結果
| 問題 | No.2413 Multiple of 99 |
| ユーザー |
 蜜蜂
|
| 提出日時 | 2023-08-11 23:49:04 |
| 言語 | C++14 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
AC
|
| 実行時間 | 2,939 ms / 8,000 ms |
| コード長 | 11,669 bytes |
| コンパイル時間 | 4,889 ms |
| コンパイル使用メモリ | 258,732 KB |
| 実行使用メモリ | 67,080 KB |
| 最終ジャッジ日時 | 2024-11-18 19:37:49 |
| 合計ジャッジ時間 | 42,617 ms |
|
ジャッジサーバーID （参考情報） |
judge1 / judge3 |
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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 | 123 ms
18,864 KB |
| testcase_01 | AC | 113 ms
19,016 KB |
| testcase_02 | AC | 313 ms
18,848 KB |
| testcase_03 | AC | 107 ms
19,044 KB |
| testcase_04 | AC | 425 ms
19,520 KB |
| testcase_05 | AC | 470 ms
20,432 KB |
| testcase_06 | AC | 451 ms
20,244 KB |
| testcase_07 | AC | 2,867 ms
66,956 KB |
| testcase_08 | AC | 397 ms
19,012 KB |
| testcase_09 | AC | 2,587 ms
66,952 KB |
| testcase_10 | AC | 2,819 ms
66,828 KB |
| testcase_11 | AC | 2,939 ms
66,948 KB |
| testcase_12 | AC | 2,858 ms
67,080 KB |
| testcase_13 | AC | 2,856 ms
66,952 KB |
| testcase_14 | AC | 2,861 ms
66,948 KB |
| testcase_15 | AC | 2,927 ms
66,956 KB |
| testcase_16 | AC | 1,614 ms
43,260 KB |
| testcase_17 | AC | 1,568 ms
42,172 KB |
| testcase_18 | AC | 2,896 ms
64,628 KB |
| testcase_19 | AC | 649 ms
23,468 KB |
| testcase_20 | AC | 496 ms
21,320 KB |
| testcase_21 | AC | 668 ms
23,604 KB |
| testcase_22 | AC | 2,849 ms
65,060 KB |
| testcase_23 | AC | 649 ms
24,648 KB |
コンパイルメッセージ
main.cpp: In member function 'FormalPowerSeries<T>::F& FormalPowerSeries<T>::multiply_inplace(std::vector<std::pair<int, E> >)':
main.cpp:152:10: warning: structured bindings only available with '-std=c++17' or '-std=gnu++17' [-Wc++17-extensions]
152 | auto [d, c] = g.front();
| ^
main.cpp:157:18: warning: structured bindings only available with '-std=c++17' or '-std=gnu++17' [-Wc++17-extensions]
157 | for (auto &[j, b] : g) {
| ^
main.cpp: In member function 'FormalPowerSeries<T>::F& FormalPowerSeries<T>::divide_inplace(std::vector<std::pair<int, E> >)':
main.cpp:168:10: warning: structured bindings only available with '-std=c++17' or '-std=gnu++17' [-Wc++17-extensions]
168 | auto [d, c] = g.front();
| ^
main.cpp:173:18: warning: structured bindings only available with '-std=c++17' or '-std=gnu++17' [-Wc++17-extensions]
173 | for (auto &[j, b] : g) {
| ^
ソースコード
//g++ 1.cpp -std=c++17 -O2 -I .
#include <bits/stdc++.h>
using namespace std;
#include <atcoder/all>
using namespace atcoder;
using ll = long long;
using ld = long double;
using vi = vector<int>;
using vvi = vector<vi>;
using vll = vector<ll>;
using vvll = vector<vll>;
using vld = vector<ld>;
using vvld = vector<vld>;
using vst = vector<string>;
using vvst = vector<vst>;
#define fi first
#define se second
#define pb push_back
#define eb emplace_back
#define pq_big(T) priority_queue<T,vector<T>,less<T>>
#define pq_small(T) priority_queue<T,vector<T>,greater<T>>
#define all(a) a.begin(),a.end()
#define rep(i,start,end) for(ll i=start;i<(ll)(end);i++)
#define per(i,start,end) for(ll i=start;i>=(ll)(end);i--)
#define uniq(a) sort(all(a));a.erase(unique(all(a)),a.end())
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,0, min(n, m)) (*this)[i] += g[i];
return *this;
}
F &operator-=(const F &g) {
int n = this->size(), m = g.size();
rep(i,0, min(n, m)) (*this)[i] -= g[i];
return *this;
}
F &operator<<=(const int d) {
int n = this->size();
if (d >= n) *this = F(n);
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,0, 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,0, 2*m) f[i] *= g[i];
internal::butterfly_inv(f);
T iz = T(2*m).inv(); iz *= -iz;
rep(i,0, 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 ÷_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 ÷_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;
per(i, n-1, 0) {
(*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 ÷_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,0, 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)) per(i, n-d-1,0) (*this)[i+d] += (*this)[i];
else if (c == T(-1)) per(i, n-d-1,0) (*this)[i+d] -= (*this)[i];
else per(i, n-d-1, 0) (*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,0, n-d) (*this)[i+d] -= (*this)[i];
else if (c == T(-1)) rep(i,0, n-d) (*this)[i+d] += (*this)[i];
else rep(i,0, 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();
rep(i, 2, n) inv[i] = - inv[p%i] * (p/i);
rep(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);
rep(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_inplace(int d = -1) {
int n = this->size();
assert(n > 0 && (*this)[0] == 1);
if (d == -1) d = n;
assert(d >= 0);
if (d < n) this->resize(d);
F f_inv = this->inv();
this->deriv_inplace();
this->multiply_inplace(f_inv);
this->integ_inplace();
return *this;
}
F log(const int d = -1) const { return F(*this).log_inplace(d); }
// O(n log n)
// https://arxiv.org/abs/1301.5804 (Figure 1, 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{1, 1};
(*this)[0] = 1;
this->resize(d);
F h_drv(this->deriv());
for (int m = 2; 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'
{
F f(m);
rep(i,0, 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,0, 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,0, 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'
if (2*m < d) {
t.resize(2*m); internal::butterfly(t);
g_fft = g; g_fft.resize(2*m); internal::butterfly(g_fft);
rep(i,0, 2*m) t[i] *= g_fft[i];
internal::butterfly_inv(t);
t.resize(m);
t /= 2*m;
}
else { // この場合分けをしても数パーセントしか速くならない
F g1(g.begin() + m/2, g.end());
F s1(t.begin() + m/2, t.end());
t.resize(m/2);
g1.resize(m), internal::butterfly(g1);
t.resize(m), internal::butterfly(t);
s1.resize(m), internal::butterfly(s1);
rep(i,0, m) s1[i] = g_fft[i] * s1[i] + g1[i] * t[i];
rep(i,0, m) t[i] *= g_fft[i];
internal::butterfly_inv(t);
internal::butterfly_inv(s1);
rep(i,0, m/2) t[i+m/2] += s1[i];
t /= m;
}
// Step 2.f'
F v(this->begin() + m, this->begin() + min<int>(d, 2*m)); v.resize(m);
t.insert(t.begin(), m-1, 0); t.push_back(0);
t.integ_inplace();
rep(i,0, m) v[i] -= t[m+i];
// Step 2.g'
v.resize(2*m); internal::butterfly(v);
rep(i,0, 2*m) v[i] *= f_fft[i];
internal::butterfly_inv(v);
v.resize(m);
v /= 2*m;
// Step 2.h'
rep(i,0, 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 && k >= 0);
if (k == 0) {
*this = F(d);
if (d > 0) (*this)[0] = 1;
return *this;
}
int l = 0;
while (l < n && (*this)[l] == 0) ++l;
if (l > (d-1)/k || l == n) return *this = F(d);
T c = (*this)[l];
this->erase(this->begin(), this->begin() + l);
*this /= c;
this->log_inplace(d - l*k);
*this *= k;
this->exp_inplace();
*this *= c.pow(k);
this->insert(this->begin(), l*k, 0);
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; }
};
constexpr ll mod = 998244353;
using mint = modint998244353;
using fps = FormalPowerSeries<mint>;
int main(){
ios::sync_with_stdio(false);
cin.tie(nullptr);
int n,k;cin>>n>>k;
int even=n/2;
fps fp(10*n,0);
// x^0 + x^1 + ... + x^9
rep(i,0,10)fp[i]=1;
fps fpeven=fp.pow_inplace(even);
fps fpodd=fpeven;
if(n%2==1){
fps fp2(10,1);
fpodd=convolution(fpodd,fp2);
}
/*rep(i,0,fpeven.size())cout<<fpeven[i].val()<<" ";
cout<<endl;
rep(i,0,fpodd.size())cout<<fpodd[i].val()<<" ";
cout<<endl;*/
fps pw(4000000);
rep(i,0,4000000){
pw[i]=pow_mod(i,k,mod);
}
mint ans=0;
/*rep(i,0,fpeven.size()){
rep(j,0,fpodd.size()){
if(i%11!=j%11)continue;
if((i+j)%9!=0)continue;
//cout<<i<<" "<<j<<" ";
ans+=pw[i+j]*fpeven[i]*fpodd[j];
//cout<<" : "<<ans.val()<<endl;
j+=90;
}
}*/
rep(i,0,11){
fps fpeven2(fpeven.size(),0),fpodd2(fpodd.size(),0);
rep(j,0,fpeven.size()){
if(j%11==i)fpeven2[j]=fpeven[j];
}
rep(j,0,fpodd.size()){
if(j%11==i)fpodd2[j]=fpodd[j];
}
fps fp3;
fp3=convolution(fpeven2,fpodd2);
rep(j,0,fp3.size()){
if(j%9==0){
ans+=pw[j]*fp3[j];
}
}
}
cout<<ans.val()<<endl;
}
/*
9 の倍数 sum = 0 mod 9
11 の倍数 奇数桁 sum = 偶数桁 sum mod 11
*/