結果

問題 No.194 フィボナッチ数列の理解(1)
ユーザー risujirohrisujiroh
提出日時 2019-03-17 05:55:45
言語 C++14
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 152 ms / 5,000 ms
コード長 3,848 bytes
コンパイル時間 1,461 ms
コンパイル使用メモリ 176,612 KB
実行使用メモリ 7,168 KB
最終ジャッジ日時 2024-07-05 19:02:06
合計ジャッジ時間 3,144 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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ファイルパターン 結果
sample AC * 3
other AC * 37
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 #
プレゼンテーションモードにする

#include <bits/stdc++.h>
using namespace std;
using lint = long long;
template<class T = int> using V = vector<T>;
template<class T = int> using VV = V< V<T> >;
template<unsigned P> struct ModInt {
using M = ModInt;
unsigned v;
ModInt() : v(0) {}
template<class Z> ModInt(Z x) : v(x >= 0 ? x % P : -x % P ? P - -x % P : 0) {}
constexpr ModInt(unsigned v, int) : v(v) {}
static constexpr unsigned p() { return P; }
M operator+() const { return *this; }
M operator-() const { return {v ? P - v : 0, 0}; }
explicit operator bool() const noexcept { return v; }
bool operator!() const noexcept { return !(bool) *this; }
M operator*(M r) const { return M(*this) *= r; }
M operator/(M r) const { return M(*this) /= r; }
M operator+(M r) const { return M(*this) += r; }
M operator-(M r) const { return M(*this) -= r; }
bool operator==(M r) const { return v == r.v; }
bool operator!=(M r) const { return !(*this == r); }
M& operator*=(M r) { v = (uint64_t) v * r.v % P; return *this; }
M& operator/=(M r) { return *this *= r.inv(); }
M& operator+=(M r) { v = r.v < P - v ? v + r.v : v - (P - r.v); return *this; }
M& operator-=(M r) { v = r.v <= v ? v - r.v : v + (P - r.v); return *this; }
M inv() const {
int a = v, b = P, x = 1, u = 0;
while (b) {
int q = a / b;
swap(a -= q * b, b);
swap(x -= q * u, u);
}
assert(a == 1);
return x;
}
template<class Z> M pow(Z n) const {
n = n >= 0 ? n % (P - 1) : P - 1 - -n % (P - 1);
M res = 1;
for (M a = *this; n; a *= a, n >>= 1) if (n & 1) res *= a;
return res;
}
template<class Z> friend M operator*(Z l, M r) { return M(l) *= r; }
template<class Z> friend M operator/(Z l, M r) { return M(l) /= r; }
template<class Z> friend M operator+(Z l, M r) { return M(l) += r; }
template<class Z> friend M operator-(Z l, M r) { return M(l) -= r; }
friend ostream& operator<<(ostream& os, M r) { return os << r.v; }
friend istream& operator>>(istream& is, M& r) { lint x; is >> x; r = x; return is; }
template<class Z> friend bool operator==(Z l, M r) { return M(l) == r; }
template<class Z> friend bool operator!=(Z l, M r) { return !(l == r); }
};
using Mint = ModInt<(unsigned) 1e9 + 7>;
template<class T> VV<T> operator*(const VV<T>& A, const VV<T>& B) {
assert(A[0].size() == B.size());
VV<T> res(A.size(), V<T>(B[0].size()));
for (int i = 0; i < A.size(); ++i) for (int k = 0; k < A[0].size(); ++k) for (int j = 0; j < B[0].size(); ++j) {
res[i][j] += A[i][k] * B[k][j];
}
return res;
}
template<class T> VV<T>& operator*=(VV<T>& A, const VV<T>& B) { return A = A * B; }
template<class T> VV<T> I(int n) {
VV<T> res(n, V<T>(n));
for (int i = 0; i < n; ++i) res[i][i] = 1;
return res;
}
template<class T> VV<T> pow(VV<T> A, lint n) {
auto res = I<T>(A.size());
while (n) {
if (n & 1) res *= A;
A *= A;
n >>= 1;
}
return res;
}
int main() {
cin.tie(nullptr); ios::sync_with_stdio(false);
lint n, k; cin >> n >> k;
V<Mint> a(n); for (auto&& e : a) cin >> e;
if (k <= 1e6) {
a.resize(k);
for (int i = n; i < 2 * n; ++i) {
for (int j = 1; j <= n; ++j) {
a[i] += a[i - j];
}
}
for (int i = 2 * n; i < k; ++i) {
a[i] = 2 * a[i - 1] - (i - n - 1 >= 0 ? a[i - n - 1] : 0);
}
Mint res = accumulate(begin(a), end(a), Mint(0));
cout << a.back() << ' ' << res << '\n';
} else {
VV<Mint> A(n + 1, V<Mint>(n + 1));
for (int j = 0; j < n; ++j) {
A[0][j] = 1;
if (j + 1 < n) A[j + 1][j] = 1;
}
A[n][n - 1] = A[n][n] = 1;
A = pow(A, k - 1);
Mint res;
for (int j = 0; j < n; ++j) {
res += A[n - 1][j] * a[n - 1 - j];
}
Mint sum = res;
for (int j = 0; j < n; ++j) {
sum += A[n][n - 1 - j] * a[j];
}
cout << res << ' ' << sum << '\n';
}
}
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