結果
問題 | No.754 畳み込みの和 |
ユーザー | ningenMe |
提出日時 | 2020-05-30 04:04:09 |
言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
結果 |
AC
|
実行時間 | 455 ms / 5,000 ms |
コード長 | 6,056 bytes |
コンパイル時間 | 2,864 ms |
コンパイル使用メモリ | 218,236 KB |
実行使用メモリ | 16,140 KB |
最終ジャッジ日時 | 2024-11-06 19:53:33 |
合計ジャッジ時間 | 5,241 ms |
ジャッジサーバーID (参考情報) |
judge2 / 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 | 451 ms
16,140 KB |
testcase_01 | AC | 455 ms
16,136 KB |
testcase_02 | AC | 454 ms
16,140 KB |
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; }