#808276 (C++17) No.891 隣接3項間の漸化式

提出ソース

結果

問題	No.891 隣接3項間の漸化式
ユーザー	rogi52
提出日時	2022-10-17 13:43:39
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	2 ms / 2,000 ms
コード長	15,456 bytes
コンパイル時間	2,751 ms
コンパイル使用メモリ	225,376 KB
実行使用メモリ	5,376 KB
最終ジャッジ日時	2024-06-28 03:58:46
合計ジャッジ時間	4,096 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	2 ms 5,248 KB
testcase_01	AC	2 ms 5,248 KB
testcase_02	AC	2 ms 5,376 KB
testcase_03	AC	2 ms 5,376 KB
testcase_04	AC	2 ms 5,376 KB
testcase_05	AC	1 ms 5,376 KB
testcase_06	AC	1 ms 5,376 KB
testcase_07	AC	2 ms 5,376 KB
testcase_08	AC	2 ms 5,376 KB
testcase_09	AC	2 ms 5,376 KB
testcase_10	AC	2 ms 5,376 KB
testcase_11	AC	2 ms 5,376 KB
testcase_12	AC	2 ms 5,376 KB
testcase_13	AC	2 ms 5,376 KB
testcase_14	AC	2 ms 5,376 KB
testcase_15	AC	2 ms 5,376 KB
testcase_16	AC	2 ms 5,376 KB
testcase_17	AC	2 ms 5,376 KB
testcase_18	AC	2 ms 5,376 KB
testcase_19	AC	2 ms 5,376 KB
testcase_20	AC	2 ms 5,376 KB
testcase_21	AC	2 ms 5,376 KB
testcase_22	AC	2 ms 5,376 KB
testcase_23	AC	2 ms 5,376 KB
testcase_24	AC	2 ms 5,376 KB
testcase_25	AC	2 ms 5,376 KB
testcase_26	AC	2 ms 5,376 KB
testcase_27	AC	2 ms 5,376 KB
testcase_28	AC	2 ms 5,376 KB
testcase_29	AC	2 ms 5,376 KB
testcase_30	AC	2 ms 5,376 KB
testcase_31	AC	2 ms 5,376 KB
testcase_32	AC	2 ms 5,376 KB
testcase_33	AC	2 ms 5,376 KB
testcase_34	AC	1 ms 5,376 KB
testcase_35	AC	2 ms 5,376 KB
testcase_36	AC	2 ms 5,376 KB
testcase_37	AC	2 ms 5,376 KB
testcase_38	AC	2 ms 5,376 KB
testcase_39	AC	2 ms 5,376 KB
testcase_40	AC	2 ms 5,376 KB
testcase_41	AC	2 ms 5,376 KB

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ソースコード

raw source code

#include <bits/stdc++.h>
#define rep(i,n) for(int i = 0; i < (n); i++)
using namespace std;
typedef long long ll;

template<int MOD> struct Fp {
    long long val;
    constexpr Fp(long long v = 0) noexcept : val(v % MOD) { if (val < 0) val += MOD; }
    constexpr int getmod() const { return MOD; }
    constexpr Fp operator - () const noexcept { return val ? MOD - val : 0; }
    constexpr Fp operator + (const Fp& r) const noexcept { return Fp(*this) += r; }
    constexpr Fp operator - (const Fp& r) const noexcept { return Fp(*this) -= r; }
    constexpr Fp operator * (const Fp& r) const noexcept { return Fp(*this) *= r; }
    constexpr Fp operator / (const Fp& r) const noexcept { return Fp(*this) /= r; }
    constexpr Fp& operator += (const Fp& r) noexcept {
        val += r.val;
        if (val >= MOD) val -= MOD;
        return *this;
    }
    constexpr Fp& operator -= (const Fp& r) noexcept {
        val -= r.val;
        if (val < 0) val += MOD;
        return *this;
    }
    constexpr Fp& operator *= (const Fp& r) noexcept {
        val = val * r.val % MOD;
        return *this;
    }
    constexpr Fp& operator /= (const Fp& r) noexcept {
        long long a = r.val, b = MOD, u = 1, v = 0;
        while (b) {
            long long t = a / b;
            a -= t * b, swap(a, b);
            u -= t * v, swap(u, v);
        }
        val = val * u % MOD;
        if (val < 0) val += MOD;
        return *this;
    }
    constexpr bool operator == (const Fp& r) const noexcept {
        return this->val == r.val;
    }
    constexpr bool operator != (const Fp& r) const noexcept {
        return this->val != r.val;
    }
    constexpr bool operator < (const Fp& r) const noexcept {
        return this->val < r.val;
    }
    friend constexpr istream& operator >> (istream& is, Fp<MOD>& x) noexcept {
        is >> x.val;
        x.val %= MOD;
        if (x.val < 0) x.val += MOD;
        return is;
    }
    friend constexpr ostream& operator << (ostream& os, const Fp<MOD>& x) noexcept {
        return os << x.val;
    }
    friend constexpr Fp<MOD> modpow(const Fp<MOD>& a, long long n) noexcept {
        if (n == 0) return 1;
        auto t = modpow(a, n / 2);
        t = t * t;
        if (n & 1) t = t * a;
        return t;
    }
};

namespace NTT {
    long long modpow(long long a, long long n, int mod) {
        long long res = 1;
        while (n > 0) {
            if (n & 1) res = res * a % mod;
            a = a * a % mod;
            n >>= 1;
        }
        return res;
    }

    long long modinv(long long a, int mod) {
        long long b = mod, u = 1, v = 0;
        while (b) {
            long long t = a / b;
            a -= t * b, swap(a, b);
            u -= t * v, swap(u, v);
        }
        u %= mod;
        if (u < 0) u += mod;
        return u;
    }

    int calc_primitive_root(int mod) {
        if (mod == 2) return 1;
        if (mod == 167772161) return 3;
        if (mod == 469762049) return 3;
        if (mod == 754974721) return 11;
        if (mod == 998244353) return 3;
        int divs[20] = {};
        divs[0] = 2;
        int cnt = 1;
        long long x = (mod - 1) / 2;
        while (x % 2 == 0) x /= 2;
        for (long long i = 3; i * i <= x; i += 2) {
            if (x % i == 0) {
                divs[cnt++] = i;
                while (x % i == 0) x /= i;
            }
        }
        if (x > 1) divs[cnt++] = x;
        for (int g = 2;; g++) {
            bool ok = true;
            for (int i = 0; i < cnt; i++) {
                if (modpow(g, (mod - 1) / divs[i], mod) == 1) {
                    ok = false;
                    break;
                }
            }
            if (ok) return g;
        }
    }

    int get_fft_size(int N, int M) {
        int size_a = 1, size_b = 1;
        while (size_a < N) size_a <<= 1;
        while (size_b < M) size_b <<= 1;
        return max(size_a, size_b) << 1;
    }

    // number-theoretic transform
    template<class mint> void trans(vector<mint> &v, bool inv = false) {
        if (v.empty()) return;
        int N = (int)v.size();
        int MOD = v[0].getmod();
        int PR = calc_primitive_root(MOD);
        static bool first = true;
        static vector<long long> vbw(30), vibw(30);
        if (first) {
            first = false;
            for (int k = 0; k < 30; ++k) {
                vbw[k] = modpow(PR, (MOD - 1) >> (k + 1), MOD);
                vibw[k] = modinv(vbw[k], MOD);
            }
        }
        for (int i = 0, j = 1; j < N - 1; j++) {
            for (int k = N >> 1; k > (i ^= k); k >>= 1);
            if (i > j) swap(v[i], v[j]);
        }
        for (int k = 0, t = 2; t <= N; ++k, t <<= 1) {
            long long bw = vbw[k];
            if (inv) bw = vibw[k];
            for (int i = 0; i < N; i += t) {
            mint w = 1;
                for (int j = 0; j < t/2; ++j) {
                    int j1 = i + j, j2 = i + j + t/2;
                    mint c1 = v[j1], c2 = v[j2] * w;
                    v[j1] = c1 + c2;
                    v[j2] = c1 - c2;
                    w *= bw;
                }
            }
        }
        if (inv) {
            long long invN = modinv(N, MOD);
            for (int i = 0; i < N; ++i) v[i] = v[i] * invN;
        }
    }

    // for garner
    static constexpr int MOD0 = 754974721;
    static constexpr int MOD1 = 167772161;
    static constexpr int MOD2 = 469762049;
    using mint0 = Fp<MOD0>;
    using mint1 = Fp<MOD1>;
    using mint2 = Fp<MOD2>;
    static const mint1 imod0 = 95869806; // modinv(MOD0, MOD1);
    static const mint2 imod1 = 104391568; // modinv(MOD1, MOD2);
    static const mint2 imod01 = 187290749; // imod1 / MOD0;

    // small case (T = mint, long long)
    template<class T> vector<T> naive_mul 
    (const vector<T> &A, const vector<T> &B) {
        if (A.empty() || B.empty()) return {};
        int N = (int)A.size(), M = (int)B.size();
        vector<T> res(N + M - 1);
        for (int i = 0; i < N; ++i)
            for (int j = 0; j < M; ++j)
                res[i + j] += A[i] * B[j];
        return res;
    }

    // mint
    template<class mint> vector<mint> mul
    (const vector<mint> &A, const vector<mint> &B) {
        if (A.empty() || B.empty()) return {};
        int N = (int)A.size(), M = (int)B.size();
        if (min(N, M) < 30) return naive_mul(A, B);
        int MOD = A[0].getmod();
        int size_fft = get_fft_size(N, M);
        if (MOD == 998244353) {
            vector<mint> a(size_fft), b(size_fft), c(size_fft);
            for (int i = 0; i < N; ++i) a[i] = A[i];
            for (int i = 0; i < M; ++i) b[i] = B[i];
            trans(a), trans(b);
            vector<mint> res(size_fft);
            for (int i = 0; i < size_fft; ++i) res[i] = a[i] * b[i];
            trans(res, true);
            res.resize(N + M - 1);
            return res;
        }
        vector<mint0> a0(size_fft, 0), b0(size_fft, 0), c0(size_fft, 0);
        vector<mint1> a1(size_fft, 0), b1(size_fft, 0), c1(size_fft, 0);
        vector<mint2> a2(size_fft, 0), b2(size_fft, 0), c2(size_fft, 0);
        for (int i = 0; i < N; ++i)
            a0[i] = A[i].val, a1[i] = A[i].val, a2[i] = A[i].val;
        for (int i = 0; i < M; ++i)
            b0[i] = B[i].val, b1[i] = B[i].val, b2[i] = B[i].val;
        trans(a0), trans(a1), trans(a2), trans(b0), trans(b1), trans(b2);
        for (int i = 0; i < size_fft; ++i) {
            c0[i] = a0[i] * b0[i];
            c1[i] = a1[i] * b1[i];
            c2[i] = a2[i] * b2[i];
        }
        trans(c0, true), trans(c1, true), trans(c2, true);
        static const mint mod0 = MOD0, mod01 = mod0 * MOD1;
        vector<mint> res(N + M - 1);
        for (int i = 0; i < N + M - 1; ++i) {
            int y0 = c0[i].val;
            int y1 = (imod0 * (c1[i] - y0)).val;
            int y2 = (imod01 * (c2[i] - y0) - imod1 * y1).val;
            res[i] = mod01 * y2 + mod0 * y1 + y0;
        }
        return res;
    }

    // long long
    vector<long long> mul_ll
    (const vector<long long> &A, const vector<long long> &B) {
        if (A.empty() || B.empty()) return {};
        int N = (int)A.size(), M = (int)B.size();
        if (min(N, M) < 30) return naive_mul(A, B);
        int size_fft = get_fft_size(N, M);
        vector<mint0> a0(size_fft, 0), b0(size_fft, 0), c0(size_fft, 0);
        vector<mint1> a1(size_fft, 0), b1(size_fft, 0), c1(size_fft, 0);
        vector<mint2> a2(size_fft, 0), b2(size_fft, 0), c2(size_fft, 0);
        for (int i = 0; i < N; ++i)
            a0[i] = A[i], a1[i] = A[i], a2[i] = A[i];
        for (int i = 0; i < M; ++i)
            b0[i] = B[i], b1[i] = B[i], b2[i] = B[i];
        trans(a0), trans(a1), trans(a2), trans(b0), trans(b1), trans(b2);
        for (int i = 0; i < size_fft; ++i) {
            c0[i] = a0[i] * b0[i];
            c1[i] = a1[i] * b1[i];
            c2[i] = a2[i] * b2[i];
        }
        trans(c0, true), trans(c1, true), trans(c2, true);
        static const long long mod0 = MOD0, mod01 = mod0 * MOD1;
        vector<long long> res(N + M - 1);
        for (int i = 0; i < N + M - 1; ++i) {
            int y0 = c0[i].val;
            int y1 = (imod0 * (c1[i] - y0)).val;
            int y2 = (imod01 * (c2[i] - y0) - imod1 * y1).val;
            res[i] = mod01 * y2 + mod0 * y1 + y0;
        }
        return res;
    }
};

// Binomial coefficient
template<class T> struct BiCoef {
    vector<T> fact_, inv_, finv_;
    constexpr BiCoef() {}
    constexpr BiCoef(int n) noexcept : fact_(n, 1), inv_(n, 1), finv_(n, 1) {
        init(n);
    }
    constexpr void init(int n) noexcept {
        fact_.assign(n, 1), inv_.assign(n, 1), finv_.assign(n, 1);
        int MOD = fact_[0].getmod();
        for(int i = 2; i < n; i++){
            fact_[i] = fact_[i-1] * i;
            inv_[i] = -inv_[MOD%i] * (MOD/i);
            finv_[i] = finv_[i-1] * inv_[i];
        }
    }
    constexpr T com(int n, int k) const noexcept {
        if (n < k || n < 0 || k < 0) return 0;
        return fact_[n] * finv_[k] * finv_[n-k];
    }
    constexpr T fact(int n) const noexcept {
        if (n < 0) return 0;
        return fact_[n];
    }
    constexpr T inv(int n) const noexcept {
        if (n < 0) return 0;
        return inv_[n];
    }
    constexpr T finv(int n) const noexcept {
        if (n < 0) return 0;
        return finv_[n];
    }
};

const int MOD = 1e9+7;
using mint = Fp<MOD>;

template < class T >
struct vec : public vector< T > {
    vec() : vector< T >() {}
    vec(int n, T e = 0) : vector< T >(n, e) {}
    vec(initializer_list< T > v) : vector< T >(v) {}
    int size() const { return vector< T >::size(); }
    vec& operator+=(const vec& rhs) {
        assert(size() == rhs.size());
        rep(i,size()) (*this)[i] += rhs[i];
        return *this;
    }
    vec& operator-=(const vec& rhs) {
        assert(size() == rhs.size());
        rep(i,size()) (*this)[i] -= rhs[i];
        return *this;
    }
    vec& operator*=(T x) {
        rep(i,size()) (*this)[i] *= x;
        return *this;
    }
    vec& operator/=(T x) {
        x = T(1) / x;
        rep(i,size()) (*this)[i] *= x;
        return *this;
    }
    vec operator+(const vec& rhs) const { return vec(*this) += rhs; }
    vec operator-(const vec& rhs) const { return vec(*this) -= rhs; }
    vec operator*(T x) const { return vec(*this) *= x; }
    vec operator/(T x) const { return vec(*this) /= x; }
    bool operator==(const vec& rhs) const {
        rep(i,size()) if((*this)[i] != rhs[i]) return false;
        return true;
    }
};

template < class T >
T dot(const vec< T >& a, const vec< T >& b) {
    assert(a.size() == b.size());
    T res(0);
    rep(i,a.size()) res += a[i] * b[i];
    return res;
}

template < class T >
struct mat : public vec< vec< T > > {
    mat(int h, int w, T e = 0) : vec< vec< T > >(h, vec< T >(w, e)) {}
    mat(initializer_list< initializer_list< T > > m) : vec< vec< T > >(m.size()) {
        auto it = m.begin();
        for(int i = 0; it != m.end(); i++, it++) (*this)[i] = vec< T >(*it);
    }
    int size() const { return vec< vec< T > >::size(); }
    mat operator*(const mat &rhs) const {
        int N = (*this).size(), M = (*this)[0].size(), K = rhs[0].size();
        assert((*this)[0].size() == rhs.size());
        mat res(N, K);
        rep(k,M)rep(i,N)rep(j,K) res[i][j] += (*this)[i][k] * rhs[k][j];
        return res;
    }
    mat& operator*=(const mat &rhs) { return *this = (*this) * rhs; }
    vec< T > operator*(const vec< T >& rhs) const {
        assert((*this)[0].size() == rhs.size());
        vec< T > res(size());
        rep(i,size()) res[i] = dot((*this)[i], rhs);
        return res;
    }
    vec< T >& operator[](int i) { return vec< vec< T > >::operator[](i); }
    const vec< T >& operator[](int i) const { return vec< vec< T > >::operator[](i); }
    mat& operator/=(T x) { rep(i,size()) (*this)[i] /= x; return *this; }
    mat operator/(T x) const { return (*this) /= x; }
    bool operator==(const mat& rhs) const {
        rep(i,size()) if((*this)[i] != rhs[i]) return false;
        return true;
    }
};

template < class T >
struct msq : public mat< T > {
    msq(int n, T e = 0) : mat< T >(n, n, e) {}
    msq(initializer_list< initializer_list< T > > m) : mat< T >(m) {}
    msq unit() const {
        msq I((*this).size());
        rep(i,(*this).size()) I[i][i] = T(1);
        return I;
    }
    msq pow(ll n) const {
        msq res = unit(), A = (*this);
        while(n > 0) {
            if(n & 1) res *= A;
            A *= A;
            n >>= 1;
        }
        return res;
    }
    T det() const {
        msq A = *this;
        T res = 1;
        rep(i,A.size()) {
            if(A[i][i] == T(0)) {
                for(int j = i + 1; j < A.size(); j++) if(A[j][i] != T(0)) {
                    for(int k = i; k < A.size(); k++) swap(A[i][k], A[j][k]);
                    res *= T(-1);
                    break;
                }
            }
            if(A[i][i] == T(0)) return T(0);
            res *= A[i][i];
            const T x = T(1) / A[i][i];
            for(int k = i; k < A.size(); k++) A[i][k] *= x;
            for(int j = i + 1; j < A.size(); j++) {
                const T x = A[j][i];
                for(int k = i; k < A.size(); k++) A[j][k] -= A[i][k] * x;
            }
        }
        return res;
    }
    msq inv() const {
        msq A = *this, B = unit();
        rep(i,A.size()) {
            if(A[i][i] == T(0)) {
                for(int j = i + 1; j < A.size(); j++) if(A[j][i] != T(0)) {
                    for(int k = i; k < A.size(); k++) swap(A[i][k], A[j][k]);
                    for(int k = 0; k < A.size(); k++) swap(B[i][k], B[j][k]);
                    break;
                }
            }
            if(A[i][i] == T(0)) throw "this matrix is not regular.";
            const T x = T(1) / A[i][i];
            for(int k = i; k < A.size(); k++) A[i][k] *= x;
            for(int k = 0; k < A.size(); k++) B[i][k] *= x;
            for(int j = 0; j < A.size(); j++) if(i != j) {
                const T x = A[j][i];
                for(int k = i; k < A.size(); k++) A[j][k] -= A[i][k] * x;
                for(int k = 0; k < A.size(); k++) B[j][k] -= B[i][k] * x;
            }
        }
        return B;
    }
};

int main(){
    cin.tie(0);
    ios::sync_with_stdio(0);
    
    ll a,b,n; cin >> a >> b >> n;
    msq<mint> A = {
        {a, b},
        {1, 0}
    };

    cout << A.pow(n)[1][0] << "\n";
}

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テストケース

ソースコード