#428820 (C++14) No.194 フィボナッチ数列の理解(1)

提出ソース

結果

問題	No.194 フィボナッチ数列の理解(1)
ユーザー	haruki_K
提出日時	2020-02-12 02:01:20
言語	C++14 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	10 ms / 5,000 ms
コード長	9,909 bytes
コンパイル時間	1,993 ms
コンパイル使用メモリ	179,832 KB
実行使用メモリ	7,168 KB
最終ジャッジ日時	2024-10-01 15:20:42
合計ジャッジ時間	3,030 ms
ジャッジサーバーID （参考情報）	judge5 / judge1

このコードへのチャレンジ
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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	1 ms 5,248 KB
testcase_02	AC	7 ms 5,248 KB
testcase_03	AC	2 ms 5,248 KB
testcase_04	AC	3 ms 5,248 KB
testcase_05	AC	3 ms 5,248 KB
testcase_06	AC	4 ms 5,248 KB
testcase_07	AC	5 ms 5,248 KB
testcase_08	AC	2 ms 5,248 KB
testcase_09	AC	4 ms 5,248 KB
testcase_10	AC	2 ms 5,248 KB
testcase_11	AC	3 ms 5,248 KB
testcase_12	AC	3 ms 5,248 KB
testcase_13	AC	2 ms 5,248 KB
testcase_14	AC	1 ms 5,248 KB
testcase_15	AC	6 ms 5,248 KB
testcase_16	AC	5 ms 5,248 KB
testcase_17	AC	2 ms 5,248 KB
testcase_18	AC	5 ms 5,248 KB
testcase_19	AC	7 ms 5,248 KB
testcase_20	AC	10 ms 7,136 KB
testcase_21	AC	10 ms 7,168 KB
testcase_22	AC	10 ms 6,948 KB
testcase_23	AC	3 ms 5,248 KB
testcase_24	AC	6 ms 5,248 KB
testcase_25	AC	5 ms 5,248 KB
testcase_26	AC	6 ms 5,248 KB
testcase_27	AC	6 ms 5,376 KB
testcase_28	AC	2 ms 5,248 KB
testcase_29	AC	10 ms 6,784 KB
testcase_30	AC	7 ms 5,248 KB
testcase_31	AC	2 ms 5,248 KB
testcase_32	AC	3 ms 5,248 KB
testcase_33	AC	4 ms 5,248 KB
testcase_34	AC	3 ms 5,248 KB
testcase_35	AC	3 ms 5,248 KB
testcase_36	AC	5 ms 5,248 KB
testcase_37	AC	1 ms 5,248 KB
testcase_38	AC	6 ms 5,248 KB
testcase_39	AC	4 ms 5,248 KB

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ソースコード

raw source code

// >>> TEMPLATES
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ld = long double;
#define int ll
#define double ld
#define rep(i,n) for (int i = 0; i < (int)(n); i++)
#define rep1(i,n) for (int i = 1; i <= (int)(n); i++)
#define repR(i,n) for (int i = (int)(n)-1; i >= 0; i--)
#define rep1R(i,n) for (int i = (int)(n); i >= 1; i--)
#define loop(i,a,B) for (int i = a; i B; i++)
#define loopR(i,a,B) for (int i = a; i B; i--)
#define all(x) (x).begin(), (x).end()
#define allR(x) (x).rbegin(), (x).rend()
#define pb push_back
#define eb emplace_back
#define mp make_pair
#define fst first
#define snd second
#define INF (numeric_limits<int>::max()/2-1)
#ifdef LOCAL
#include "debug.hpp"
#define dump(...) cerr << "[" << __LINE__ << ":" << __FUNCTION__ << "] ", dump_impl(#__VA_ARGS__, __VA_ARGS__)
#define say(x) cerr << "[" << __LINE__ << ":" << __FUNCTION__ << "] " << x << endl
#define debug if (1)
#else
#define dump(...) (void)(0)
#define say(x) (void)(0)
#define debug if (0)
#endif
template <class T> using pque_max = priority_queue<T>;
template <class T> using pque_min = priority_queue<T, vector<T>, greater<T> >;
template <class T, class = typename T::iterator, class = typename enable_if<!is_same<T, string>::value>::type>
ostream& operator<<(ostream& os, T const& v) { bool f = true; for (auto const& x : v) os << (f ? "" : " ") << x, f = false; return os; }
template <class T, class = typename T::iterator, class = typename enable_if<!is_same<T, string>::value>::type>
istream& operator>>(istream& is, T &v) { for (auto& x : v) is >> x; return is; }
template <class T, class S> istream& operator>>(istream& is, pair<T,S>& p) { return is >> p.first >> p.second; }
struct IOSetup { IOSetup() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(15); } } iosetup;
template <class F> struct FixPoint : private F {
    constexpr FixPoint(F&& f) : F(forward<F>(f)) {}
    template <class... T> constexpr auto operator()(T&&... x) const { return F::operator()(*this, forward<T>(x)...); }
};
struct MakeFixPoint {
    template <class F> constexpr auto operator|(F&& f) const { return FixPoint<F>(forward<F>(f)); }
};
#define MFP MakeFixPoint()|
#define def(name, ...) auto name = MFP [&](auto &&name, __VA_ARGS__)
template <class T, size_t d> struct vec_impl {
    using type = vector<typename vec_impl<T,d-1>::type>;
    template <class... U> static type make_v(size_t n, U&&... x) { return type(n, vec_impl<T,d-1>::make_v(forward<U>(x)...)); }
};
template <class T> struct vec_impl<T,0> { using type = T; static type make_v(T const& x = {}) { return x; } };
template <class T, size_t d = 1> using vec = typename vec_impl<T,d>::type;
template <class T, size_t d = 1, class... Args> auto make_v(Args&&... args) { return vec_impl<T,d>::make_v(forward<Args>(args)...); }
template <class T> void quit(T const& x) { cout << x << endl; exit(0); }
template <class T> constexpr bool chmin(T& x, T const& y) { if (x > y) { x = y; return true; } return false; }
template <class T> constexpr bool chmax(T& x, T const& y) { if (x < y) { x = y; return true; } return false; }
template <class It> constexpr auto sumof(It b, It e) { return accumulate(b,e,typename iterator_traits<It>::value_type{}); }
template <class T> int sz(T const& x) { return x.size(); }
template <class C, class T> int lbd(C const& v, T const& x) {
    return lower_bound(v.begin(), v.end(), x)-v.begin();
}
template <class C, class T> int ubd(C const& v, T const& x) {
    return upper_bound(v.begin(), v.end(), x)-v.begin();
}
// <<<
// >>> modint
template <uint32_t MOD>
struct ModInt {
    using u32 = uint32_t;
    using u64 = uint64_t;
    using i64 = int64_t;
    using M = ModInt;

    static constexpr u32 mul_inv(u32 n, int e = 5, u32 x = 1) {
        return e == 0 ? x : mul_inv(n, e-1, x*(2-x*n));
    }
    static constexpr u32 mod = MOD;
    static constexpr u32 nn = mul_inv(MOD);
    static constexpr u32 r2 = -u64(MOD) % MOD;

    u32 x;
    constexpr ModInt(i64 x = 0) : x(reduce(((x%=MOD)<0 ? x+MOD : x)*r2)) {}
    static constexpr u32 reduce(u64 w) {
        return u32(w >> 32) + MOD - i64((u64(u32(w) * nn) * MOD) >> 32);
    }
    constexpr i64 val() const {
        i64 r = reduce(x);
        if (r >= MOD) r -= MOD;
        return r;
    }
    constexpr explicit operator i64() const { return val(); }
    constexpr bool operator==(M p) const { return val() == p.val(); }
    constexpr bool operator!=(M p) const { return val() != p.val(); }
    constexpr M operator+() const { return *this; }
    constexpr M operator-() const { M r; r.x = x ? i64(2*MOD)-x : 0; return r; }
    constexpr M &operator+=(M p) {
        i64 t = x; if (((t += p.x) -= 2*MOD) < 0) t += 2*MOD;
        x = t;
        return *this;
    }
    constexpr M &operator-=(M p) { return *this += -p; }
    constexpr M &operator*=(M p) { x = reduce(u64(x)*p.x); return *this; }
    constexpr M &operator/=(M p) { *this *= p.inv(); return *this; }

    constexpr M operator+(M p) const { return M(*this) += p; }
    constexpr M operator-(M p) const { return M(*this) -= p; }
    constexpr M operator*(M p) const { return M(*this) *= p; }
    constexpr M operator/(M p) const { return M(*this) /= p; }
    friend constexpr M operator+(i64 x, M y) { return M(x)+y; }
    friend constexpr M operator-(i64 x, M y) { return M(x)-y; }
    friend constexpr M operator*(i64 x, M y) { return M(x)*y; }
    friend constexpr M operator/(i64 x, M y) { return M(x)/y; }

    constexpr M inv() const { return pow(MOD - 2); }
    constexpr M pow(i64 n) const {
        if (n < 0) return inv().pow(-n);
        M v = *this, r = 1;
        for (; n > 0; n >>= 1, v *= v) if (n&1) r *= v;
        return r;
    }

    friend ostream &operator<<(ostream &os, M p) {
        return os << p.val();
    }
    friend istream &operator>>(istream &is, M &a) {
        u32 t; is >> t; a = t; return is;
    }
#ifdef LOCAL
    friend string to_s(M const& p) { return to_s(p.val(), MOD); }
#endif
};
// <<<
//constexpr int64_t MOD = 998244353;
constexpr int64_t MOD = 1e9+7;
using mint = ModInt<MOD>;
// >>> matrix
template <class T>
struct Matrix {
    int n,m;
    vector<vector<T> > a;
    Matrix() {}
    Matrix(int n, int m) : n(n), m(m), a(n) {
        assert(n > 0 && m > 0);
        rep (i,n) a[i].resize(m);
    }
    Matrix(initializer_list<initializer_list<T> > init) {
        for (auto ls : init) {
            a.emplace_back();
            for (auto x : ls) a.back().emplace_back(x);
        }
        n = a.size(); assert(n > 0);
        m = a[0].size(); assert(m > 0);
    }
    vector<T> const& operator[](int i) const {
        assert(0 <= i && i < n);
        return a[i];
    }
    vector<T> & operator[](int i) {
        assert(0 <= i && i < n);
        return a[i];
    }
    bool operator==(Matrix const& x) const {
        if (n != x.n || m != x.m) return false;
        rep (i,n) rep (j,m) if (a[i][j] != x[i][j]) return false;
        return true;
    }
    bool operator!=(Matrix const& x) const {
        return !(*this == x);
    }
    Matrix& operator+=(Matrix const& x) {
        assert(n == x.n && m == x.m);
        rep (i,n) rep (j,m) a[i][j] += x[i][j];
        return *this;
    }
    Matrix& operator-=(Matrix const& x) {
        assert(n == x.n && m == x.m);
        rep (i,n) rep (j,m) a[i][j] -= x[i][j];
        return *this;
    }
    Matrix operator+(Matrix const& x) const { return Matrix(*this) += x; }
    Matrix operator-(Matrix const& x) const { return Matrix(*this) -= x; }
    Matrix operator*(Matrix const& x) const {
        assert(m == x.n);
        Matrix ret(n,x.m);
        rep (i,n) rep (j,m) rep (k,x.m) ret[i][k] += a[i][j] * x[j][k];
        return ret;
    }
    Matrix& operator*=(Matrix const& x) {
        auto res = (*this)*x;
        swap(a, res.a);
        return *this;
    }
	Matrix operator+() const { return *this; }
	Matrix operator-() const {
		Matrix x = *this;
        rep (i,n) rep (j,m) x[i][j] = -x[i][j];
		return x;
	}
    Matrix& operator*=(T const& c) {
        rep (i,n) rep (j,m) a[i][j] *= c;
        return *this;
    }
    Matrix operator*(T const& c) const { return Matrix(*this) *= c; }
    friend Matrix operator*(T const& c, Matrix const& x) {
        Matrix ret = x;
        rep (i,x.n) rep (j,x.m) ret[i][j] = c*x[i][j];
        return ret;
    }
    Matrix& operator/=(T const& c) {
        rep (i,n) rep (j,m) a[i][j] /= c;
        return *this;
    }
    Matrix operator/(T const& c) const {
        return Matrix(*this) /= c;
    }
    static Matrix identity(int n) {
        Matrix ret(n,n);
        rep (i,n) ret[i][i] = 1;
        return ret;
    }
    Matrix pow(ll k) const {
        assert(n == m); assert(k >= 0);
        Matrix v = *this, r = Matrix::identity(n);
        for (; k > 0; k >>= 1, v *= v) if (k&1) r *= v;
        return r;
    }
    friend istream& operator>>(istream& is, Matrix& x) {
        rep (i,x.n) rep (j,x.m) is >> x[i][j];
        return is;
    }
#ifdef LOCAL
    friend string to_s(Matrix const& x) {
        string ret;
        rep (i,x.n) {
            ret += "\n(";
            rep (j,x.m) ret += " " + to_s(x[i][j]);
            ret += " )";
        }
        return ret += "\n";
    }
#endif
};
// <<<

int32_t main() {
    int n,k; cin >> n >> k;
    vector<int> a(n); cin >> a;

    if (k <= int(1e6+10)) {
        vector<mint> s(k+1);
        rep (i,n) s[i+1] = s[i] + a[i];
        loop (i,n,<k) s[i+1] = 2*s[i] - s[i-n];
        cout << s[k]-s[k-1] << " " << s[k] << endl;
    } else {
        Matrix<mint> mat(n+1,n+1);
        mat[0][0] = 2; mat[0][n] = -1;
        rep (i,n) mat[i+1][i] = 1;
        dump(mat);
        auto res = mat.pow(k-n);

        vector<mint> s(n+1);
        rep (i,n) s[i+1] = s[i] + a[i];

        mint x = 0, y = 0;
        rep (i,n+1) x += res[0][i] * s[n-i];
        rep (i,n+1) y += res[1][i] * s[n-i];
        cout << x-y << " " << x << endl;
    }
}

yukicoder

結果

テストケース

ソースコード