結果

問題 No.891 隣接3項間の漸化式
ユーザー alexara1123alexara1123
提出日時 2019-09-21 00:02:25
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 5,889 bytes
コンパイル時間 1,232 ms
コンパイル使用メモリ 101,752 KB
実行使用メモリ 6,948 KB
最終ジャッジ日時 2024-09-15 05:54:26
合計ジャッジ時間 2,797 ms
ジャッジサーバーID
(参考情報)
judge1 / judge3
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 * 39
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 <cstdio>
#include <cstdlib>
#include <algorithm>
#include <vector>
#include <cstring>
#include <queue>
#include <set>
#include <unordered_set>
#include <unordered_map>
#include <map>
#include <functional>
#include <cmath>
#include <cassert>
#include <string>
#include <iostream>
using namespace std;
typedef long long ll;
ll MOD = 1000000007;
typedef pair<int, int> P;
template <class T>
ostream &operator<<(ostream &o, const vector<T> &v)
{
o << "{";
for (int i = 0; i < (int)v.size(); i++)
o << (i > 0 ? ", " : "") << v[i];
o << "}";
return o;
}
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);
}
};
const int mod = 1e9 + 7;
using modint = ModInt<mod>;
template <class T>
struct Matrix
{
vector<vector<T>> A;
Matrix() {}
Matrix(size_t n, size_t m) : A(n, vector<T>(m, 0)) {}
Matrix(size_t n) : A(n, vector<T>(n, 0)){};
size_t height() const
{
return (A.size());
}
size_t width() const
{
return (A[0].size());
}
inline const vector<T> &operator[](int k) const
{
return (A.at(k));
}
inline 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());
vector<vector<T>> C(n, 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^=(long long k)
{
Matrix B = Matrix::I(height());
while (k > 0)
{
if (k & 1)
B *= *this;
*this *= *this;
k >>= 1LL;
}
A.swap(B.A);
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);
}
Matrix operator^(const long long k) const
{
return (Matrix(*this) ^= k);
}
friend ostream &operator<<(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);
}
};
int main()
{
ios::sync_with_stdio(false);
cin.tie(0);
int a, b, n;
cin >> a >> b >> n;
Matrix<modint> m(2);
m[0][0] = a;
m[0][1] = b;
m[1][0] = 1;
//m[1][1] = 0;
m ^= n;
cout << m[1][0] << endl;
}
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