結果
問題 | No.2507 Yet Another Subgraph Counting |
ユーザー |
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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 |
ソースコード
#include <bits/stdc++.h>#ifdef LOCAL#include <debug.hpp>#else#define debug(...) void(0)#endifnamespace 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 internaltemplate <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; }/*辺部分集合であって、閉路に含まれる頂点集合が互いに非交差である連結成分ごとf(S) = 頂点集合 S を連結とし、閉路に含まれる頂点が非交差であるような、S 内の辺部分集合の総数exp f (V) が答えf(S) は?閉路を 1 つの連結成分に潰す閉路内ではその外周以外に辺が含まれない(閉路が 2 つ以上できるから)閉路を潰すと木になるc(S) = S を閉路とするような辺部分集合の総数bit dp で計算*/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 を閉路とする S 内の辺部分集合の総数{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 を連結とし、閉路内の頂点が互いに非交差であるような S 内の辺部分集合の総数f[0] = 0;for (int C = 1; C < 1 << n; C++) {/*p を含む閉路 C を固定{p 未満の頂点} \ C の連結成分 T_1, ... , T_kC から T_i への辺の総数を重みづけて subset convolution計算量は?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^pO(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;}