/**
* This program will...
* 1) Recieve information from the user on the degree of a polynomail, followed by the coefficients of each term
* 2) Interpret the information and display the polynomial in standard form
* 3) Evaluate the polynomial at a user-given value
* 4) Evaluate the first and then second derivative of the polynomial at user-given value
* 5) Receive a second polynomial from the user and then compare the second polynomial to the first derivative of the first polynomial
* Course: csc1253 Section 001
* Programming Project #: 5
* Instructor: Dr. Duncan
* @author BLAKE LALONDE
* @since 11 / 21 / 2019
* @version 2
*/



#include <iostream>
#include <iomanip>
#include <string>
#include <cmath>
#include <sstream>

using namespace std;

class Polynomial
{

private:
	double* poly;

public:
	// Creates the zero polynomial //
	Polynomial()
	{
		poly = new double[2];
		poly[0] = 0;
		poly[1] = 0;
	}

	// Creates a polynomial using the contents of the degCoeffs array //
	Polynomial(double degCoeffs[])
	{
		int i;
		double size = degCoeffs[0] + 2;
		poly = new double[size];
		for (i = 0; i <= size; i++)
		{
			poly[i] = degCoeffs[i];
		}
	}

	// Used to deallocate the memory associated with this polynomial //
	~Polynomial()
	{

	}

	// Evaluates the polynomial at the specified value //
	double eval(double x) const
	{
		int i;
		int power = poly[0];
		double sum = poly[1];
		int size = power + 2;
		for (i = 2; i < size; i++)
		{
			sum = sum * x + poly[i];
		}
		if (sum == -0)
			return 0;
		return sum;
	}

	// Gives a string representation of this polynomial in standard form where zero terms, coefficeints 1 or -1, and exponents 1 are not displayed //
	string str() const
	{
		stringstream sout;
		int power = poly[0];
		int i;
		int	powerChanger = power - 1;
		int size = power + 2;

		if (size < 2)
		{
			sout << "0";
			string exception = sout.str();
			return exception;
		}
		else if (poly[1] == 1)
			sout << "x^" << power;
		else if (poly[1] == -1)
			sout << "-x^" << power;
		else if (poly[1] == 0)
			sout << "";
		else
		{
			if (power == 1)
			{
				if (poly[1] == 1)
					sout << "x";
				else if (poly[1] == -1)
					sout << " - x";
				else
					sout << poly[1] << "x";
			}
			else if (power > 1)
				sout << poly[1] << "x^" << power;
		}

		if (poly[0] == 0)
			sout << poly[1];

		for (i = 2; i <= power + 2 && powerChanger >= 0; i++, powerChanger--)
		{
			if (powerChanger == 0)
			{
				if (poly[power + 1] > 0)
					sout << " + " << poly[power + 1];
				else if (poly[power + 1] < 0)
					sout << " - " << abs(poly[power + 1]);
			}
			else if (powerChanger == 1)
			{
				if (poly[i] < -1)
					sout << " - " << abs(poly[i]) << "x";
				else if (poly[i] == -1)
					sout << " - x";
				else if (poly[i] == 0)
					sout << "";
				else if (poly[i] == 1)
					sout << " + x";
				else
					sout << " + " << poly[i] << "x";
			}
			else
			{
				if (poly[i] == 1)
					sout << " + x^" << powerChanger;
				else if (poly[i] == -1)
					sout << " - x^" << powerChanger;
				else if (poly[i] == 0)
					sout << "";
				else
				{
					if (poly[i] > 0)
						sout << " + " << poly[i] << "x^" << powerChanger;
					else if (poly[i] < 0)
						sout << " - " << abs(poly[i]) << "x^" << powerChanger;
				}
			}
		}
		string polynomial = sout.str();
		return polynomial;
	}

	// Determines whether this polynomial is equivalent to the specified polynomial //
	bool equals(const Polynomial& other) const
	{
		int i;
		double size1 = poly[0] + 2;
		double size2 = other.poly[0] + 2;
		if (size1 != size2)
			return false;
		for (i = 0; i < size1; i++)
		{
			if (poly[i] != other.poly[i])
				return false;
		}
		return true;
	}

	// Generates a polynomial that represents the derivative of the given polynomial //
	Polynomial differentiate() const
	{
		double size = poly[0] + 2;
		double degree = poly[0];
		poly[0] = degree - 1;
		if (size <= 1)
		{
			double polyException[] = { 0, 0 };
			return Polynomial();
		}
		else
			for (int i = 1; i <= size; i++)
			{
				poly[i] = degree * poly[i];
				degree--;
			}
		return Polynomial(poly);
	}
};



int main()
{
	int i;
	double polyDegree;
	double polySize;
	cout << "Enter the degree of the polynomial -> ";
	cin >> polyDegree;
	if (polyDegree < 0)
	{
		cout << "Please enter a positive degree." << endl;
		return 0;
	}
	double* polyList = new double[polyDegree + 2];
	polyList[0] = polyDegree;
	polySize = polyDegree + 2;
	cout << "Enter the coefficients -> ";
	for (i = 1; i < polySize; i++)
		cin >> polyList[i];

	Polynomial original = Polynomial(polyList);
	cout << endl << "f(x) = " << original.str() << endl;
	cout << "Enter a value at which to evaluate this polynomial -> ";
	double x;
	cin >> x;
	cout << "f(" << x << ") = " << original.eval(x) << endl << endl;

	Polynomial firstDeriv = Polynomial(polyList);
	cout << "f'(x) = " << firstDeriv.differentiate().str() << endl;
	cout << "Enter a value at which to evaluate the first derivative -> ";
	cin >> x;
	cout << "f'(" << x << ") = " << firstDeriv.eval(x) << endl << endl;

	Polynomial secondDeriv = Polynomial(polyList);
	cout << "f'(x) = " << secondDeriv.differentiate().differentiate().str() << endl;
	cout << "Enter a value at which to evaluate the second derivative -> ";
	cin >> x;
	cout << "f\"(" << x << ") = " << secondDeriv.differentiate().eval(x) << endl << endl;

	double newPolyDegree;
	double newPolySize;
	cout << "Enter the degree of the second polynomial -> ";
	cin >> newPolyDegree;
	double* newPolyList = new double[newPolyDegree + 2];
	newPolyList[0] = newPolyDegree;
	newPolySize = newPolyDegree + 2;
	cout << "Enter the coefficents -> ";
	for (i = 1; i < newPolySize; i++)
		cin >> newPolyList[i];
	Polynomial newPolynomial = Polynomial(newPolyList);
	cout << endl << "g(x) = " << newPolynomial.str() << endl;
	if (firstDeriv.equals(newPolynomial))
		cout << "g(x) = f'(x)";
	else
		cout << "g(x) <> f'(x)";
}