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


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

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

    def calculate_mean(self):
        """
        Function to calculate the mean from p and n for a binomial distribution:
            mean = p * 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.
            standard deviation = sqrt(n * p * (1 - p))
        
        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 update the n attribute of the binomial distribution
            updates the p value of the binomial distribution by calculating the
            number of positive trials divided by the total trials
        
        Args: 
            None
        Returns: 
            float: the p value
            float: the n value
        """
        self.n = len(self.data)
        self.p = sum(self.data) / len(self.data)
        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(x=['0', '1'], height=[(1 - self.p) * self.n, self.p * self.n])
        plt.title("Bar Chart of Data")
        plt.xlabel("Outcomes")
        plt.ylabel("Frequency")

    def pdf(self, k):
        """
        Probability density function calculator for the binomial distribution.
        Args:
            k (float): point for calculating the probability density function
        Returns:
            float: probability density function output
        """
        numerator = math.factorial(self.n)
        denominator = math.factorial(k) * math.factorial(self.n - k)
        fraction = numerator / denominator
        left = fraction * self.p ** k
        right = (1 - self.p) ** (self.n - k)
        bin_pdf = left * right

        return bin_pdf

    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 = list(range(self.n + 1))
        y = [self.pdf(k=k) for k in x]
        plt.bar(x, y)
        plt.title("Distribution of Outcomes")
        plt.xlabel("Outcomes")
        plt.ylabel("Probability")

        return x, y

    def __add__(self, other):
        """
        Function to add together two Binomial distributions with equal p
            p: one_bin.p == two_bin.p
            n: one_bin.n + two_bin.n
        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

        result = Binomial()
        result.n = self.n + other.n
        result.p = self.p
        result.calculate_mean()
        result.calculate_stdev()

        return result
        
    def __repr__(self):
        """
        Function to output the characteristics of the Binomial instance
        Args:
            None
        Returns:
            string: characteristics of the Gaussian
        """
        representation = "mean {}, standard deviation {}, p {}, n {}".\
            format(self.mean, self.stdev, self.p, self.n)
