#include <iostream>

using namespace std;

int    menu();
double squareRoot(double);
double powerOf(double, int);
void   primeNumbers(int);
double hypotenuse(double, double);

int main()
{
  int option;

  //main loop
  while ((option = menu()) != 5) {
    int    n, y;
    double a, b, p, x;

    switch (option) {
      case 1: //Compute the square root of a double using the Babylonian algorithm
        cout << "Enter a value to compute the square root of:";
        cin >> p;

        cout << "The square root of " << p << " is " << squareRoot(p) << endl << endl;

        break;
      case 2: //Compute X raised to the Y power
        cout << "Enter a value:";
        cin >> x;
        cout << "What value would you like to raise it to?:";
        cin >> y;

        cout << x << " raised to the power of " << y << " is " << powerOf(x, y) << endl << endl;

        break;
      case 3: //Print out prime numbers up to a pre-specified number
        cout << "Enter a number up to which all prime numbers will be printed:";
        cin >> n;

        cout << "Prime numbers up to " << n << ":" << endl;
        primeNumbers(n);
        cout << endl;

        break;
      case 4: //The value of the hypotenuse of a right triangle.
        cout << "Enter the length of side A of the triangle:";
        cin >> a;
        cout << "Enter the length of side B of the triangle:";
        cin >> b;

        cout << "The length of the hypotenuse of the triangle is " << hypotenuse(a, b) << endl << endl;

        break;
    }
  }

  return 0;
}

int menu()
{
  int a = -999;

  do {
    if (a != -999) //if the user enters an invalid input display this message
      cout << "Invalid input, please try again." << endl << endl;
    cout << "MatLab Junior" << endl
         << "  1) Compute the square root of a double using the Babylonian algorithm" << endl
         << "  2) Compute X raised to the Y power" << endl
         << "  3) Print out prime numbers up to a pre-specified number" << endl
         << "  4) The value of the hypotenuse of a right triangle." << endl
         << "  5) Quit the Program" << endl
         << "Please enter a number (1-5) ->";
    cin >> a;
  } while (!(a > 0 && a < 6)); //test for valid input

  cout << endl;
  return a;
}

double squareRoot(double n)
{
  int BABYLONIAN_ITERATIONS = 10; //number of times to repeat babylonian algorithm

  double guess = n;

  //compute square root
  for (int i = 0; i < BABYLONIAN_ITERATIONS; i++) {
    double tmp = n / guess;
    guess = (guess + tmp) / 2;
  }

  //4 decimal places
  guess *= 10000;
  guess = (int)guess;
  guess /= 10000;

  return guess;
}

double powerOf(double x, int y)
{
  double p = x;

  //multiply by itself y times
  for (int i = 1; i < y; i++)
    p *= x;

  return p;
}

void primeNumbers(int n)
{
  // all numbers from 2 to n
  for (int i = 2; i < n; i++) {
    bool isPrime = true;

    //test if i is prime
    for (int j = 2; j <= squareRoot(i); j++) {
      if (i % j == 0)
        isPrime = false;
    }

    //if it is print it
    if (isPrime)
      cout << i << endl;
  }
}

double hypotenuse(double a, double b)
{
  //a^2 + b^2 = c^2
  double c;
  c = powerOf(a, 2) + powerOf(b, 2);
  c = squareRoot(c);
  return c;
}