結果
| 問題 |
No.754 畳み込みの和
|
| コンテスト | |
| ユーザー |
 ningenMe
|
| 提出日時 | 2020-05-30 04:04:09 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 539 ms / 5,000 ms |
| コード長 | 6,056 bytes |
| コンパイル時間 | 3,105 ms |
| コンパイル使用メモリ | 209,444 KB |
| 最終ジャッジ日時 | 2025-01-10 19:08:16 |
|
ジャッジサーバーID （参考情報） |
judge1 / judge3 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| other | AC * 3 |
ソースコード
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
#define ALL(obj) (obj).begin(),(obj).end()
#define SPEED cin.tie(0);ios::sync_with_stdio(false);
template<class T> using PQ = priority_queue<T>;
template<class T> using PQR = priority_queue<T,vector<T>,greater<T>>;
constexpr long long MOD = (long long)1e9 + 7;
constexpr long long MOD2 = 998244353;
constexpr long long HIGHINF = (long long)1e18;
constexpr long long LOWINF = (long long)1e15;
constexpr long double PI = 3.1415926535897932384626433L;
template <class T> vector<T> multivector(size_t N,T init){return vector<T>(N,init);}
template <class... T> auto multivector(size_t N,T... t){return vector<decltype(multivector(t...))>(N,multivector(t...));}
template <class T> void corner(bool flg, T hoge) {if (flg) {cout << hoge << endl; exit(0);}}
template <class T, class U>ostream &operator<<(ostream &o, const map<T, U>&obj) {o << "{"; for (auto &x : obj) o << " {" << x.first << " : " << x.second << "}" << ","; o << " }"; return o;}
template <class T>ostream &operator<<(ostream &o, const set<T>&obj) {o << "{"; for (auto itr = obj.begin(); itr != obj.end(); ++itr) o << (itr != obj.begin() ? ", " : "") << *itr; o << "}"; return o;}
template <class T>ostream &operator<<(ostream &o, const multiset<T>&obj) {o << "{"; for (auto itr = obj.begin(); itr != obj.end(); ++itr) o << (itr != obj.begin() ? ", " : "") << *itr; o << "}"; return o;}
template <class T>ostream &operator<<(ostream &o, const vector<T>&obj) {o << "{"; for (int i = 0; i < (int)obj.size(); ++i)o << (i > 0 ? ", " : "") << obj[i]; o << "}"; return o;}
template <class T, class U>ostream &operator<<(ostream &o, const pair<T, U>&obj) {o << "{" << obj.first << ", " << obj.second << "}"; return o;}
template <template <class tmp> class T, class U> ostream &operator<<(ostream &o, const T<U> &obj) {o << "{"; for (auto itr = obj.begin(); itr != obj.end(); ++itr)o << (itr != obj.begin() ? ", " : "") << *itr; o << "}"; return o;}
void print(void) {cout << endl;}
template <class Head> void print(Head&& head) {cout << head;print();}
template <class Head, class... Tail> void print(Head&& head, Tail&&... tail) {cout << head << " ";print(forward<Tail>(tail)...);}
template <class T> void chmax(T& a, const T b){a=max(a,b);}
template <class T> void chmin(T& a, const T b){a=min(a,b);}
void YN(bool flg) {cout << (flg ? "YES" : "NO") << endl;}
void Yn(bool flg) {cout << (flg ? "Yes" : "No") << endl;}
void yn(bool flg) {cout << (flg ? "yes" : "no") << endl;}
template<class T> T extgcd(T a, T b, T& x, T& y) { for (T u = y = 1, v = x = 0; a;) { T q = b / a; swap(x -= q * u, u); swap(y -= q * v, v); swap(b -= q * a, a); } return b; }
template<class T> T mod_inv(T a, T m) { T x, y; extgcd(a, m, x, y); return (m + x % m) % m; }
ll mod_pow(ll a, ll n, ll mod) { ll ret = 1; ll p = a % mod; while (n) { if (n & 1) ret = ret * p % mod; p = p * p % mod; n >>= 1; } return ret; }
template<int mod, int primitive_root> class NTT {
public:
int get_mod() const { return mod; }
void _ntt(vector<ll>& a, int sign) {
const int n = a.size();
assert((n ^ (n&-n)) == 0); //n = 2^k
const int g = 3; //g is primitive root of mod
int h = (int)mod_pow(g, (mod - 1) / n, mod); // h^n = 1
if (sign == -1) h = (int)mod_inv(h, mod); //h = h^-1 % mod
//bit reverse
int i = 0;
for (int j = 1; j < n - 1; ++j) {
for (int k = n >> 1; k >(i ^= k); k >>= 1);
if (j < i) swap(a[i], a[j]);
}
for (int m = 1; m < n; m *= 2) {
const int m2 = 2 * m;
const ll base = mod_pow(h, n / m2, mod);
ll w = 1;
for(ll x= 0;x < m; ++x) {
for (int s = x; s < n; s += m2) {
ll u = a[s];
ll d = a[s + m] * w % mod;
a[s] = u + d;
if (a[s] >= mod) a[s] -= mod;
a[s + m] = u - d;
if (a[s + m] < 0) a[s + m] += mod;
}
w = w * base % mod;
}
}
for (auto& x : a) if (x < 0) x += mod;
}
void ntt(vector<ll>& input) {
_ntt(input, 1);
}
void intt(vector<ll>& input) {
_ntt(input, -1);
const int n_inv = mod_inv((int)input.size(), mod);
for (auto& x : input) x = x * n_inv % mod;
}
// 畳み込み演算を行う
vector<ll> convolution(const vector<ll>& a, const vector<ll>& b){
int ntt_size = 1;
while (ntt_size < a.size() + b.size()) ntt_size *= 2;
vector<ll> _a = a, _b = b;
_a.resize(ntt_size); _b.resize(ntt_size);
ntt(_a);
ntt(_b);
for(int i = 0; i < ntt_size; ++i){
(_a[i] *= _b[i]) %= mod;
}
intt(_a);
return _a;
}
};
ll garner(vector<pair<ll,ll>> mr, int mod){
mr.emplace_back(mod, 0);
vector<ll> coffs(mr.size(), 1);
vector<ll> constants(mr.size(), 0);
for(int i = 0; i < mr.size() - 1; ++i) {
// coffs[i] * v + constants[i] == mr[i].second (mod mr[i].first) を解く
ll v = (mr[i].second - constants[i]) * mod_inv<ll>(coffs[i], mr[i].first) % mr[i].first;
if (v < 0) v += mr[i].first;
for (int j = i + 1; j < mr.size(); j++) {
(constants[j] += coffs[j] * v) %= mr[j].first;
(coffs[j] *= mr[i].first) %= mr[j].first;
}
}
return constants[mr.size() - 1];
}
typedef NTT<167772161, 3> NTT_1;
typedef NTT<469762049, 3> NTT_2;
typedef NTT<1224736769, 3> NTT_3;
//任意のmodで畳み込み演算 O(n log n)
vector<ll> int32mod_convolution(vector<ll> a, vector<ll> b,int mod){
for (auto& x : a) x %= mod;
for (auto& x : b) x %= mod;
NTT_1 ntt1; NTT_2 ntt2; NTT_3 ntt3;
auto x = ntt1.convolution(a, b);
auto y = ntt2.convolution(a, b);
auto z = ntt3.convolution(a, b);
vector<ll> ret(x.size());
vector<pair<ll,ll>> mr(3);
for(int i=0; i < x.size(); ++i){
mr[0].first = ntt1.get_mod(), mr[0].second = (int)x[i];
mr[1].first = ntt2.get_mod(), mr[1].second = (int)y[i];
mr[2].first = ntt3.get_mod(), mr[2].second = (int)z[i];
ret[i] = garner(mr, mod);
}
return ret;
}
int main() {
int N; cin >> N;
vector<ll> A(N+1),B(N+1);
for(int i = 0; i < N+1; ++i) cin >> A[i];
for(int i = 0; i < N+1; ++i) cin >> B[i];
auto C = int32mod_convolution(A,B,MOD);
ll ans = 0;
for(int i = 0; i <= N; ++i) (ans += C[i]) %= MOD;
cout << ans << endl;
return 0;
}