Merge pull request #66 from prateekiiest/master

Update Normal Distribution QuickSort Readme
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Anup Kumar Panwar 2017-02-04 18:15:16 +05:30 committed by GitHub
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###### View the algorithm in [action][quick-toptal] ###### View the algorithm in [action][quick-toptal]
![Normal Distribution QuickSort](https://github.com/prateekiiest/Python/blob/master/sorts/normal_distribution_QuickSort_README.md)
### Selection ### Selection
![alt text][selection-image] ![alt text][selection-image]

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#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
```python
>>> 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.
```python
>>> 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()
```
![Array_Element_Distribution](https://github.com/prateekiiest/Algorithms/blob/master/normaldistributionforarrayelements.png)
---
---------------------
--
##Plotting the function for Checking 'The Number of Comparisons' taking place between Normal Distribution QuickSort and Ordinary QuickSort
```python
>>>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()
```
----
###The Plot
* X axis denotes the number of elements to be sorted.
* Y axis denotes the number of comparisons taking place
![Plot](https://github.com/prateekiiest/Algorithms/blob/master/normaldist.png)
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