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

    """

    #  TODO: Fill out all TODOs in the functions below
    
    #  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=0.5, size=20):

        #  TODO: store the probability of the distribution in an instance variable p
        #  TODO: store the size of the distribution in an instance variable n

        #  TODO:
        #  Now that you know p and n, you can calculate the mean and standard deviation
        #  Use the calculate_mean() and calculate_stdev() methods to calculate the
        #  distribution mean and standard deviation
        #
        #  Then use the init function from the Distribution class to initialize the
        #  mean and the standard deviation of the distribution
        #
        #  Hint: You need to define the calculate_mean() and calculate_stdev() methods
        #          farther down in the code starting in line 55.
        #          The init function can get access to these methods via the self
        #          variable.

        self. p = prob
        self.n = size
        Distribution.__init__(self, mu=self.calculate_mean(), sigma=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

        """

        #  TODO:
        #  Calculate the mean of the Binomial distribution. Store the mean
        #  via the self variable and also return the new mean value
        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

        """

        #  TODO:
        #  Calculate the standard deviation of the Binomial distribution. Store
        #  the result in the self standard deviation attribute. Return the value
        #  of the standard deviation.
        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

        """

        #  TODO:
        #  The read_data_file() from the Generaldistribution class can read in a data
        #  file. Because the Binomaildistribution class inherits from the Generaldistribution class,
        #  you don't need to re-write this method. However,  the method
        #  doesn't update the mean or standard deviation of
        #  a distribution. Hence you are going to write a method that calculates n, p, mean and
        #  standard deviation from a data set and then updates the n, p, mean and stdev attributes.
        #  Assume that the data is a list of zeros and ones like [0 1 0 1 1 0 1].
        #
        #  Write code that:
        #      updates 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
        #      updates the mean attribute
        #      updates the standard deviation attribute
        #
        #  Hint: You can use the calculate_mean() and calculate_stdev() methods
        #      defined previously.

        self.read_data_file("numbers_binomial.txt")
        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
        """

        #  TODO:
        #  Use the matplotlib package to plot a bar chart of the data
        #  The x-axis should have the value zero or one
        #  The y-axis should have the count of results for each case
        #
        #  For example, say you have a coin where heads = 1 and tails = 0.
        #  If you flipped a coin 35 times, and the coin landed on
        #  heads 20 times and tails 15 times, the bar chart would have two bars:
        #  0 on the x-axis and 15 on the y-axis
        #  1 on the x-axis and 20 on the y-axis
        #
        #  Make sure to label the chart with a title, x-axis label and y-axis label

        counts = [self.data.count[0], self.data.count[1]]
        x_values = [0, 1]

        plt.bar(x_values, counts)

        plt.xlabel("Success or Failure")
        plt.ylabel("Frequency/Count")
        plt.title("Bar Chart of Binomial Data")
        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
        """

        #  TODO:
        #  Calculate the probability density function for a binomial distribution
        #  For a binomial distribution with n trials and probability p,
        #  the probability density function calculates the likelihood of getting
        #  k positive outcomes.
        #
        #  For example, if you flip a coin n = 60 times, with p = .5,
        #  what's the likelihood that the coin lands on heads 40 out of 60 times?

        comb = math.factorial(self.n) / (math.factorial(k) * math.factorial(self.n - k))

        return comb * (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

        """

        #  TODO:
        #  Use a bar chart to plot the probability density function from
        #  k = 0 to k = n
        #
        #  Hint: You'll need to use the pdf() method defined above to calculate the
        #  density function for every value of k.
        #
        #  Be sure to label the bar chart with a title, x label and y label
        #
        #  This method should also return the x and y values used to make the chart
        #  The x and y values should be stored in separate lists

        x_values, y_values = [], []

        for i in range(0, self.n+1):
            x.values.append(i)
            y_values.append(self.pdf(i))

        plt.bar(x_values, y_values)
        plt.xlabel(" ")
        plt.ylabel("PDF / PMF Value")
        plt.title("Plotting PDF / PMF from k = 0 to k = n")

        plt.show()

    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

        #  TODO:
        #  Define addition for two binomial distributions. Assume that the
        #  p values of the two distributions are the same. The formula for
        #  summing two binomial distributions with different p values is more complicated,
        #  so you are only expected to implement the case for two distributions with equal p.
        #
        #  The try, except statement above will raise an exception if the p values are not equal
        #
        #  Hint: You need to instantiate a new binomial object with the correct n, p,
        #  mean and standard deviation values. The __add__ method should return this
        #  new binomial object.
        #
        #  When adding two binomial distributions, the p value remains the same
        #  The new n value is the sum of the n values of the two distributions.

        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

        """

        #  TODO:
        #  Define the representation method so that the output looks like
        #  mean 5, standard deviation 4.5, p .8, n 20
        #
        #  with the values replaced by whatever the actual distributions values are
        #  The method should return a string in the expected format

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