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'''Binary Sort''' (aka half-interval search/logarithmic search) is a search algorithm that finds a target value within a sorted array by comparing the target to the middle element, if unequal, the half of integers where the target cannot lie is unlimited. This process is continued unless target is identified.  

'''Binary Sort''' (aka half-interval search/logarithmic search) is a search algorithm that finds a target value within a sorted array by comparing the target to the middle element, if unequal, the half of integers where the target cannot lie is unlimited. This process is continued unless target is identified. In other words, this function will look for an item in an array by dividing the list in half every time it searches.

EX:  1, 7, 27, 33, 45,  57 , 66, 77, 89, 99, 101, 129, 156, 234

EX:  1, 7, 27, 33, 45,  57 , 66, 77, 89, 99, 101, 129, 156, 234

   while first <=last and not found:  ### this is a while loop that runs the logarithmic structure of the heap sort until the indicated element is found  

   while first <=last and not found:  ### this is a while loop that runs the logarithmic structure of the heap sort until the indicated element is found  

       midpoint = (first + last)// 2  ### this is the logic equation of the python code to run, this finds the midpoint element of the array by adding the first and last integer of that array and diving it by 2

       midpoint = (first + last)// 2  ### this is the logic equation of the python code to run,  

                                                  ###this finds the midpoint element of the array by adding the first and last integer of that array and diving it by 2

       if alist[midpoint] == item ### if the midpoint from the previous equation equates to the indicated integer, then element is found

       if alist[midpoint] == item ### if the midpoint from the previous equation equates to the indicated integer, then element is found

         found = True

         found = True

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'''Heap Sort Algorithm'''

'''Heap Sort Algorithm'''

=== Writing Your Own Algorithms ===

=== Writing Your Own Algorithms ===