結果

問題 No.2062 Sum of Subset mod 999630629
ユーザー shobonvip
提出日時 2022-08-27 00:05:17
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
WA  
実行時間 -
コード長 11,523 bytes
コンパイル時間 5,618 ms
コンパイル使用メモリ 278,300 KB
最終ジャッジ日時 2025-01-31 06:00:19
ジャッジサーバーID
(参考情報)
judge3 / judge4
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 10 WA * 14 TLE * 5
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ソースコード

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プレゼンテーションモードにする

#include<bits/stdc++.h>
#include<atcoder/all>
using namespace std;
using namespace atcoder;
istream &operator>>(istream &is, modint998244353 &a) { long long v; is >> v; a = v; return is; }
ostream &operator<<(ostream &os, const modint998244353 &a) { return os << a.val(); }
istream &operator>>(istream &is, modint1000000007 &a) { long long v; is >> v; a = v; return is; }
ostream &operator<<(ostream &os, const modint1000000007 &a) { return os << a.val(); }
template<int m> istream &operator>>(istream &is, static_modint<m> &a) { long long v; is >> v; a = v; return is; }
template<int m> istream &operator>>(istream &is, dynamic_modint<m> &a) { long long v; is >> v; a = v; return is; }
template<int m> ostream &operator<<(ostream &os, const static_modint<m> &a) { return os << a.val(); }
template<int m> ostream &operator<<(ostream &os, const dynamic_modint<m> &a) { return os << a.val(); }
#define rep2(i, m, n) for (int i = (m); i < (n); ++i)
#define rep(i, n) rep2(i, 0, n)
#define drep2(i, m, n) for (int i = (m)-1; i >= (n); --i)
#define drep(i, n) drep2(i, n, 0)
using ll = long long;
template<class T> istream &operator>>(istream &is, vector<T> &v) { for (auto &e : v) is >> e; return is; }
template<class T> ostream &operator<<(ostream &os, const vector<T> &v) { for (auto &e : v) os << e << ' '; return os; }
struct fast_ios { fast_ios(){ cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(20); }; } fast_ios_;
// verified by:
// https://judge.yosupo.jp/problem/convolution_mod
// https://judge.yosupo.jp/problem/inv_of_formal_power_series
// https://judge.yosupo.jp/problem/log_of_formal_power_series
// https://judge.yosupo.jp/problem/exp_of_formal_power_series
// https://judge.yosupo.jp/problem/pow_of_formal_power_series
template<class T>
struct FormalPowerSeries : vector<T> {
using vector<T>::vector;
using vector<T>::operator=;
using F = FormalPowerSeries;
F operator-() const {
F res(*this);
for (auto &e : res) e = -e;
return res;
}
F &operator*=(const T &g) {
for (auto &e : *this) e *= g;
return *this;
}
F &operator/=(const T &g) {
assert(g != T(0));
*this *= g.inv();
return *this;
}
F &operator+=(const F &g) {
int n = this->size(), m = g.size();
rep(i, min(n, m)) (*this)[i] += g[i];
return *this;
}
F &operator-=(const F &g) {
int n = this->size(), m = g.size();
rep(i, min(n, m)) (*this)[i] -= g[i];
return *this;
}
F &operator<<=(const int d) {
int n = this->size();
this->insert(this->begin(), d, 0);
this->resize(n);
return *this;
}
F &operator>>=(const int d) {
int n = this->size();
this->erase(this->begin(), this->begin() + min(n, d));
this->resize(n);
return *this;
}
// O(n log n)
F inv(int d = -1) const {
int n = this->size();
assert(n != 0 && (*this)[0] != 0);
if (d == -1) d = n;
assert(d >= 0);
F res{(*this)[0].inv()};
for (int m = 1; m < d; m *= 2) {
F f(this->begin(), this->begin() + min(n, 2*m));
F g(res);
f.resize(2*m), internal::butterfly(f);
g.resize(2*m), internal::butterfly(g);
rep(i, 2*m) f[i] *= g[i];
internal::butterfly_inv(f);
f.erase(f.begin(), f.begin() + m);
f.resize(2*m), internal::butterfly(f);
rep(i, 2*m) f[i] *= g[i];
internal::butterfly_inv(f);
T iz = T(2*m).inv(); iz *= -iz;
rep(i, m) f[i] *= iz;
res.insert(res.end(), f.begin(), f.begin() + m);
}
res.resize(d);
return res;
}
// fast: FMT-friendly modulus only
// O(n log n)
F &multiply_inplace(const F &g, int d = -1) {
int n = this->size();
if (d == -1) d = n;
assert(d >= 0);
*this = convolution(move(*this), g);
this->resize(d);
return *this;
}
F multiply(const F &g, const int d = -1) const { return F(*this).multiply_inplace(g, d); }
// O(n log n)
F &divide_inplace(const F &g, int d = -1) {
int n = this->size();
if (d == -1) d = n;
assert(d >= 0);
*this = convolution(move(*this), g.inv(d));
this->resize(d);
return *this;
}
F divide(const F &g, const int d = -1) const { return F(*this).divide_inplace(g, d); }
// // naive
// // O(n^2)
// F &multiply_inplace(const F &g) {
// int n = this->size(), m = g.size();
// drep(i, n) {
// (*this)[i] *= g[0];
// rep2(j, 1, min(i+1, m)) (*this)[i] += (*this)[i-j] * g[j];
// }
// return *this;
// }
// F multiply(const F &g) const { return F(*this).multiply_inplace(g); }
// // O(n^2)
// F &divide_inplace(const F &g) {
// assert(g[0] != T(0));
// T ig0 = g[0].inv();
// int n = this->size(), m = g.size();
// rep(i, n) {
// rep2(j, 1, min(i+1, m)) (*this)[i] -= (*this)[i-j] * g[j];
// (*this)[i] *= ig0;
// }
// return *this;
// }
// F divide(const F &g) const { return F(*this).divide_inplace(g); }
// sparse
// O(nk)
F &multiply_inplace(vector<pair<int, T>> g) {
int n = this->size();
auto [d, c] = g.front();
if (d == 0) g.erase(g.begin());
else c = 0;
drep(i, n) {
(*this)[i] *= c;
for (auto &[j, b] : g) {
if (j > i) break;
(*this)[i] += (*this)[i-j] * b;
}
}
return *this;
}
F multiply(const vector<pair<int, T>> &g) const { return F(*this).multiply_inplace(g); }
// O(nk)
F &divide_inplace(vector<pair<int, T>> g) {
int n = this->size();
auto [d, c] = g.front();
assert(d == 0 && c != T(0));
T ic = c.inv();
g.erase(g.begin());
rep(i, n) {
for (auto &[j, b] : g) {
if (j > i) break;
(*this)[i] -= (*this)[i-j] * b;
}
(*this)[i] *= ic;
}
return *this;
}
F divide(const vector<pair<int, T>> &g) const { return F(*this).divide_inplace(g); }
// multiply and divide (1 + cz^d)
// O(n)
void multiply_inplace(const int d, const T c) {
int n = this->size();
if (c == T(1)) drep(i, n-d) (*this)[i+d] += (*this)[i];
else if (c == T(-1)) drep(i, n-d) (*this)[i+d] -= (*this)[i];
else drep(i, n-d) (*this)[i+d] += (*this)[i] * c;
}
// O(n)
void divide_inplace(const int d, const T c) {
int n = this->size();
if (c == T(1)) rep(i, n-d) (*this)[i+d] -= (*this)[i];
else if (c == T(-1)) rep(i, n-d) (*this)[i+d] += (*this)[i];
else rep(i, n-d) (*this)[i+d] -= (*this)[i] * c;
}
// O(n)
T eval(const T &a) const {
T x(1), res(0);
for (auto e : *this) res += e * x, x *= a;
return res;
}
// O(n)
F &integ_inplace() {
int n = this->size();
assert(n > 0);
if (n == 1) return *this = F{0};
this->insert(this->begin(), 0);
this->pop_back();
vector<T> inv(n);
inv[1] = 1;
int p = T::mod();
rep2(i, 2, n) inv[i] = - inv[p%i] * (p/i);
rep2(i, 2, n) (*this)[i] *= inv[i];
return *this;
}
F integ() const { return F(*this).integ_inplace(); }
// O(n)
F &deriv_inplace() {
int n = this->size();
assert(n > 0);
rep2(i, 2, n) (*this)[i] *= i;
this->erase(this->begin());
this->push_back(0);
return *this;
}
F deriv() const { return F(*this).deriv_inplace(); }
// O(n log n)
F log(int d = -1) const {
int n = this->size();
assert(n > 0 && (*this)[0] == 1);
if (d == -1) d = n;
assert(d > 0);
F res(this->deriv());
res.divide_inplace(*this, d);
res.integ_inplace();
return res;
}
// O(n log n)
// https://arxiv.org/abs/1301.5804 (Figure 2, right)
F &exp_inplace(int d = -1) {
int n = this->size();
assert(n > 0 && (*this)[0] == 0);
if (d == -1) d = n;
assert(d >= 0);
F g{1}, g_fft;
this->resize(d);
(*this)[0] = 1;
F h_drv(this->deriv());
for (int m = 1; m < d; m *= 2) {
// prepare
F f_fft(this->begin(), this->begin() + m);
f_fft.resize(2*m), internal::butterfly(f_fft);
// Step 2.a'
if (m > 1) {
F _f(m);
rep(i, m) _f[i] = f_fft[i] * g_fft[i];
internal::butterfly_inv(_f);
_f.erase(_f.begin(), _f.begin() + m/2);
_f.resize(m), internal::butterfly(_f);
rep(i, m) _f[i] *= g_fft[i];
internal::butterfly_inv(_f);
_f.resize(m/2);
_f /= T(-m) * m;
g.insert(g.end(), _f.begin(), _f.begin() + m/2);
}
// Step 2.b'--d'
F t(this->begin(), this->begin() + m);
t.deriv_inplace();
{
// Step 2.b'
F r{h_drv.begin(), h_drv.begin() + m-1};
// Step 2.c'
r.resize(m); internal::butterfly(r);
rep(i, m) r[i] *= f_fft[i];
internal::butterfly_inv(r);
r /= -m;
// Step 2.d'
t += r;
t.insert(t.begin(), t.back()); t.pop_back();
}
// Step 2.e'
t.resize(2*m); internal::butterfly(t);
g_fft = g; g_fft.resize(2*m); internal::butterfly(g_fft);
rep(i, 2*m) t[i] *= g_fft[i];
internal::butterfly_inv(t);
t.resize(m);
t /= 2*m;
// Step 2.f'
F v(this->begin() + m, this->begin() + min(d, 2*m)); v.resize(m);
t.insert(t.begin(), m-1, 0); t.push_back(0);
t.integ_inplace();
rep(i, m) v[i] -= t[m+i];
// Step 2.g'
v.resize(2*m); internal::butterfly(v);
rep(i, 2*m) v[i] *= f_fft[i];
internal::butterfly_inv(v);
v.resize(m);
v /= 2*m;
// Step 2.h'
rep(i, min(d-m, m)) (*this)[m+i] = v[i];
}
return *this;
}
F exp(const int d = -1) const { return F(*this).exp_inplace(d); }
// O(n log n)
F &pow_inplace(ll k, int d = -1) {
int n = this->size();
if (d == -1) d = n;
assert(d >= 0);
int l = 0;
while ((*this)[l] == 0) ++l;
if (l > d/k) return *this = F(d);
T ic = (*this)[l].inv();
T pc = (*this)[l].pow(k);
this->erase(this->begin(), this->begin() + l);
*this *= ic;
*this = this->log();
*this *= k;
this->exp_inplace();
*this *= pc;
this->insert(this->begin(), l*k, 0);
this->resize(d);
return *this;
}
F pow(const ll k, const int d = -1) const { return F(*this).pow_inplace(k, d); }
F operator*(const T &g) const { return F(*this) *= g; }
F operator/(const T &g) const { return F(*this) /= g; }
F operator+(const F &g) const { return F(*this) += g; }
F operator-(const F &g) const { return F(*this) -= g; }
F operator<<(const int d) const { return F(*this) <<= d; }
F operator>>(const int d) const { return F(*this) >>= d; }
F operator*(const F &g) const { return F(*this) *= g; }
F operator/(const F &g) const { return F(*this) /= g; }
F operator*(const vector<pair<int, T>> &g) const { return F(*this) *= g; }
F operator/(const vector<pair<int, T>> &g) const { return F(*this) /= g; }
};
typedef modint998244353 mint;
typedef FormalPowerSeries<mint> fps;
//--------
typedef long long ll;
int main(){
// sum(A[i]), .
int N;
cin >> N;
vector<int> A(N);
mint ans = 0;
mint nnv = mint(2).pow(N-1);
vector<int> Q(10001);
int asum = 0;
for (int i=0; i<N; i++){
cin >> A[i];
ans += nnv * A[i];
Q[A[i]] += 1;
asum += A[i];
}
if (asum >= 999630629){
int l = asum - 999630629 + 1;
fps F(l);
for (int i=0; i<min(l, 10001); i++){
if (Q[i] > 0){
fps G(l);
G[0] = 1;
G[i] = 1;
G = G.log();
G *= Q[i];
G = G.exp();
F.multiply(G);
}
}
mint jogai = 0;
for (int i=0; i<asum - 999630629 + 1; i++){
jogai += F[i];
}
ans -= jogai * mint(999630629);
}
cout << ans.val() << endl;
}
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