package edu.neu.ccs.evergreen.util;

/**
 * Generic polynomial class.
 */
public class Polynomial {
	/**
	 * How close close doubles need to be to be considered equal.
	 */
	public static final double DELTA = Math.pow(10, -6);

	private double coefficients[] = new double[4];

	/**
	 * Create a new polynomial with the given coefficients.
	 * 
	 * @param x_3
	 *            Coefficient for x^3
	 * @param x_2
	 *            Coefficient for x^2
	 * @param x_1
	 *            Coefficient for x^1
	 * @param x_0
	 *            Coefficient for x^0
	 */
	public Polynomial(double x_3, double x_2, double x_1, double x_0) {
		coefficients[0] = x_0;
		coefficients[1] = x_1;
		coefficients[2] = x_2;
		coefficients[3] = x_3;
	}

	/**
	 * Used internally when creating results.
	 */
	private Polynomial() {
	}

	/**
	 * Multiple all coefficients in the polynomial by the given value.
	 * 
	 * @param value
	 *            Value to multiply by
	 * @return Polynomial with all values multiplied
	 */
	public Polynomial multiply(double value) {
		Polynomial result = new Polynomial();
		for (int i = 0; i < coefficients.length; i++) {
			result.coefficients[i] = coefficients[i] * value;
		}
		return result;
	}

	/**
	 * Add one polynomial to another.
	 * 
	 * @param polynomial
	 *            Polynomial to add
	 * @return Sum of the two polynomials
	 */
	public Polynomial add(Polynomial polynomial) {
		Polynomial result = new Polynomial();
		for (int i = 0; i < coefficients.length; i++) {
			result.coefficients[i] = coefficients[i]
					+ polynomial.coefficients[i];
		}
		return result;
	}

	/**
	 * Add one polynomial to another.
	 * 
	 * @param polynomial
	 *            Polynomial to add
	 * @return Sum of the two polynomials
	 */
	public Polynomial subtract(Polynomial polynomial) {
		Polynomial result = new Polynomial();
		for (int i = 0; i < coefficients.length; i++) {
			result.coefficients[i] = coefficients[i]
					- polynomial.coefficients[i];
		}
		return result;
	}

	/**
	 * Compute and return the derivative of the polynomial.
	 * 
	 * @return Derivative
	 */
	public Polynomial differentiate() {
		Polynomial result = new Polynomial();
		result.coefficients[2] = coefficients[3] * 3;
		result.coefficients[1] = coefficients[2] * 2;
		result.coefficients[0] = coefficients[1];
		return result;
	}

	/**
	 * Return the coefficient for the given power.
	 * 
	 * @param power
	 *            Power to return
	 * @return Coefficient
	 */
	public double getCoefficient(int power) {
		return coefficients[power];
	}

	/**
	 * Determine if the value is equal to 0 within the set tolerance.
	 * 
	 * @param value
	 *            Value to check
	 * @return True if equal to 0
	 */
	private boolean equalToZero(double value) {
		return (Math.abs(0 - value) <= DELTA);
	}

	/**
	 * Return the degree of the polynomial.
	 * 
	 * @return degree
	 */
	public int degree() {
		for (int i = 3; i > 0; i--) {
			if (!equalToZero(coefficients[i])) {
				return i;
			}
		}
		return 0;
	}

	/**
	 * Solve the polynomial for when it equals 0.
	 * 
	 * @return Array of solutions
	 */
	public double[] solve0() {
		int degree = degree();
		if ((degree == 3) || (degree == 0)) {
			throw new UnsupportedOperationException("Can't solve degree "
					+ degree + ".");
		}
		if (degree == 2) {
			double temp = coefficients[1] * coefficients[1] - 4
					* coefficients[2] * coefficients[0];
			if (temp < 0.0) {
				return new double[] {};
			}
			double plus = (-coefficients[1] + Math.sqrt(temp))
					/ (2 * coefficients[2]);
			double minus = (-coefficients[1] - Math.sqrt(temp))
					/ (2 * coefficients[2]);
			return new double[] { plus, minus };
		}
		return new double[] { (-coefficients[0]) / coefficients[1] };
	}

	/**
	 * Compute the value of the polynomial for the given x.
	 * 
	 * @param x
	 *            X
	 * @return value
	 */
	public double eval(double x) {
		double result = 0;
		for (int i = 0; i < coefficients.length; i++) {
			result += coefficients[i] * Math.pow(x, i);
		}
		return result;
	}

	// r(R) s r(R)-s x^s*(1-x)^(r(R)-s) x^3 x^2 x^1 x^0
	// 0 0 0 x^0*(1-x)^0 0 0 0 1
	// 1 0 1 x^0*(1-x)^1 0 0 -1 1
	// 2 0 2 x^0*(1-x)^2 0 1 -2 1
	// 3 0 3 x^0*(1-x)^3 -1 3 -3 1
	// 1 1 0 x^1*(1-x)^0 0 0 1 0
	// 2 1 1 x^1*(1-x)^1 0 -1 1 0
	// 3 1 2 x^1*(1-x)^2 1 -2 1 0
	// 2 2 0 x^2*(1-x)^0 0 1 0 0
	// 3 2 1 x^2*(1-x)^1 -1 1 0 0
	// 3 3 0 x^3*(1-x)^0 1 0 0 0
	private static final Polynomial C00 = new Polynomial(0, 0, 0, 1);

	private static final Polynomial C01 = new Polynomial(0, 0, -1, 1);

	private static final Polynomial C02 = new Polynomial(0, 1, -2, 1);

	private static final Polynomial C03 = new Polynomial(-1, 3, -3, 1);

	private static final Polynomial C10 = new Polynomial(0, 0, 1, 0);

	private static final Polynomial C11 = new Polynomial(0, -1, 1, 0);

	private static final Polynomial C12 = new Polynomial(1, -2, 1, 0);

	private static final Polynomial C20 = new Polynomial(0, 1, 0, 0);

	private static final Polynomial C21 = new Polynomial(-1, 1, 0, 0);

	private static final Polynomial C30 = new Polynomial(1, 0, 0, 0);

	/**
	 * Return the polynomial for the given rank and s.
	 * 
	 * @param rank
	 *            Rank
	 * @param s
	 *            S
	 * @return coefficients
	 */
	public static Polynomial getPolynomial(int rank, int s) {
		int rank_minus_s = rank - s;
		if ((s == 0) && (rank_minus_s == 0)) {
			return C00;
		}
		if ((s == 0) && (rank_minus_s == 1)) {
			return C01;
		}
		if ((s == 0) && (rank_minus_s == 2)) {
			return C02;
		}
		if ((s == 0) && (rank_minus_s == 3)) {
			return C03;
		}
		if ((s == 1) && (rank_minus_s == 0)) {
			return C10;
		}
		if ((s == 1) && (rank_minus_s == 1)) {
			return C11;
		}
		if ((s == 1) && (rank_minus_s == 2)) {
			return C12;
		}
		if ((s == 2) && (rank_minus_s == 0)) {
			return C20;
		}
		if ((s == 2) && (rank_minus_s == 1)) {
			return C21;
		}
		if ((s == 3) && (rank_minus_s == 0)) {
			return C30;
		}
		throw new IllegalArgumentException("S = " + s + " and Rank = " + rank
				+ " is not valid.");
	}

	/**
	 * @see java.lang.Object#toString()
	 */
	@Override
	public String toString() {
		StringBuffer data = new StringBuffer();
		for (int i = coefficients.length - 1; i >= 0; i--) {
			if (!equalToZero(coefficients[i])) {
				if ((data.length() > 0) && (coefficients[i] >= 0.0)) {
					data.append("+");
				}
				data.append(coefficients[i]);
				if (i > 0) {
					data.append("x");
					if (i > 1) {
						data.append("^");
						data.append(i);
					}
				}
			}
		}
		return data.toString();
	}
}