結果
問題 | No.2062 Sum of Subset mod 999630629 |
ユーザー | torisasami4 |
提出日時 | 2022-08-26 22:50:06 |
言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
結果 |
AC
|
実行時間 | 1,093 ms / 5,000 ms |
コード長 | 21,830 bytes |
コンパイル時間 | 4,138 ms |
コンパイル使用メモリ | 272,672 KB |
実行使用メモリ | 37,968 KB |
最終ジャッジ日時 | 2024-10-14 01:07:07 |
合計ジャッジ時間 | 13,897 ms |
ジャッジサーバーID (参考情報) |
judge3 / judge4 |
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テストケース
テストケース表示入力 | 結果 | 実行時間 実行使用メモリ |
---|---|---|
testcase_00 | AC | 1 ms
5,248 KB |
testcase_01 | AC | 2 ms
5,248 KB |
testcase_02 | AC | 1 ms
5,248 KB |
testcase_03 | AC | 2 ms
5,248 KB |
testcase_04 | AC | 1 ms
5,248 KB |
testcase_05 | AC | 1 ms
5,248 KB |
testcase_06 | AC | 2 ms
5,248 KB |
testcase_07 | AC | 1 ms
5,248 KB |
testcase_08 | AC | 17 ms
5,248 KB |
testcase_09 | AC | 13 ms
5,248 KB |
testcase_10 | AC | 13 ms
5,248 KB |
testcase_11 | AC | 291 ms
24,440 KB |
testcase_12 | AC | 337 ms
24,548 KB |
testcase_13 | AC | 179 ms
22,272 KB |
testcase_14 | AC | 326 ms
24,544 KB |
testcase_15 | AC | 67 ms
20,096 KB |
testcase_16 | AC | 258 ms
24,080 KB |
testcase_17 | AC | 284 ms
24,288 KB |
testcase_18 | AC | 177 ms
22,272 KB |
testcase_19 | AC | 69 ms
20,224 KB |
testcase_20 | AC | 102 ms
21,120 KB |
testcase_21 | AC | 142 ms
22,000 KB |
testcase_22 | AC | 105 ms
20,992 KB |
testcase_23 | AC | 15 ms
5,248 KB |
testcase_24 | AC | 15 ms
5,248 KB |
testcase_25 | AC | 1,084 ms
37,840 KB |
testcase_26 | AC | 1,093 ms
37,844 KB |
testcase_27 | AC | 1,076 ms
37,836 KB |
testcase_28 | AC | 1,093 ms
37,844 KB |
testcase_29 | AC | 1,076 ms
37,968 KB |
testcase_30 | AC | 668 ms
29,352 KB |
testcase_31 | AC | 660 ms
29,208 KB |
ソースコード
#pragma GCC optimize("Ofast,no-stack-protector,unroll-loops,fast-math") #include <bits/stdc++.h> using namespace std; #define rep(i, n) for (int i = 0; i < int(n); i++) #define per(i, n) for (int i = (n)-1; 0 <= i; i--) #define rep2(i, l, r) for (int i = (l); i < int(r); i++) #define per2(i, l, r) for (int i = (r)-1; int(l) <= i; i--) #define MM << " " << #define pb push_back #define eb emplace_back #define all(x) begin(x), end(x) #define rall(x) rbegin(x), rend(x) #define sz(x) (int)x.size() 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'; } using ll = long long; using pii = pair<int, int>; using pll = pair<ll, ll>; template <typename T> bool chmax(T &x, const T &y) { return (x < y) ? (x = y, true) : false; } template <typename T> bool chmin(T &x, const T &y) { return (x > y) ? (x = y, true) : false; } template <class T> using minheap = std::priority_queue<T, std::vector<T>, std::greater<T>>; template <class T> using maxheap = std::priority_queue<T>; template <typename T> int lb(const vector<T> &v, T x) { return lower_bound(begin(v), end(v), x) - begin(v); } template <typename T> int ub(const vector<T> &v, T x) { return upper_bound(begin(v), end(v), x) - begin(v); } template <typename T> void rearrange(vector<T> &v) { sort(begin(v), end(v)); v.erase(unique(begin(v), end(v)), end(v)); } // __int128_t gcd(__int128_t a, __int128_t b) { // if (a == 0) // return b; // if (b == 0) // return a; // __int128_t cnt = a % b; // while (cnt != 0) { // a = b; // b = cnt; // cnt = a % b; // } // return b; // } long long extGCD(long long a, long long b, long long &x, long long &y) { if (b == 0) { x = 1; y = 0; return a; } long long d = extGCD(b, a % b, y, x); y -= a / b * x; return d; } struct UnionFind { vector<int> data; int num; UnionFind(int sz) { data.assign(sz, -1); num = sz; } bool unite(int x, int y) { x = find(x), y = find(y); if (x == y) return (false); if (data[x] > data[y]) swap(x, y); data[x] += data[y]; data[y] = x; num--; return (true); } int find(int k) { if (data[k] < 0) return (k); return (data[k] = find(data[k])); } int size(int k) { return (-data[find(k)]); } bool same(int x, int y) { return find(x) == find(y); } int operator[](int k) { return find(k); } }; template <int mod> struct Mod_Int { int x; Mod_Int() : x(0) { } Mod_Int(long long y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) { } static int get_mod() { return mod; } Mod_Int &operator+=(const Mod_Int &p) { if ((x += p.x) >= mod) x -= mod; return *this; } Mod_Int &operator-=(const Mod_Int &p) { if ((x += mod - p.x) >= mod) x -= mod; return *this; } Mod_Int &operator*=(const Mod_Int &p) { x = (int)(1LL * x * p.x % mod); return *this; } Mod_Int &operator/=(const Mod_Int &p) { *this *= p.inverse(); return *this; } Mod_Int &operator++() { return *this += Mod_Int(1); } Mod_Int operator++(int) { Mod_Int tmp = *this; ++*this; return tmp; } Mod_Int &operator--() { return *this -= Mod_Int(1); } Mod_Int operator--(int) { Mod_Int tmp = *this; --*this; return tmp; } Mod_Int operator-() const { return Mod_Int(-x); } Mod_Int operator+(const Mod_Int &p) const { return Mod_Int(*this) += p; } Mod_Int operator-(const Mod_Int &p) const { return Mod_Int(*this) -= p; } Mod_Int operator*(const Mod_Int &p) const { return Mod_Int(*this) *= p; } Mod_Int operator/(const Mod_Int &p) const { return Mod_Int(*this) /= p; } bool operator==(const Mod_Int &p) const { return x == p.x; } bool operator!=(const Mod_Int &p) const { return x != p.x; } Mod_Int inverse() const { assert(*this != Mod_Int(0)); return pow(mod - 2); } Mod_Int pow(long long k) const { Mod_Int now = *this, ret = 1; for (; k > 0; k >>= 1, now *= now) { if (k & 1) ret *= now; } return ret; } friend ostream &operator<<(ostream &os, const Mod_Int &p) { return os << p.x; } friend istream &operator>>(istream &is, Mod_Int &p) { long long a; is >> a; p = Mod_Int<mod>(a); return is; } }; ll mpow2(ll x, ll n, ll mod) { ll ans = 1; x %= mod; while (n != 0) { if (n & 1) ans = ans * x % mod; x = x * x % mod; n = n >> 1; } ans %= mod; return ans; } ll modinv2(ll a, ll mod) { ll b = mod, u = 1, v = 0; while (b) { ll t = a / b; a -= t * b; swap(a, b); u -= t * v; swap(u, v); } u %= mod; if (u < 0) u += mod; return u; } ll divide_int(ll a, ll b) { return (a >= 0 ? a / b : (a - b + 1) / b); } // const int MOD = 1000000007; const int MOD = 998244353; using mint = Mod_Int<MOD>; mint mpow(mint x, ll n) { bool rev = n < 0; n = abs(n); mint ans = 1; while (n != 0) { if (n & 1) ans *= x; x *= x; n = n >> 1; } return (rev ? ans.inverse() : ans); } // ----- library ------- template <typename T> struct Number_Theoretic_Transform { static int max_base; static T root; static vector<T> r, ir; Number_Theoretic_Transform() { } static void init() { if (!r.empty()) return; int mod = T::get_mod(); int tmp = mod - 1; root = 2; while (root.pow(tmp >> 1) == 1) root++; max_base = 0; while (tmp % 2 == 0) tmp >>= 1, max_base++; r.resize(max_base), ir.resize(max_base); for (int i = 0; i < max_base; i++) { r[i] = -root.pow((mod - 1) >> (i + 2)); // r[i] := 1 の 2^(i+2) 乗根 ir[i] = r[i].inverse(); // ir[i] := 1/r[i] } } static void ntt(vector<T> &a) { init(); int n = a.size(); assert((n & (n - 1)) == 0); assert(n <= (1 << max_base)); for (int k = n; k >>= 1;) { T w = 1; for (int s = 0, t = 0; s < n; s += 2 * k) { for (int i = s, j = s + k; i < s + k; i++, j++) { T x = a[i], y = w * a[j]; a[i] = x + y, a[j] = x - y; } w *= r[__builtin_ctz(++t)]; } } } static void intt(vector<T> &a) { init(); int n = a.size(); assert((n & (n - 1)) == 0); assert(n <= (1 << max_base)); for (int k = 1; k < n; k <<= 1) { T w = 1; for (int s = 0, t = 0; s < n; s += 2 * k) { for (int i = s, j = s + k; i < s + k; i++, j++) { T x = a[i], y = a[j]; a[i] = x + y, a[j] = w * (x - y); } w *= ir[__builtin_ctz(++t)]; } } T inv = T(n).inverse(); for (auto &e : a) e *= inv; } static vector<T> convolve(vector<T> a, vector<T> b) { if (a.empty() || b.empty()) return {}; int k = (int)a.size() + (int)b.size() - 1, n = 1; while (n < k) n <<= 1; a.resize(n), b.resize(n); ntt(a), ntt(b); for (int i = 0; i < n; i++) a[i] *= b[i]; intt(a), a.resize(k); return a; } }; template <typename T> int Number_Theoretic_Transform<T>::max_base = 0; template <typename T> T Number_Theoretic_Transform<T>::root = T(); template <typename T> vector<T> Number_Theoretic_Transform<T>::r = vector<T>(); template <typename T> vector<T> Number_Theoretic_Transform<T>::ir = vector<T>(); template <typename T> struct Formal_Power_Series : vector<T> { using NTT_ = Number_Theoretic_Transform<T>; using vector<T>::vector; Formal_Power_Series(const vector<T> &v) : vector<T>(v) { } Formal_Power_Series pre(int n) const { return Formal_Power_Series(begin(*this), begin(*this) + min((int)this->size(), n)); } Formal_Power_Series rev(int deg = -1) const { Formal_Power_Series ret = *this; if (deg != -1) ret.resize(deg, T(0)); reverse(begin(ret), end(ret)); return ret; } void normalize() { while (!this->empty() && this->back() == 0) this->pop_back(); } Formal_Power_Series operator-() const { Formal_Power_Series ret = *this; for (int i = 0; i < (int)ret.size(); i++) ret[i] = -ret[i]; return ret; } Formal_Power_Series &operator+=(const T &x) { if (this->empty()) this->resize(1); (*this)[0] += x; return *this; } Formal_Power_Series &operator+=(const Formal_Power_Series &v) { if (v.size() > this->size()) this->resize(v.size()); for (int i = 0; i < (int)v.size(); i++) (*this)[i] += v[i]; this->normalize(); return *this; } Formal_Power_Series &operator-=(const T &x) { if (this->empty()) this->resize(1); *this[0] -= x; return *this; } Formal_Power_Series &operator-=(const Formal_Power_Series &v) { if (v.size() > this->size()) this->resize(v.size()); for (int i = 0; i < (int)v.size(); i++) (*this)[i] -= v[i]; this->normalize(); return *this; } Formal_Power_Series &operator*=(const T &x) { for (int i = 0; i < (int)this->size(); i++) (*this)[i] *= x; return *this; } Formal_Power_Series &operator*=(const Formal_Power_Series &v) { if (this->empty() || empty(v)) { this->clear(); return *this; } return *this = NTT_::convolve(*this, v); } Formal_Power_Series &operator/=(const T &x) { assert(x != 0); T inv = x.inverse(); for (int i = 0; i < (int)this->size(); i++) (*this)[i] *= inv; return *this; } Formal_Power_Series &operator/=(const Formal_Power_Series &v) { if (v.size() > this->size()) { this->clear(); return *this; } int n = this->size() - (int)v.size() + 1; return *this = (rev().pre(n) * v.rev().inv(n)).pre(n).rev(n); } Formal_Power_Series &operator%=(const Formal_Power_Series &v) { return *this -= (*this / v) * v; } Formal_Power_Series &operator<<=(int x) { Formal_Power_Series ret(x, 0); ret.insert(end(ret), begin(*this), end(*this)); return *this = ret; } Formal_Power_Series &operator>>=(int x) { Formal_Power_Series ret; ret.insert(end(ret), begin(*this) + x, end(*this)); return *this = ret; } Formal_Power_Series operator+(const T &x) const { return Formal_Power_Series(*this) += x; } Formal_Power_Series operator+(const Formal_Power_Series &v) const { return Formal_Power_Series(*this) += v; } Formal_Power_Series operator-(const T &x) const { return Formal_Power_Series(*this) -= x; } Formal_Power_Series operator-(const Formal_Power_Series &v) const { return Formal_Power_Series(*this) -= v; } Formal_Power_Series operator*(const T &x) const { return Formal_Power_Series(*this) *= x; } Formal_Power_Series operator*(const Formal_Power_Series &v) const { return Formal_Power_Series(*this) *= v; } Formal_Power_Series operator/(const T &x) const { return Formal_Power_Series(*this) /= x; } Formal_Power_Series operator/(const Formal_Power_Series &v) const { return Formal_Power_Series(*this) /= v; } Formal_Power_Series operator%(const Formal_Power_Series &v) const { return Formal_Power_Series(*this) %= v; } Formal_Power_Series operator<<(int x) const { return Formal_Power_Series(*this) <<= x; } Formal_Power_Series operator>>(int x) const { return Formal_Power_Series(*this) >>= x; } T val(const T &x) const { T ret = 0; for (int i = (int)this->size() - 1; i >= 0; i--) ret *= x, ret += (*this)[i]; return ret; } Formal_Power_Series diff() const { // df/dx int n = this->size(); Formal_Power_Series ret(n - 1); for (int i = 1; i < n; i++) ret[i - 1] = (*this)[i] * i; return ret; } Formal_Power_Series integral() const { // ∫f(x)dx int n = this->size(); Formal_Power_Series ret(n + 1); for (int i = 0; i < n; i++) ret[i + 1] = (*this)[i] / (i + 1); return ret; } Formal_Power_Series inv(int deg) const { // 1/f(x) (f[0] != 0) assert((*this)[0] != T(0)); Formal_Power_Series ret(1, (*this)[0].inverse()); for (int i = 1; i < deg; i <<= 1) { Formal_Power_Series f = pre(2 * i), g = ret; f.resize(2 * i), g.resize(2 * i); NTT_::ntt(f), NTT_::ntt(g); Formal_Power_Series h(2 * i); for (int j = 0; j < 2 * i; j++) h[j] = f[j] * g[j]; NTT_::intt(h); for (int j = 0; j < i; j++) h[j] = 0; NTT_::ntt(h); for (int j = 0; j < 2 * i; j++) h[j] *= g[j]; NTT_::intt(h); for (int j = 0; j < i; j++) h[j] = 0; ret -= h; } ret.resize(deg); return ret; } Formal_Power_Series inv() const { return inv(this->size()); } Formal_Power_Series log(int deg) const { // log(f(x)) (f[0] = 1) assert((*this)[0] == 1); Formal_Power_Series ret = (diff() * inv(deg)).pre(deg - 1).integral(); ret.resize(deg); return ret; } Formal_Power_Series log() const { return log(this->size()); } Formal_Power_Series exp(int deg) const { // exp(f(x)) (f[0] = 0) assert((*this)[0] == 0); Formal_Power_Series inv; inv.reserve(deg + 1); inv.push_back(0), inv.push_back(1); auto inplace_integral = [&](Formal_Power_Series &F) -> void { int n = F.size(); int mod = T::get_mod(); while ((int)inv.size() <= n) { int i = inv.size(); inv.push_back((-inv[mod % i]) * (mod / i)); } F.insert(begin(F), 0); for (int i = 1; i <= n; i++) F[i] *= inv[i]; }; auto inplace_diff = [](Formal_Power_Series &F) -> void { if (F.empty()) return; F.erase(begin(F)); T coeff = 1, one = 1; for (int i = 0; i < (int)F.size(); i++) { F[i] *= coeff; coeff += one; } }; Formal_Power_Series ret{1, this->size() > 1 ? (*this)[1] : 0}, c{1}, z1, z2{1, 1}; for (int m = 2; m < deg; m *= 2) { auto y = ret; y.resize(2 * m); NTT_::ntt(y); z1 = z2; Formal_Power_Series z(m); for (int i = 0; i < m; i++) z[i] = y[i] * z1[i]; NTT_::intt(z); fill(begin(z), begin(z) + m / 2, 0); NTT_::ntt(z); for (int i = 0; i < m; i++) z[i] *= -z1[i]; NTT_::intt(z); c.insert(end(c), begin(z) + m / 2, end(z)); z2 = c, z2.resize(2 * m); NTT_::ntt(z2); Formal_Power_Series x(begin(*this), begin(*this) + min((int)this->size(), m)); inplace_diff(x); x.push_back(0); NTT_::ntt(x); for (int i = 0; i < m; i++) x[i] *= y[i]; NTT_::intt(x); x -= ret.diff(), x.resize(2 * m); for (int i = 0; i < m - 1; i++) x[m + i] = x[i], x[i] = 0; NTT_::ntt(x); for (int i = 0; i < 2 * m; i++) x[i] *= z2[i]; NTT_::intt(x); x.pop_back(); inplace_integral(x); for (int i = m; i < min((int)this->size(), 2 * m); i++) x[i] += (*this)[i]; fill(begin(x), begin(x) + m, 0); NTT_::ntt(x); for (int i = 0; i < 2 * m; i++) x[i] *= y[i]; NTT_::intt(x); ret.insert(end(ret), begin(x) + m, end(x)); } ret.resize(deg); return ret; } Formal_Power_Series exp() const { return exp(this->size()); } Formal_Power_Series pow(long long k, int deg) const { // f(x)^k int n = this->size(); for (int i = 0; i < n; i++) { if ((*this)[i] == 0) continue; T rev = (*this)[i].inverse(); Formal_Power_Series C(*this * rev), D(n - i, 0); for (int j = i; j < n; j++) D[j - i] = C[j]; D = (D.log() * k).exp() * ((*this)[i].pow(k)); Formal_Power_Series E(deg, 0); if (i > 0 && k > deg / i) return E; long long S = i * k; for (int j = 0; j + S < deg && j < D.size(); j++) E[j + S] = D[j]; E.resize(deg); return E; } return Formal_Power_Series(deg, 0); } Formal_Power_Series pow(long long k) const { return pow(k, this->size()); } Formal_Power_Series Taylor_shift(T c) const { // f(x+c) int n = this->size(); vector<T> ifac(n, 1); Formal_Power_Series f(n), g(n); for (int i = 0; i < n; i++) { f[n - 1 - i] = (*this)[i] * ifac[n - 1]; if (i < n - 1) ifac[n - 1] *= i + 1; } ifac[n - 1] = ifac[n - 1].inverse(); for (int i = n - 1; i > 0; i--) ifac[i - 1] = ifac[i] * i; T pw = 1; for (int i = 0; i < n; i++) { g[i] = pw * ifac[i]; pw *= c; } f *= g; Formal_Power_Series b(n); for (int i = 0; i < n; i++) b[i] = f[n - 1 - i] * ifac[i]; return b; } }; using FPS = Formal_Power_Series<mint>; template <typename T> struct Combination { vector<T> _fac, _ifac; Combination() { init(); } Combination(int n) { init(n); } void init(int n = 2000010) { _fac.resize(n + 1), _ifac.resize(n + 1); _fac[0] = 1; for (int i = 1; i <= n; i++) _fac[i] = _fac[i - 1] * i; _ifac[n] = _fac[n].inverse(); for (int i = n; i >= 1; i--) _ifac[i - 1] = _ifac[i] * i; } T fac(int k) { return _fac[k]; } T ifac(int k) { return _ifac[k]; } T inv(int k) { return fac(k - 1) * ifac(k); } T P(int n, int k) { if (k < 0 || n < k) return 0; return fac(n) * ifac(n - k); } T C(int n, int k) { if (k < 0 || n < k) return 0; return fac(n) * ifac(n - k) * ifac(k); } T H(int n, int k) { // k個の区別できない玉をn個の区別できる箱に入れる場合の数 if (n < 0 || k < 0) return 0; return k == 0 ? 1 : C(n + k - 1, k); } T second_stirling_number(int n, int k) { // n個の区別できる玉を、k個の区別しない箱に、各箱に1個以上玉が入るように入れる場合の数 T ret = 0; for (int i = 0; i <= k; i++) { T tmp = C(k, i) * T(i).pow(n); ret += ((k - i) & 1) ? -tmp : tmp; } return ret * ifac(k); } T bell_number(int n, int k) { // n個の区別できる玉を、k個の区別しない箱に入れる場合の数 if (n == 0) return 1; k = min(k, n); vector<T> pref(k + 1); pref[0] = 1; for (int i = 1; i <= k; i++) { if (i & 1) pref[i] = pref[i - 1] - ifac(i); else pref[i] = pref[i - 1] + ifac(i); } T ret = 0; for (int i = 1; i <= k; i++) ret += T(i).pow(n) * ifac(i) * pref[k - i]; return ret; } }; using comb = Combination<mint>; vector<mint> Subset_Sum(vector<int> a, int M) { vector<int> c(M + 1, 0); for (int i = 0; i < a.size(); i++) { if (a[i] <= M) c[a[i]]++; } comb comb; FPS f(M + 1, 0); for (int i = 1; i <= M; i++) { for (int j = 1; j * i <= M; j++) { mint tmp = mint(j).inverse() * c[i]; f[j * i] += (j & 1 ? tmp : -tmp); } } return f.exp(); } // ----- library ------- int main() { ios::sync_with_stdio(false); std::cin.tie(nullptr); cout << fixed << setprecision(15); int n; cin >> n; vector<int> a(n); rep(i, n) cin >> a[i]; mint ans = 0; rep(i, n) ans += mpow(2, n - 1) * a[i]; int sum = accumulate(all(a), 0) - 999630629; if (sum >= 0) { auto f = Subset_Sum(a, sum); rep(i, sum + 1) ans -= f[i] * 999630629; } cout << ans << endl; }