import math
import matplotlib.pyplot as plt
from .Generaldistribution import Distribution

class Binomial(Distribution):
    """ Binomial distribution class for calculating and
    visualizing a Binomial distribution.

    Attributes:
        mean (float) representing the mean value of the distribution
        stdev (float) representing the standard deviation of the distribution
        data_list (list of floats) a list of floats to be extracted from the data file
        p (float) representing the probability of an event occurring
        n (int) the total number of trials

    """

    #       A binomial distribution is defined by two variables:
    #           the probability of getting a positive outcome
    #           the number of trials

    #       If you know these two values, you can calculate the mean and the standard deviation
    #
    #       For example, if you flip a fair coin 25 times, p = 0.5 and n = 25
    #       You can then calculate the mean and standard deviation with the following formula:
    #           mean = p * n
    #           standard deviation = sqrt(n * p * (1 - p))

    #

    def __init__(self, prob=.5, size=20):

        self.p = prob
        self.n = size
        self.calculate_mean()
        self.calculate_stdev()

        Distribution.__init__(self, self.calculate_mean(), self.calculate_stdev())


    def calculate_mean(self):

        """Function to calculate the mean from p and n

        Args:
            None

        Returns:
            float: mean of the data set

        """

        self.mean = self.p * self.n
        return self.mean


    def calculate_stdev(self):

        """Function to calculate the standard deviation from p and n.

        Args:
            None

        Returns:
            float: standard deviation of the data set

        """

        self.stdev = (self.n * self.p * (1 - self.p))**(1/2)
        return self.stdev


    def replace_stats_with_data(self):

        """Function to calculate p and n from the data set

        Args:
            None

        Returns:
            float: the p value
            float: the n value

        """

        self.read_data_file(file_name='numbers_binomial.txt')

        if not self.data:
            return self.p, self.n

        self.n = len(self.data)
        self.p = sum(self.data)/self.n
        self.calculate_mean()
        self.calculate_stdev()

        return self.p, self.n


    def plot_bar(self):
        """Function to output a histogram of the instance variable data using
        matplotlib pyplot library.

        Args:
            None

        Returns:
            None
        """

        plt.bar(x = ['0', '1'], height = [(1 - self.p) * self.n, self.p * self.n])
        plt.title('Bar Chart of Data')
        plt.xlabel('outcome')
        plt.ylabel('count')


    def pdf(self, k):
        """Probability density function calculator for the gaussian distribution.

        Args:
            k (float): point for calculating the probability density function


        Returns:
            float: probability density function output
        """

        n = self.n
        p = self.p
        return (
            (math.factorial(n))/(math.factorial(n-k)
            * math.factorial(k)))*((p)**(k))*((1-p)**(n-k)
        )


    def plot_bar_pdf(self):

        """Function to plot the pdf of the binomial distribution

        Args:
            None

        Returns:
            list: x values for the pdf plot
            list: y values for the pdf plot

        """

        x = []
        y = []

        # calculate the x values to visualize
        for i in range(self.n + 1):
            x.append(i)
            y.append(self.pdf(i))

        # make the plots
        plt.bar(x, y)
        plt.title('Distribution of Outcomes')
        plt.ylabel('Probability')
        plt.xlabel('Outcome')

        plt.show()

        return x, y


    def __add__(self, other):

        """Function to add together two Binomial distributions with equal p

        Args:
            other (Binomial): Binomial instance

        Returns:
            Binomial: Binomial distribution

        """

        try:
            assert self.p == other.p, 'p values are not equal'
        except AssertionError as error:
            raise

        return Binomial(prob=self.p, size=self.n+other.n)


    def __repr__(self):

        """Function to output the characteristics of the Binomial instance

        Args:
            None

        Returns:
            string: characteristics of the Gaussian

        """

        return "mean {}, standard deviation {}, p {}, n {}".\
        format(self.mean, self.stdev, self.p, self.n)
