結果
| 問題 |
No.720 行列のできるフィボナッチ数列道場 (2)
|
| コンテスト | |
| ユーザー |
 🍮かんプリン
|
| 提出日時 | 2020-10-06 16:27:27 |
| 言語 | C++14 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 2 ms / 2,000 ms |
| コード長 | 6,166 bytes |
| コンパイル時間 | 1,685 ms |
| コンパイル使用メモリ | 175,344 KB |
| 実行使用メモリ | 5,376 KB |
| 最終ジャッジ日時 | 2024-07-20 02:06:39 |
| 合計ジャッジ時間 | 2,369 ms |
|
ジャッジサーバーID （参考情報） |
judge4 / judge3 |
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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
/**
* @FileName a.cpp
* @Author kanpurin
* @Created 2020.10.06 16:27:22
**/
#include "bits/stdc++.h"
using namespace std;
typedef long long ll;
template< int MOD >
struct mint {
public:
long long x;
mint(long long x = 0) :x((x%MOD+MOD)%MOD) {}
mint(std::string &s) {
long long z = 0;
for (int i = 0; i < s.size(); i++) {
z *= 10;
z += s[i] - '0';
z %= MOD;
}
this->x = z;
}
mint& operator+=(const mint &a) {
if ((x += a.x) >= MOD) x -= MOD;
return *this;
}
mint& operator-=(const mint &a) {
if ((x += MOD - a.x) >= MOD) x -= MOD;
return *this;
}
mint& operator*=(const mint &a) {
(x *= a.x) %= MOD;
return *this;
}
mint& operator/=(const mint &a) {
long long n = MOD - 2;
mint u = 1, b = a;
while (n > 0) {
if (n & 1) {
u *= b;
}
b *= b;
n >>= 1;
}
return *this *= u;
}
mint operator+(const mint &a) const {
mint res(*this);
return res += a;
}
mint operator-() const {return mint() -= *this; }
mint operator-(const mint &a) const {
mint res(*this);
return res -= a;
}
mint operator*(const mint &a) const {
mint res(*this);
return res *= a;
}
mint operator/(const mint &a) const {
mint res(*this);
return res /= a;
}
friend std::ostream& operator<<(std::ostream &os, const mint &n) {
return os << n.x;
}
friend std::istream &operator>>(std::istream &is, mint &n) {
long long x;
is >> x;
n = mint(x);
return is;
}
bool operator==(const mint &a) const {
return this->x == a.x;
}
mint pow(long long k) const {
mint ret = 1;
mint p = this->x;
while (k > 0) {
if (k & 1) {
ret *= p;
}
p *= p;
k >>= 1;
}
return ret;
}
};
constexpr int MOD = 1e9 + 7;
template< class T >
struct Matrix {
std::vector< std::vector< T > > A;
Matrix() {}
Matrix(size_t n, size_t m) : A(n, std::vector< T >(m, 0)) {}
Matrix(size_t n) : A(n, std::vector< T >(n, 0)) {};
size_t height() const {
return (A.size());
}
size_t width() const {
return (A[0].size());
}
inline const std::vector< T > &operator[](int k) const {
return (A.at(k));
}
inline std::vector< T > &operator[](int k) {
return (A.at(k));
}
static Matrix I(size_t n) {
Matrix mat(n);
for (int i = 0; i < n; i++) mat[i][i] = 1;
return (mat);
}
Matrix &operator+=(const Matrix &B) {
size_t n = height(), m = width();
assert(n == B.height() && m == B.width());
for (int i = 0; i < n; i++)
for (int j = 0; j < m; j++)
(*this)[i][j] += B[i][j];
return (*this);
}
Matrix &operator-=(const Matrix &B) {
size_t n = height(), m = width();
assert(n == B.height() && m == B.width());
for (int i = 0; i < n; i++)
for (int j = 0; j < m; j++)
(*this)[i][j] -= B[i][j];
return (*this);
}
Matrix &operator*=(const Matrix &B) {
size_t n = height(), m = B.width(), p = width();
assert(p == B.height());
std::vector< std::vector< T > > C(n, std::vector< T >(m, 0));
for (int i = 0; i < n; i++)
for (int j = 0; j < m; j++)
for (int k = 0; k < p; k++)
C[i][j] = (C[i][j] + (*this)[i][k] * B[k][j]);
A.swap(C);
return (*this);
}
Matrix operator+(const Matrix &B) const {
return (Matrix(*this) += B);
}
Matrix operator-(const Matrix &B) const {
return (Matrix(*this) -= B);
}
Matrix operator*(const Matrix &B) const {
return (Matrix(*this) *= B);
}
bool operator==(const Matrix &B) const {
assert(this->A.size() == B.A.size() && this->A[0].size() == B.A[0].size());
int n = this->A.size();
int m = this->A[0].size();
for (int i = 0; i < n; i++)
for (int j = 0; j < m; j++)
if (this->A[i][j] != B.A[i][j]) return false;
return true;
}
bool operator!=(const Matrix &B) const {
return !(*this == B);
}
friend std::ostream &operator<<(std::ostream &os, Matrix &p) {
size_t n = p.height(), m = p.width();
for (int i = 0; i < n; i++) {
os << "[";
for (int j = 0; j < m; j++) {
os << p[i][j] << (j + 1 == m ? "]\n" : ",");
}
}
return (os);
}
T determinant() {
Matrix B(*this);
assert(width() == height());
T ret = 1;
for (int i = 0; i < width(); i++) {
int idx = -1;
for (int j = i; j < width(); j++) {
if (B[j][i] != 0) idx = j;
}
if (idx == -1) return (0);
if (i != idx) {
ret *= -1;
swap(B[i], B[idx]);
}
ret *= B[i][i];
T vv = B[i][i];
for (int j = 0; j < width(); j++) {
B[i][j] /= vv;
}
for (int j = i + 1; j < width(); j++) {
T a = B[j][i];
for (int k = 0; k < width(); k++) {
B[j][k] -= B[i][k] * a;
}
}
}
return (ret);
}
Matrix pow(ll k) const {
auto res = I(A.size());
auto M = *this;
while (k > 0) {
if (k & 1) {
res *= M;
}
M *= M;
k >>= 1;
}
return res;
}
};
int main() {
ll n,m;cin >> n >> m;
Matrix<mint<MOD>> mat1(3),mat2(3);
mat1[0][0] = mat1[1][1] = mat1[2][0] = mat1[2][2] = 1;
mat2[0][0] = mat2[0][1] = mat2[1][0] = mat2[2][2] = 1;
mat1 = (mat1 * mat2.pow(m)).pow(n);
cout << mat1[2][1] << endl;
return 0;
}