結果

問題 No.754 畳み込みの和
ユーザー IKyoproIKyopro
提出日時 2020-01-01 14:52:38
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 133 ms / 5,000 ms
コード長 7,515 bytes
コンパイル時間 1,212 ms
コンパイル使用メモリ 100,248 KB
実行使用メモリ 19,968 KB
最終ジャッジ日時 2024-11-22 04:51:15
合計ジャッジ時間 2,687 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 133 ms
19,840 KB
testcase_01 AC 133 ms
19,968 KB
testcase_02 AC 133 ms
19,968 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 <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;
}
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