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QuickSort

Like Merge Sort, QuickSort is a Divide and Conquer algorithm. 
It picks an element as pivot and partitions the given array 
around the picked pivot. There are many different versions of quickSort 
that pick pivot in different ways. 


Always pick first element as pivot.
Always pick last element as pivot (implemented below)
Pick a random element as pivot.
Pick median as pivot.

The key process in quickSort is partition(). 
Target of partitions is, given an array and an element x of array as pivot, 
put x at its correct position in sorted array and put all smaller elements 
(smaller than x) before x, and put all greater elements (greater than x) after x. 
All this should be done in linear time.

Partition Algorithm 
There can be many ways to do partition, 
following pseudo code adopts the method given in CLRS book. 
The logic is simple, we start from the leftmost element and 
keep track of index of smaller (or equal to) elements as i. 
While traversing, if we find a smaller element, we swap current 
element with arr[i]. Otherwise we ignore current element.


arr[] = {10, 80, 30, 90, 40, 50, 70}
Indexes:  0   1   2   3   4   5   6 

low = 0, high =  6, pivot = arr[h] = 70
Initialize index of smaller element, i = -1

Traverse elements from j = low to high-1
j = 0 : Since arr[j] <= pivot, do i++ and swap(arr[i], arr[j])
i = 0 
arr[] = {10, 80, 30, 90, 40, 50, 70} // No change as i and j 
                                     // are same

j = 1 : Since arr[j] > pivot, do nothing
// No change in i and arr[]

j = 2 : Since arr[j] <= pivot, do i++ and swap(arr[i], arr[j])
i = 1
arr[] = {10, 30, 80, 90, 40, 50, 70} // We swap 80 and 30 

j = 3 : Since arr[j] > pivot, do nothing
// No change in i and arr[]

j = 4 : Since arr[j] <= pivot, do i++ and swap(arr[i], arr[j])
i = 2
arr[] = {10, 30, 40, 90, 80, 50, 70} // 80 and 40 Swapped
j = 5 : Since arr[j] <= pivot, do i++ and swap arr[i] with arr[j] 
i = 3 
arr[] = {10, 30, 40, 50, 80, 90, 70} // 90 and 50 Swapped 

We come out of loop because j is now equal to high-1.
Finally we place pivot at correct position by swapping
arr[i+1] and arr[high] (or pivot) 
arr[] = {10, 30, 40, 50, 70, 90, 80} // 80 and 70 Swapped 

Now 70 is at its correct place. All elements smaller than
70 are before it and all elements greater than 70 are after
it.


'''