結果

問題 No.754 畳み込みの和
ユーザー ningenMeningenMe
提出日時 2020-05-30 14:25:02
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 633 ms / 5,000 ms
コード長 7,186 bytes
コンパイル時間 2,511 ms
コンパイル使用メモリ 215,004 KB
実行使用メモリ 16,268 KB
最終ジャッジ日時 2024-11-07 16:20:28
合計ジャッジ時間 5,890 ms
ジャッジサーバーID
（参考情報） 		judge5 / 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 628 ms
16,268 KB
testcase_01 AC 632 ms
16,232 KB
testcase_02 AC 633 ms
16,096 KB
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 # 

#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;}


/*
 * @title Garner
 */
class Garner{
	inline static constexpr long long gcd(long long a, long long b) {
		return (b ? gcd(b, a % b):a);
	}
	inline static long long ext_gcd(long long a, long long b, long long &x, long long &y) {
		long long res;
		if (b == 0) res = a,x = 1,y = 0;
		else res = ext_gcd(b, a%b, y, x), y -= a/b * x;
		return res;
	}
	inline static long long inv_mod(long long a, long long b) {
		long long x, y;
		ext_gcd(a, b, x, y);
		return (x%b+b)%b;
	}
public:
	// O(N^2) x mod m_i = b_i なる x を返却　, b_iがすべて0のときは0ではなくm_iのlcmを返す
	// return x
	inline static long long garner(vector<long long> b, vector<long long> m, long long mod){
		int N=b.size();
		vector<long long> coe(N+1,1),val(N+1,0);
		long long g,gl,gr,sum=accumulate(b.begin(),b.end(),0LL);
		//互いに素になるように処理
		for (int l = 0; l < N; ++l) {
			for (int r = l+1; r < N; ++r) {
				g = gcd(m[l], m[r]);
				if (sum && (b[l] - b[r]) % g != 0) return -1;
				m[l] /= g, m[r] /= g;
				gl = gcd(m[l], g), gr = g/gl;
				do {
					g = gcd(gl, gr);
					gl *= g, gr /= g;
				} while (g != 1);
				m[l] *= gl, m[r] *= gr;
				b[l] %= m[l], b[r] %= m[r];
			}
		}
		if(!sum) {
			long long lcm = 1;
			for(auto& e:m) (lcm*=e)%=mod;
			return lcm;
		}
		m.push_back(mod);
		for(int i = 0; i < N; ++i) {
			long long t = (b[i] - val[i]) * inv_mod(coe[i], m[i]);
			((t %= m[i]) += m[i]) %= m[i];
			for (int j = i+1; j <= N; ++j) {
				(val[j] += t * coe[j]) %= m[j];
				(coe[j] *= m[i]) %= m[j];
			}
		}
		return val.back();
	}
};

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; }
long long mod_pow(long long a, long long n, long long mod) { long long ret = 1; long long 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<long long>& 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 long long base = mod_pow(h, n / m2, mod);
			long long w = 1;
			for(long long x= 0;x < m; ++x) {
				for (int s = x; s < n; s += m2) {
					long long u = a[s];
					long long 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<long long>& input) {
		_ntt(input, 1);
	}
	void intt(vector<long long>& 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<long long> convolution(const vector<long long>& a, const vector<long long>& b){
		int ntt_size = 1;
		while (ntt_size < a.size() + b.size()) ntt_size *= 2;

		vector<long long> _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;
	}
};


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<long long> int32mod_convolution(vector<long long> g, vector<long long> h,long long mod){
	for (auto& a : g) a %= mod;
	for (auto& a : h) a %= mod;
	NTT_1 ntt1; NTT_2 ntt2; NTT_3 ntt3;
	auto x = ntt1.convolution(g, h);
	auto y = ntt2.convolution(g, h);
	auto z = ntt3.convolution(g, h);

	vector<long long> res(x.size());
	vector<long long> b(3),m(3);
	for(int i=0; i < x.size(); ++i){
		m[0] = ntt1.get_mod(), b[0] = x[i];
		m[1] = ntt2.get_mod(), b[1] = y[i];
		m[2] = ntt3.get_mod(), b[2] = z[i];
		res[i] = Garner::garner(b, m, mod);
	}
	return res;
}

int main() {
    int N; cin >> N;
    vector<long long> 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);
    long long ans = 0;
    for(int i = 0; i <= N; ++i) (ans += C[i]) %= MOD;
    cout << ans << endl;
    return 0;
}
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