Update Normal Distribution QuickSort Readme

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]
 

sorts/normal_distribution_QuickSort_README.md

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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)
+
+```
+
+------
+
+#### 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)
+
+
+------------------

sorts/random_normaldistribution_quicksort.py

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+from random import randint
+from tempfile import TemporaryFile
+import numpy as np
+import math
+
+
+
+def _inPlaceQuickSort(A,start,end):  
+    count = 0
+    if start<end:
+        pivot=randint(start,end)
+        temp=A[end]
+        A[end]=A[pivot]
+        A[pivot]=temp
+
+        p,count= _inPlacePartition(A,start,end)
+        count += _inPlaceQuickSort(A,start,p-1)
+        count += _inPlaceQuickSort(A,p+1,end)
+    return count
+
+def _inPlacePartition(A,start,end):
+
+    count = 0
+    pivot= randint(start,end)
+    temp=A[end]
+    A[end]=A[pivot]
+    A[pivot]=temp
+    newPivotIndex=start-1
+    for index in range(start,end):
+
+        count += 1
+        if A[index]<A[end]:#check if current val is less than pivot value
+            newPivotIndex=newPivotIndex+1
+            temp=A[newPivotIndex]
+            A[newPivotIndex]=A[index]
+            A[index]=temp
+
+    temp=A[newPivotIndex+1]
+    A[newPivotIndex+1]=A[end]
+    A[end]=temp
+    return newPivotIndex+1,count
+
+outfile = TemporaryFile()    
+p = 100 # 1000 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)
+
+
+
+
+
+
+outfile.seek(0)  # using the same array
+M = np.load(outfile)
+r = (len(M)-1)
+z = _inPlaceQuickSort(M,0,r) 
+
+print("No of Comparisons for 100 elements selected from a standard normal distribution is :")
+print(z)