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| // (c) 2019, Lutfi Shihab
#include <iostream>
#include <vector>
// todo
template <typename T>
class Matrix
{
public:
Matrix(int rows, int cols) : m_rows(rows), m_cols(cols) {}
private:
int m_rows;
int m_cols;
};
/* function that returns nth Fibonacci number */
template <typename T>
class Fibonacci
{
public:
Fibonacci(T n) { m_fibNum = fib(n); }
operator T() const { return m_fibNum; }
operator int() const { return m_fibNum; }
friend std::ostream& operator<<(std::ostream& os, Fibonacci<T>& f)
{
return os << f.m_fibNum;
}
Fibonacci<T> operator+=(int k) { return m_fibNum += k; }
Fibonacci<T> operator %(int k) { return m_fibNum % k; }
Fibonacci<T> operator /(int k) { return m_fibNum / k; }
bool operator<=(int k) { return m_fibNum < k; }
bool operator >(int k) { return m_fibNum > k; }
bool operator==(int k) { return m_fibNum == k; }
private:
void multiply(T F[2][2], T M[2][2])
{
T x = F[0][0]*M[0][0] + F[0][1]*M[1][0];
T y = F[0][0]*M[0][1] + F[0][1]*M[1][1];
T z = F[1][0]*M[0][0] + F[1][1]*M[1][0];
T w = F[1][0]*M[0][1] + F[1][1]*M[1][1];
F[0][0] = x;
F[0][1] = y;
F[1][0] = z;
F[1][1] = w;
}
/* Optimized version of power() */
void power(T F[2][2], T n)
{
if( n == 0 || n == 1)
return;
T M[2][2] = {{1,1},{1,0}};
this->power(F, n/2);
multiply(F, F);
if (n%2 != 0)
multiply(F, M);
}
T fib(T n)
{
T F[2][2] = {{1,1},{1,0}};
if (n == 0)
{
return 0;
}
power(F, n-1);
return F[0][0];
}
T m_fibNum;
};
// Returns n! (the factorial of n)
int Factorial(int n)
{
int result = 1;
for (int i = 1; i <= n; i++)
{
result *= i;
}
return result;
}
// Returns true if n is a prime number
template<typename T>
bool IsPrime(T n)
{
// Trivial case 1: small numbers
if (n <= 1) return false;
// Trivial case 2: even numbers
if (n % 2 == 0) return n == 2;
// Now, we have that n is odd and n >= 3.
// Try to divide n by every odd number i, starting from 3
for (T i = 3; ; i += 2)
{
// We only have to try i up to the squre root of n
if (i > n/i) break;
// Now, we have i <= n/i < n.
// If n is divisible by i, n is not prime.
if (n % i == 0) return false;
}
// n has no integer factor in the range (1, n), and thus is prime.
return true;
}
int main()
{
for(int i=0; i<300; ++i)
{
Fibonacci<unsigned long> f(i);
if (IsPrime(f))
{
std::cout << f << " is a prime number\n";
}
}
}
|
