結果

問題 No.2507 Yet Another Subgraph Counting
ユーザー tokusakuraitokusakurai
提出日時 2023-10-23 12:24:16
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 310 ms / 2,000 ms
コード長 6,069 bytes
コンパイル時間 2,352 ms
コンパイル使用メモリ 208,212 KB
最終ジャッジ日時 2025-02-17 13:17:27
ジャッジサーバーID
(参考情報)
judge1 / judge2
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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>
using namespace std;
struct io_setup {
io_setup() {
ios_base::sync_with_stdio(false);
cin.tie(NULL);
cout << fixed << setprecision(15);
}
} io_setup;
template <typename T>
void print(const vector<T> &v, T x = 0) {
int n = v.size();
for (int i = 0; i < n; i++) cout << v[i] + x << (i == n - 1 ? '\n' : ' ');
if (v.empty()) cout << '\n';
}
constexpr int MOD = 998244353;
template <typename T>
void fast_zeta_transform(vector<T> &a, bool upper) {
int n = a.size();
assert((n & (n - 1)) == 0);
for (int i = 1; i < n; i <<= 1) {
for (int j = 0; j < n; j++) {
if (!(j & i)) {
if (upper) {
a[j] += a[j | i];
} else {
a[j | i] += a[j];
}
}
}
}
}
template <typename T>
void fast_mobius_transform(vector<T> &a, bool upper) {
int n = a.size();
assert((n & (n - 1)) == 0);
for (int i = 1; i < n; i <<= 1) {
for (int j = 0; j < n; j++) {
if (!(j & i)) {
if (upper) {
a[j] -= a[j | i];
} else {
a[j | i] -= a[j];
}
}
}
}
}
template <typename T>
void fast_hadamard_transform(vector<T> &a, bool inverse = false) {
int n = a.size();
assert((n & (n - 1)) == 0);
for (int i = 1; i < n; i <<= 1) {
for (int j = 0; j < n; j++) {
if (!(j & i)) {
T x = a[j], y = a[j | i];
a[j] = x + y, a[j | i] = x - y;
}
}
}
if (inverse) {
T inv = T(1) / T(n);
for (auto &e : a) e *= inv;
}
}
template <typename T>
vector<T> bitwise_and_convolve(vector<T> a, vector<T> b) {
int n = a.size();
assert((int)b.size() == n && (n & (n - 1)) == 0);
fast_zeta_transform(a, true), fast_zeta_transform(b, true);
for (int i = 0; i < n; i++) a[i] *= b[i];
fast_mobius_transform(a, true);
return a;
}
template <typename T>
vector<T> bitwise_or_convolve(vector<T> a, vector<T> b) {
int n = a.size();
assert((int)b.size() == n && (n & (n - 1)) == 0);
fast_zeta_transform(a, false), fast_zeta_transform(b, false);
for (int i = 0; i < n; i++) a[i] *= b[i];
fast_mobius_transform(a, false);
return a;
}
template <typename T>
vector<T> bitwise_xor_convolve(vector<T> a, vector<T> b) {
int n = a.size();
assert((int)b.size() == n && (n & (n - 1)) == 0);
fast_hadamard_transform(a), fast_hadamard_transform(b);
for (int i = 0; i < n; i++) a[i] *= b[i];
fast_hadamard_transform(a, true);
return a;
}
template <typename T>
vector<T> subset_convolve(const vector<T> &a, const vector<T> &b) {
int n = a.size();
assert((int)b.size() == n && (n & (n - 1)) == 0);
int k = __builtin_ctz(n);
vector<vector<T>> A(k + 1, vector<T>(n, 0)), B(k + 1, vector<T>(n, 0)), C(k + 1, vector<T>(n, 0));
for (int i = 0; i < n; i++) {
int t = __builtin_popcount(i);
A[t][i] = a[i], B[t][i] = b[i];
}
for (int i = 0; i <= k; i++) fast_zeta_transform(A[i], false), fast_zeta_transform(B[i], false);
for (int i = 0; i <= k; i++) {
for (int j = 0; j <= k - i; j++) {
for (int l = 0; l < n; l++) C[i + j][l] += A[i][l] * B[j][l];
}
}
for (int i = 0; i <= k; i++) fast_mobius_transform(C[i], false);
vector<T> c(n);
for (int i = 0; i < n; i++) c[i] = C[__builtin_popcount(i)][i];
return c;
}
template <typename T>
vector<T> multiple_subset_convolve(const vector<T> &a) {
int n = a.size();
assert((n & (n - 1)) == 0);
assert(a[0] == T(0));
vector<T> b(1, 1);
for (int k = 1; k < n; k <<= 1) {
vector<T> a_sub(begin(a) + k, begin(a) + k * 2);
vector<T> b_sub = subset_convolve(a_sub, b);
b.insert(end(b), begin(b_sub), end(b_sub));
}
return b;
}
using ll = long long;
int main() {
int N, M;
cin >> N >> M;
vector<int> es(N, 0);
for (int i = 0; i < M; i++) {
int u, v;
cin >> u >> v;
u--, v--;
es[u] |= 1 << v;
es[v] |= 1 << u;
}
auto cut_size = [&](int S, int T) {
int ret = 0;
for (int i = 0; i < N; i++) {
if (!(S >> i & 1)) continue;
ret += __builtin_popcount(es[i] & T);
}
return ret;
};
vector<vector<ll>> dp(N, vector<ll>(1 << N, 0));
for (int s = 0; s < N; s++) {
vector<vector<ll>> dp1(1 << N, vector<ll>(N, 0));
dp1[1 << s][s] = 1;
for (int S = 0; S < (1 << N); S++) {
for (int t = 0; t < N; t++) {
if (__builtin_popcount(S) != 2 && (es[t] >> s) & 1) dp[0][S] += dp1[S][t];
for (int nt = s; nt < N; nt++) {
if ((S >> nt) & 1) continue;
if (!(es[t] >> nt & 1)) continue;
int nS = S | (1 << nt);
dp1[nS][nt] += dp1[S][t];
}
}
}
dp[0][1 << s] += 1;
}
for (int S = 0; S < (1 << N); S++) {
if (__builtin_popcount(S) >= 3) {
assert(dp[0][S] % 2 == 0);
dp[0][S] /= 2;
}
}
for (int S = 1; S < (1 << N); S++) {
for (int X = (S - 1) & S; X > 0; X--, X &= S) {
int Y = S & ~X;
if (X < Y) continue;
int c = cut_size(X, Y);
for (int i = 0; i < N; i++) {
for (int j = 0; j < N; j++) {
if (i + j < N - 1) dp[i + j + 1][S] += dp[i][X] * dp[j][Y] * c;
}
}
}
for (int i = 1; i < N; i++) {
assert(dp[i][S] % i == 0);
dp[i][S] /= i;
}
}
// for (int i = 0; i < N; i++) print(dp[i]);
vector<ll> a(1 << N, 0);
for (int S = 0; S < (1 << N); S++) {
for (int i = 0; i < N; i++) a[S] += dp[i][S];
}
// print(a);
auto b = multiple_subset_convolve(a);
cout << b.back() << '\n';
}
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