1 << n; mask++) {
for (int start = 0; start < n; start++) {
for (int cur = 0; cur < n; cur++) {
ll& val = dp[mask][start][cur];
if (val == 0) continue;
for (int nxt = 0; nxt < n; nxt++) {
if (mask >> nxt & 1) continue;
if (~G[cur] >> nxt & 1) continue;
dp[mask | 1 << nxt][start][nxt] += val;
}
if (__builtin_popcount(mask) > 2 and (G[cur] >> start & 1)) c[mask] += val;
}
}
}
for (int mask = 0; mask < 1 << n; mask++) {
if (popcount(mask) == 1) continue;
ll& val = c[mask];
if (val == 0) continue;
val /= popcount(mask) * 2;
}
}
vector<ll> f(1 << n); // S S
f[0] = 0;
for (int C = 1; C < 1 << n; C++) {
/*
p C
{p } \ C T_1, ... , T_k
C T_i subset convolution
sum_C (p - (|C| - 1))^2 2^{p - (|C| - 1)}
<= n^2 sum_{p = 0}^{n - 1} sum_{i = 0}^p binom(p, i) 2^{p - i + 1}
= n^2 sum_{p = 0}^{n - 1} 2 * 3^p
O(n^2 3^n)
*/
int p = topbit(C);
vector<int> rest;
for (int i = 0; i < p; i++) {
if (~C >> i & 1) {
rest.emplace_back(i);
}
}
auto convert = [&](int mask) {
int res = 0;
for (int i = 0; i < int(rest.size()); i++) {
if (mask >> i & 1) {
res |= 1 << rest[i];
}
}
return res;
};
int len = rest.size();
vector<ll> g(1 << len);
for (int T = 0; T < 1 << len; T++) {
int U = convert(T), es = 0;
for (int i = 0; i < p; i++) {
if (U >> i & 1) {
es += popcount(G[i] & C);
}
}
g[T] = f[U] * es;
}
g = exp_of_set_power_series(g);
for (int T = 0; T < 1 << len; T++) f[convert(T) | C] += g[T] * c[C];
}
f = exp_of_set_power_series(f);
ll ans = f.back();
cout << ans << '\n';
return 0;
}
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