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
    """

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

        self.p = prob
        self.n = size
        self.mean = self.calculate_mean()
        self.stdev = self.calculate_stdev()
        Distribution.__init__(self, prob, size)

    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.n * self.p
        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 = math.sqrt(self.n * self.p * (1 - self.p))
        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.n = len(self.data)
        self.p = sum(self.data) / self.n
        self.mean = self.calculate_mean()
        self.stdev = 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(['0', '1'], [(1 - self.p) * self.n, self.p * self.n])
        plt.title('Data Barchart')
        plt.ylabel('outcome')
        plt.xlabel('count')
        plt.show()

    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
        """
        fact = lambda x: 1 if x == 0 else x * fact(x - 1)
        return (fact(self.n) / (fact(k) * fact(self.n - k))) * (self.p ** k) * (1 - self.p) ** (self.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 = [i for i in range(self.n + 1)]
        y = [self.pdf(i) for i in x]
        plt.bar(x, y)
        plt.title('Data pdf outcome')
        plt.ylabel('probability')
        plt.xlabel('outcome')
        plt.show()
        return x, y

    def __add__(self, other):

        """Function to add together two Binomial gndb_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

        m = self.mean + other.mean
        s = self.stdev + other.stdev
        n = self.n + other.n
        return Binomial(self.p, 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)
