diff --git a/README.md b/README.md index 1d8d3386e..fd3de1465 100644 --- a/README.md +++ b/README.md @@ -59,6 +59,12 @@ __Properties__ ###### View the algorithm in [action][quick-toptal] + + + +![Normal Distribution QuickSort](https://github.com/prateekiiest/Python/blob/master/sorts/normal_distribution_QuickSort_README.md) + + ### Selection ![alt text][selection-image] diff --git a/sorts/normal_distribution_QuickSort_README.md b/sorts/normal_distribution_QuickSort_README.md new file mode 100644 index 000000000..fc6d55ed5 --- /dev/null +++ b/sorts/normal_distribution_QuickSort_README.md @@ -0,0 +1,80 @@ +#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) + +``` + +------ + +#### 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) + + +------------------