結果
問題 |
No.718 行列のできるフィボナッチ数列道場 (1)
|
ユーザー |
|
提出日時 | 2023-01-02 21:53:53 |
言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 2 ms / 2,000 ms |
コード長 | 3,229 bytes |
コンパイル時間 | 1,938 ms |
コンパイル使用メモリ | 202,564 KB |
最終ジャッジ日時 | 2025-02-09 23:05:49 |
ジャッジサーバーID (参考情報) |
judge5 / judge4 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 3 |
other | AC * 20 |
ソースコード
#include <bits/stdc++.h> using namespace std; const int mod = 1000000007; template< int mod > struct ModInt { int 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 = (int) (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 { int 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 int get_mod() { return mod; } }; using mint = ModInt< mod >; vector<vector<mint>> mul(vector<vector<mint>> &A, vector<vector<mint>> &B) { int a = A.size(); int b = B[0].size(); int c = B.size(); vector<vector<mint>> ret(a, vector<mint>(b)); for (int i = 0; i < a; i++) { for (int j = 0; j < b; j++) { for (int k = 0; k < c; k++) { ret[i][j] += A[i][k] * B[k][j]; } } } return ret; } vector<vector<mint>> A = {{1, 1, 2}, {1, 0, 0}, {1, 0, 1}}; vector<mint> b = {1, 0, 0}; int main() { long long N; cin >> N; N -= 3; vector<vector<mint>> B(6, vector<mint>(6)); for (int i = 0; i < 3; i++) { for (int j = 0; j < 3; j++) { B[i][j] = B[i][j+3] = A[i][j]; } B[i+3][i+3] = 1; } vector<vector<mint>> E(6, vector<mint>(6)); for (int i = 0; i < 6; i++) E[i][i] = 1; while (N > 0) { if (N & 1) { E = mul(B, E); } B = mul(B, B); N >>= 1; } vector<vector<mint>> C(6, vector<mint>(3)); for (int i = 0; i < 3; i++) { for (int j = 0; j < 3; j++) { C[i][j] = A[i][j]; } C[i+3][i] = 1; } E = mul(E, C); mint ans = 2; for (int i = 0; i < 3; i++) ans += E[0][i]; cout << ans << endl; }