結果

問題 No.2062 Sum of Subset mod 999630629
ユーザー shobonvip
提出日時 2022-08-27 02:32:52
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
TLE  
実行時間 -
コード長 6,012 bytes
コンパイル時間 4,883 ms
コンパイル使用メモリ 260,136 KB
最終ジャッジ日時 2025-01-31 06:05:33
ジャッジサーバーID
(参考情報)
judge4 / judge5
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 * 28 TLE * 1
権限があれば一括ダウンロードができます

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>
#include<atcoder/all>
using namespace std;
using namespace atcoder;
typedef modint998244353 mint;
typedef long long ll;
// shobonfps
// code from: https://opt-cp.com/fps-implementation/
// but replaced "rep, drep" to "for"
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();
for(int i=0; i<min(n, m); i++) (*this)[i] += g[i];
return *this;
}
F &operator-=(const F &g) {
int n = (*this).size(), m = g.size();
for(int i=0; i<min(n, m); i++) (*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;
}
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()};
while (res.size() < d) {
int m = size(res);
F f(begin(*this), begin(*this) + min(n, 2*m));
F r(res);
f.resize(2*m), internal::butterfly(f);
r.resize(2*m), internal::butterfly(r);
for(int i=0; i<2*m; i++) f[i] *= r[i];
internal::butterfly_inv(f);
f.erase(f.begin(), f.begin() + m);
f.resize(2*m), internal::butterfly(f);
for(int i=0; i<2*m; i++) f[i] *= r[i];
internal::butterfly_inv(f);
T iz = T(2*m).inv(); iz *= -iz;
for(int i=0; i<m; i++) f[i] *= iz;
res.insert(res.end(), f.begin(), f.begin() + m);
}
return {res.begin(), res.begin() + d};
}
// fast: FMT-friendly modulus only
F &operator*=(const F &g) {
int n = (*this).size();
*this = convolution(*this, g);
(*this).resize(n);
return *this;
}
F &operator/=(const F &g) {
int n = (*this).size();
*this = convolution(*this, g.inv(n));
(*this).resize(n);
return *this;
}
// // naive
// F &operator*=(const F &g) {
// int n = (*this).size(), m = g.size();
// for(int i=n-1; i>=0; i--) {
// (*this)[i] *= g[0];
// for(int j=1; j<min(i+1, m); j++) (*this)[i] += (*this)[i-j] * g[j];
// }
// return *this;
// }
// F &operator/=(const F &g) {
// assert(g[0] != T(0));
// T ig0 = g[0].inv();
// int n = (*this).size(), m = g.size();
// for(int i=0; i<n; i++) {
// for(int j=1; j<min(i+1, m); j++) (*this)[i] -= (*this)[i-j] * g[j];
// (*this)[i] *= ig0;
// }
// return *this;
// }
// sparse
F &operator*=(vector<pair<int, T>> g) {
int n = (*this).size();
auto [d, c] = g.front();
if (d == 0) g.erase(g.begin());
else c = 0;
for(int i=n-1; i>=0; i--) {
(*this)[i] *= c;
for (auto &[j, b] : g) {
if (j > i) break;
(*this)[i] += (*this)[i-j] * b;
}
}
return *this;
}
F &operator/=(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());
for(int i=0; i<n; i++) {
for (auto &[j, b] : g) {
if (j > i) break;
(*this)[i] -= (*this)[i-j] * b;
}
(*this)[i] *= ic;
}
return *this;
}
// multiply and divide (1 + cz^d)
void multiply(const int d, const T c) {
int n = (*this).size();
if (c == T(1)) for(int i=n-d-1; i>=0; i--) (*this)[i+d] += (*this)[i];
else if (c == T(-1)) for(int i=n-d-1; i>=0; i--) (*this)[i+d] -= (*this)[i];
else for(int i=n-d-1; i>=0; i--) (*this)[i+d] += (*this)[i] * c;
}
void divide(const int d, const T c) {
int n = (*this).size();
if (c == T(1)) for(int i=0; i<n-d; i++) (*this)[i+d] -= (*this)[i];
else if (c == T(-1)) for(int i=0; i<n-d; i++) (*this)[i+d] += (*this)[i];
else for(int i=0; i<n-d; i++) (*this)[i+d] -= (*this)[i] * c;
}
T eval(const T &a) const {
T x(1), res(0);
for (auto e : *this) res += e * x, x *= a;
return res;
}
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*(vector<pair<int, T>> g) const { return F(*this) *= g; }
F operator/(vector<pair<int, T>> g) const { return F(*this) /= g; }
};
typedef FormalPowerSeries<mint> fps;
typedef vector<pair<int,mint>> sfps;
//--------
//defmodfact
const int COMinitMAX = 200000;
mint fact[COMinitMAX+1], factinv[COMinitMAX+1];
void modfact(){
fact[0] = 1;
for (int i=1; i<=COMinitMAX; i++){
fact[i] = fact[i-1] * i;
}
factinv[COMinitMAX] = fact[COMinitMAX].inv();
for (int i=COMinitMAX-1; i>=0; i--){
factinv[i] = factinv[i+1] * (i+1);
}
}
mint cmb(int a, int b){
if (a<b || b<0) return mint(0);
return fact[a]*factinv[b]*factinv[a-b];
}
//--------
int main(){
modfact();
int N;
cin >> N;
vector<int> A(N);
for (int i=0; i<N; i++){
cin >> A[i];
}
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);
fps G(l);
F[0] = 1;
for (int i=1; i<min(l, 10001); i++){
if (Q[i] > 0){
for (int j=0; j<l; j+=i){
G[j] = cmb(Q[i], j/i);
}
F *= G;
for (int j=0; j<l; j+=i){
G[j] = 0;
}
}
}
mint jogai = 0;
for (int i=0; i<l; i++){
jogai += F[i];
}
ans -= jogai * mint(999630629);
}
cout << ans.val() << endl;
}
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