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=.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
        
        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 = math.sqrt(self.p*self.n*(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 = 1.0 * 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('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
        """
        a = math.factorial(self.n) / (math.factorial(k) * (math.factorial(self.n - k)))
        b = (self.p ** k) * (1 - self.p) ** (self.n - k)
        
        return a * b      

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