#include <iostream>
#include <cmath>
#include <climits>
#include <cstdlib>
#include <string>

/*
 * Created by Drake Vidkjer on 10/25/15
 * Last modified on 10/25/15
 * Version .1
 * Assignment 4
 * 
 */

using namespace std;

//declare funciton prototypes
bool inGood(string);
char promptDo();
void checkDo(char);
void prompt_for_variables();
bool checkVariables(int, float, float, float);
void integrate();
void sum();
bool allGood(string, string, string);
void convertVals(string, string, string);
float solveFunct(float);
bool posGood(string);
void integrate_rectangle();
void integrate_trap();

//define global variables
float upBoundVal, lowBoundVal;
int functVal;

int main()
{
	char whatDo;

	while(whatDo != 'E')
	{
		//Call prompt function to see what to do
		whatDo = promptDo();		

		//check what to do and do it
		checkDo(whatDo);
	}

	return 0; 
}

//check if user input is a good positive integer
//precondition: 
bool inGood(string input)
{
	//check if first is a negative sign
	if(input[0] == 45 || (input[0] > 48 && input[0] < 57))
	{
		for(int j = 1; j < input.size(); j++)
		{
			if((input[j] < 48 || input[j] > 57) && input[j] != 46)
			{
				cout << "Bad input, enter a new guess" << endl;
				return false;
			}
		} 
	}

	return true;
}

bool posGood(string input)
{
   for(int x = 0; x < input.size(); x++)
   {
      if(input[x] < 48 || input[x] > 57)
      {
	 cout << "Bad input, enter a new guess" << endl;
	 return false;
      }
   } 

   return true;
}

//Ask user what to do
char promptDo()
{
	//define local variables
	char usIn;

	//prompt user and take in input
	cout << "What would you like to do? (S)um, (I)ntegrate, or (E)xit?: ";
	cin >> usIn;

	return usIn;
}

//Check what user wants to do and call correct function
void checkDo(char whatDo)
{
	//check input to see what to do
	if(whatDo == 'S')
	{
		sum();
	}
	else if(whatDo == 'I')
	{
		integrate();
	}

	return;
}

//Prompt user for bounds, value for x and function to be used
void prompt_for_variables()
{
	//Define local variables
	bool good = false;
	string funct, upBound, lowBound;

	while(good == false)
	{

		//ask which function to use
		cout << "1) f(x)= 2x^5+x^3-10x+2 \n2) f(x)= 6x^2-x+10 \n3) f(x)= 5x+3 \n4) f(x)= 2x^3+120 \n5) f(x)= 2x^2 \nWhich function would you like to use?: ";
		cin >> funct;
		
		cout << "Enter lower bound: ";
		cin >> lowBound;

		//ask for upper/lower bounds
		cout << "Enter upper bound: ";
		cin >> upBound;

		//make sure all the valuse are good
		good = allGood(funct, upBound, lowBound);
		//Convert values to floats
		convertVals(funct, upBound, lowBound);
		if(functVal < 1 || functVal > 5)
		{
			good = false;
			cout << "Sorry, bad function input" << endl;
		}
		else if (lowBoundVal > upBoundVal)
		{
			good = false;
			cout << "Sorry, lower bound greater than upper bound" << endl;
		}
	}

	//Convert values to floats
	convertVals(funct, upBound, lowBound);
}

//check to make sure all the values entered are good
bool allGood(string funct, string upBound, string lowBound)
{
	if(inGood(funct) == false)
	{
		return false;
	}
	else if(inGood(upBound) == false)
	{
		return false;
	}
	else if(inGood(lowBound) == false)
	{
		return false;
	}
	else
	{
		return true;
	}
}

//convert all the inputed values into floats and ints
void convertVals(string funct, string upBound, string lowBound)
{
	functVal = atoi(funct.c_str());
	upBoundVal = strtof(upBound.c_str(), NULL);
	lowBoundVal = strtof(lowBound.c_str(), NULL);
}

//solve the appropriate function with the x value inputed
float solveFunct(float x)
{
	if(functVal == 1)
	{
		return (2*pow(x, 5) + pow(x, 3) - 10*x + 2);
	}
	else if(functVal == 2)
	{
		return (6*pow(x, 2) - x + 10);
	}
	else if(functVal == 3)
	{
		return (5*x+3);
	}
	else if(functVal == 5)
	{
		return (2*pow(x, 2));
	}
	else
		return 0;
}

//sum a function over certain bounds
void sum()
{
	//define local variables
	double answer;
	
	//call prompt_for_variables
	prompt_for_variables();
	
	for (int i = lowBoundVal; i <= upBoundVal; i++)
	{
		answer = answer + solveFunct(i);
	}
	
	cout << "Sum of f" << functVal << " from " << lowBoundVal << " to " << upBoundVal << " is " << answer << endl;
	//cout << "functVal, upBoundVal, lowBoundVal\n" << functVal << " " << upBoundVal << " " << lowBoundVal << endl;
}

void integrate_rectangle()
{
	string rects;
	int rectangles;
	double rectSize, answer;
	bool rectsGood = false;
	
	while(rectsGood == false)
	{
		cout << "How many rectangles do you want?: ";
		cin >> rects;
		
		rectsGood = posGood(rects);
	}
	rectangles = atoi(rects.c_str());
	rectSize = (upBoundVal - lowBoundVal)/rectangles;
	
	for(double z = lowBoundVal; z <= upBoundVal; z = z+rectSize)
	{
		answer = answer + (solveFunct(z)*rectSize);
		//cout << answer << endl;
	}
	
	//print answer
	cout << "The answer is: " << answer << endl;
}

void integrate_trap()
{
	string traps;
	int trapezoids;
	double trapSize, answer;
	bool trapsGood = false;
	
	while(trapsGood == false)
	{
		cout << "How many trapezoids do you want?: ";
		cin >> traps;
		
		trapsGood = posGood(traps);
	}
	trapezoids = atoi(traps.c_str());
	trapSize = (upBoundVal - lowBoundVal)/trapezoids;
	
	for(double z = lowBoundVal; z <= upBoundVal; z = z+trapSize)
	{
		answer = answer + (((solveFunct(z)+solveFunct(z+trapSize))/2)*trapSize);
	}
	
	//print answer
	cout << "The answer is: " << answer << endl;
}

//integrate a funciton over certain bounds
void integrate()
{
	//define local variables
	char trapRect;
	
	//call prompt_for_variables
	prompt_for_variables();
	
	//calculate things
	//Ask if trapezoid or rectangle or both and do that accordingly
	while(1)
	{
		cout << "Would you like to use the (T)rapezoidal or (R)ectangle method or (B)oth?: ";
		cin >> trapRect;
		
		if(trapRect == 'R')
		{
			integrate_rectangle();
			break;
		}
		else if(trapRect == 'T')
		{
			integrate_trap();
			break;
		}
		else if(trapRect == 'B')
		{
			integrate_rectangle();
			integrate_trap();
			break;
		}
	}
}