// ===========================================================================
// Week 15: Algorithms
// ===========================================================================


// p. 9

double max (double array[], int len)
{
  if (len == 1) // stopping condition
    return array[0];
  else 
  {
    // recursive call
    double subMax = max (array, len - 1); 
    if (array[len - 1] > subMax)
      return array[len - 1];
    else
      return subMax;
  }
}






// p. 10

int factorial (int n)
{
  if (n == 1) // stopping condition
    return 1;
  else
    // recursive call
    return factorial (n - 1) * n;
}





// p. 13

int fib (int n)
{
  if (n == 1)
    return 1;
  else if (n == 2)
    return 1;
  else // two recursive calls
    return (fib (n-1) + fib (n-2));
}





// p. 15

double fibRepetitive (int n)
{
  if (n == 1)
    return 1;
  else if (n == 2)
    return 1;
  double* fib = new double[n];
  fib[0] = 1;
  fib[1] = 1;
  for (int i = 2; i < n; i++)
    fib[i] = fib[i - 1] + fib[i - 2];
  double result = fib[n - 1];
  delete[] fib;
  return result;
}







// p. 16

int main () // <iostream>, <ctime>, <iomanip>
{
  int n = 0;
  cin >> n; 
  time_t stTime = 0, endTime = 0;
  double duration = 0;	
  stTime = clock();
  cout << setprecision(100) << fibRepetitive(n) << endl; // algorithm 1
  endTime = clock();
  duration = static_cast<double>(endTime - stTime) / CLK_TCK;
  cout << "seconds for algorithm 1: " << setprecision(5) << duration << endl; 
 
  stTime = clock();
  cout << setprecision(100) << fib(n) << endl; // algorithm 2
  endTime = clock();
  duration = static_cast<double>(endTime - stTime) / CLK_TCK;
  cout << "seconds for algorithm 2: " << setprecision(5) << duration << endl; 
  return 0;
}







// p. 18

#include <iostream>
using namespace std;

void hanoi (char from, char via, char to, int disc)
{
  if (disc == 1)
    cout << "From " << from << " to " << to << endl;
  else
  {
    hanoi (from, to, via, disc - 1);
    cout << "From " << from << " to " << to << endl;
    hanoi (via, from, to, disc - 1);
  }
}

int main ()
{
  int disc = 0; // number of discs
  cin >> disc;
  char a = 'A', b = 'B', c = 'C';
	
  hanoi (a, b, c, disc);
	
  return 0;
}