結果
問題 | No.754 畳み込みの和 |
ユーザー |
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提出日時 | 2020-01-01 14:52:38 |
言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 146 ms / 5,000 ms |
コード長 | 7,515 bytes |
コンパイル時間 | 1,533 ms |
コンパイル使用メモリ | 99,200 KB |
最終ジャッジ日時 | 2025-01-08 15:17:18 |
ジャッジサーバーID (参考情報) |
judge1 / judge3 |
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ファイルパターン | 結果 |
---|---|
other | AC * 3 |
ソースコード
#include <iostream>#include <vector>#include <cassert>#include <cmath>using namespace std;using ll = long long;template<class T> using vec = vector<T>;template<class T> using vvec = vector<vec<T>>;template< ll mod >struct ModInt {ll x;ModInt() : x(0) {}ModInt(int64_t y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}ModInt &operator+=(const ModInt &p) {if((x += p.x) >= mod) x -= mod;return *this;}ModInt &operator-=(const ModInt &p) {if((x += mod - p.x) >= mod) x -= mod;return *this;}ModInt &operator*=(const ModInt &p) {x = (1LL * x * p.x % mod);return *this;}ModInt &operator/=(const ModInt &p) {*this *= p.inverse();return *this;}ModInt operator-() const { return ModInt(-x); }ModInt operator+(const ModInt &p) const { return ModInt(*this) += p; }ModInt operator-(const ModInt &p) const { return ModInt(*this) -= p; }ModInt operator*(const ModInt &p) const { return ModInt(*this) *= p; }ModInt operator/(const ModInt &p) const { return ModInt(*this) /= p; }bool operator==(const ModInt &p) const { return x == p.x; }bool operator!=(const ModInt &p) const { return x != p.x; }ModInt inverse() const {ll a = x, b = mod, u = 1, v = 0, t;while(b > 0) {t = a / b;swap(a -= t * b, b);swap(u -= t * v, v);}return ModInt(u);}ModInt pow(int64_t n) const {ModInt ret(1), mul(x);while(n > 0) {if(n & 1) ret *= mul;mul *= mul;n >>= 1;}return ret;}friend ostream &operator<<(ostream &os, const ModInt &p) {return os << p.x;}friend istream &operator>>(istream &is, ModInt &a) {int64_t t;is >> t;a = ModInt<mod>(t);return (is);}static ll get_mod() { return mod; }};using mint = ModInt<1000000007>;namespace FastFourierTransform {using real = double;struct C {real x, y;C() : x(0), y(0) {}C(real x, real y) : x(x), y(y) {}inline C operator+(const C &c) const { return C(x + c.x, y + c.y); }inline C operator-(const C &c) const { return C(x - c.x, y - c.y); }inline C operator*(const C &c) const { return C(x * c.x - y * c.y, x * c.y + y * c.x); }inline C conj() const { return C(x, -y); }};const real PI = acosl(-1);int base = 1;vector< C > rts = { {0, 0},{1, 0} };vector< int > rev = {0, 1};void ensure_base(int nbase) {if(nbase <= base) return;rev.resize(1 << nbase);rts.resize(1 << nbase);for(int i = 0; i < (1 << nbase); i++) {rev[i] = (rev[i >> 1] >> 1) + ((i & 1) << (nbase - 1));}while(base < nbase) {real angle = PI * 2.0 / (1 << (base + 1));for(int i = 1 << (base - 1); i < (1 << base); i++) {rts[i << 1] = rts[i];real angle_i = angle * (2 * i + 1 - (1 << base));rts[(i << 1) + 1] = C(cos(angle_i), sin(angle_i));}++base;}}void fft(vector< C > &a, int n) {assert((n & (n - 1)) == 0);int zeros = __builtin_ctz(n);ensure_base(zeros);int shift = base - zeros;for(int i = 0; i < n; i++) {if(i < (rev[i] >> shift)) {swap(a[i], a[rev[i] >> shift]);}}for(int k = 1; k < n; k <<= 1) {for(int i = 0; i < n; i += 2 * k) {for(int j = 0; j < k; j++) {C z = a[i + j + k] * rts[j + k];a[i + j + k] = a[i + j] - z;a[i + j] = a[i + j] + z;}}}}vector< int64_t > multiply(const vector< int > &a, const vector< int > &b) {int need = (int) a.size() + (int) b.size() - 1;int nbase = 1;while((1 << nbase) < need) nbase++;ensure_base(nbase);int sz = 1 << nbase;vector< C > fa(sz);for(int i = 0; i < sz; i++) {int x = (i < (int) a.size() ? a[i] : 0);int y = (i < (int) b.size() ? b[i] : 0);fa[i] = C(x, y);}fft(fa, sz);C r(0, -0.25 / (sz >> 1)), s(0, 1), t(0.5, 0);for(int i = 0; i <= (sz >> 1); i++) {int j = (sz - i) & (sz - 1);C z = (fa[j] * fa[j] - (fa[i] * fa[i]).conj()) * r;fa[j] = (fa[i] * fa[i] - (fa[j] * fa[j]).conj()) * r;fa[i] = z;}for(int i = 0; i < (sz >> 1); i++) {C A0 = (fa[i] + fa[i + (sz >> 1)]) * t;C A1 = (fa[i] - fa[i + (sz >> 1)]) * t * rts[(sz >> 1) + i];fa[i] = A0 + A1 * s;}fft(fa, sz >> 1);vector< int64_t > ret(need);for(int i = 0; i < need; i++) {ret[i] = llround(i & 1 ? fa[i >> 1].y : fa[i >> 1].x);}return ret;}};template< typename T >struct ArbitraryModConvolution {using real = FastFourierTransform::real;using C = FastFourierTransform::C;ArbitraryModConvolution() = default;vector< T > multiply(const vector< T > &a, const vector< T > &b, int need = -1) {if(need == -1) need = a.size() + b.size() - 1;int nbase = 0;while((1 << nbase) < need) nbase++;FastFourierTransform::ensure_base(nbase);int sz = 1 << nbase;vector< C > fa(sz);for(int i = 0; i < a.size(); i++) {fa[i] = C(a[i].x & ((1 << 15) - 1), a[i].x >> 15);}fft(fa, sz);vector< C > fb(sz);if(a == b) {fb = fa;}else{for(int i = 0; i < b.size(); i++) {fb[i] = C(b[i].x & ((1 << 15) - 1), b[i].x >> 15);}fft(fb, sz);}real ratio = 0.25 / sz;C r2(0, -1), r3(ratio, 0), r4(0, -ratio), r5(0, 1);for(int i = 0; i <= (sz >> 1); i++) {int j = (sz - i) & (sz - 1);C a1 = (fa[i] + fa[j].conj());C a2 = (fa[i] - fa[j].conj()) * r2;C b1 = (fb[i] + fb[j].conj()) * r3;C b2 = (fb[i] - fb[j].conj()) * r4;if(i != j) {C c1 = (fa[j] + fa[i].conj());C c2 = (fa[j] - fa[i].conj()) * r2;C d1 = (fb[j] + fb[i].conj()) * r3;C d2 = (fb[j] - fb[i].conj()) * r4;fa[i] = c1 * d1 + c2 * d2 * r5;fb[i] = c1 * d2 + c2 * d1;}fa[j] = a1 * b1 + a2 * b2 * r5;fb[j] = a1 * b2 + a2 * b1;}fft(fa, sz);fft(fb, sz);vector< T > ret(need);for(int i = 0; i < need; i++) {int64_t aa = llround(fa[i].x);int64_t bb = llround(fb[i].x);int64_t cc = llround(fa[i].y);aa = T(aa).x, bb = T(bb).x, cc = T(cc).x;ret[i] = aa + (bb << 15) + (cc << 30);}return ret;}};int main(){int N;cin >> N;vec<mint> 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];ArbitraryModConvolution<mint> NTT;vec<mint> C = NTT.multiply(A,B);mint ans = 0;for(int i=0;i<=N;i++) ans += C[i];cout << ans << endl;}