normal_distribution_quick_sort.md

Normal Distribution QuickSort

Algorithm implementing QuickSort Algorithm where the pivot element is chosen randomly between first and last elements of the array and the array elements are taken from a Standard Normal Distribution. This is different from the ordinary quicksort in the sense, that it applies more to real life problems , where elements usually follow a normal distribution. Also the pivot is randomized to make it a more generic one.

Array Elements

The array elements are taken from a Standard Normal Distribution , having mean = 0 and standard deviation 1.

The code

>>> import numpy as np 
>>> from tempfile import TemporaryFile
>>> outfile = TemporaryFile()    
>>> p = 100 # 100 elements are to be sorted
>>> mu, sigma = 0, 1 # mean and standard deviation
>>> X = np.random.normal(mu, sigma, p)
>>> np.save(outfile, X)
>>> print('The array is')
>>> print(X)

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The Distribution of the Array elements.

>>> mu, sigma = 0, 1 # mean and standard deviation
>>> s = np.random.normal(mu, sigma, p)
>>> count, bins, ignored = plt.hist(s, 30, normed=True)
>>> plt.plot(bins , 1/(sigma * np.sqrt(2 * np.pi)) *np.exp( - (bins - mu)**2 / (2 * sigma**2) ),linewidth=2, color='r')
>>> plt.show()   

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Plotting the function for Checking 'The Number of Comparisons' taking place between Normal Distribution QuickSort and Ordinary QuickSort

>>>import matplotlib.pyplot as plt

    
    # Normal Disrtibution QuickSort is red
>>> plt.plot([1,2,4,16,32,64,128,256,512,1024,2048],[1,1,6,15,43,136,340,800,2156,6821,16325],linewidth=2, color='r')
    
    #Ordinary QuickSort is green
>>> plt.plot([1,2,4,16,32,64,128,256,512,1024,2048],[1,1,4,16,67,122,362,949,2131,5086,12866],linewidth=2, color='g')

>>> plt.show()

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