//
// Example 14.12. Function to evaluate f(1) + f(2) + ... + f(n)
// for a variety of functions, f, and values of positive integer n
//

#include <iostream>
#include <iomanip>
#include <cmath>

using namespace std;

const int TRIPLE_FUN  = 1;
const int SQR_FUN     = 2;
const int SQRT_3X_FUN = 3;
const int QUIT        = 4;

int main()
{
   void  menu(int& choice, int& n);
   float sigma(float (*f)(int i), int n);
   float triple(int i);
   float sqr(int i);
   float sqrt3x(int i);
   float (*funPtr)(int i);

   int choice;   // menu choice
   int n;        // number of summands
   float sum;    // f(1) + f(2) + ... + f(n)

   menu(choice, n);     // priming read
   while (choice != QUIT)
   {
       if (choice == TRIPLE_FUN)
          funPtr = triple;
       else if (choice == SQR_FUN)
          funPtr = sqr;
       else if (choice == SQRT_3X_FUN)
          funPtr = sqrt3x;

       cout << endl << "f("   << n <<   ") = "
            << fixed << showpoint 
            << setprecision(2) << (*funPtr)(n) << endl;
       sum = sigma(funPtr, n);
       cout << "f(1) + f(2) + ... + f(" << n << ") = " << sum << endl;

       menu(choice, n); // another choice
   }
   cout << endl << "Thank you" << endl;

   return 0;
}

//
// Function to give a menu of function choices and to
// return that choice. The function also reads and returns
// the number of summands.
// Pre:  none
// Post: A menu choice (choice) and a number of summands
//       (n) was returned.
//

void menu(int& choice, int& n)
{
   cout << "Program evaluates f(n) & f(1) + f(2) + ... + f(n)" << endl;

   do
   {
       cout << "Choose a function" << endl;
       cout << "\t1 f(x) = 3x" << endl;
       cout << "\t2 f(x) = x^2" << endl;
       cout << "\t3 f(x) = square root of 3x" << endl;
       cout << "\t4 Quit" << endl << endl;
       cout << "Your choice: ";
       cin  >> choice;
   }
   while (choice < 1 || choice > 4);

   if (choice == QUIT) // no function, don't pick n
      n = 0;
   else 	// function chosen, pick n

       do
       {
          cout << "Give a positive integer value for n: ";
          cin  >> n;
       }
       while (n < 1);
}

//
// Function to return f(1) + f(2) + ... + f(n) for
// a function to which f points and positive integer n
// Pre:  n is a positive integer.
// Post: A floating point sum f(1) + f(2) + ... + f(n)
//       was returned.
//

float sigma(float (*f)(int i), int n)
{
   float sum = 0;    // f(1) + f(2) + ... + f(n)

   for (int k = 1; k <= n; ++k)
       sum += (*f)(k);

   return sum;
}

//
// Function to return float 3i for integer i
// Pre: 	 i is an integer.
// Post: float 3i was returned.
//

float triple(int i)
{
   return float(3 * i);
}

//
// Function to return float i^2 for integer i
// Pre: 	 i is an integer.
// Post: float i^2 was returned.
//

float sqr(int i)
{
   return float(i * i);
}

//
// Function to return float sqrt(3i) for integer i
// Pre: 	 i is an integer.
// Post: float sqrt(3i) was returned.
//

float sqrt3x(int i)
{
   return float(sqrt(3 * i));
}