"""
 heap.py
 
 a miminal implementation of a priority queue
 as a binary heap including heapsort
 
 See https://runestone.academy/runestone/books/published/pythonds/Trees/BinaryHeapImplementation.html
 
 We'll do at least these operations.
 
  - create
  - add an element
  - remve an element

The heap stores these indeces

   0 1 2 3 4 5 6 

as these places in a binary tree

               0
          1        2
        3   4     5   6          

and we can find the index of parents and children
with these formulas.

     left_child        2*i + 1     (for parent at i)
     right_child       2*i + 2

     parent           (n-1)//2   (for child at n)

     check : 
     (5 - 1) // 2       =>   2
     (6 - 1) // 2  = 5 //2 =  round_down(2.5) => 2

"""

def parent(i):
    """ return the index of the parent of node with index i 
        >>> parent(5)
        2
        >>> parent(6)
        2
    """
    # Remember that // is the "integer division" operator in python.
    return (i-1) // 2

def left_child(i):
    """ return index of the left child of the node with index i """
    return 2*i + 1

def right_child(i):
    """ return index of the left child of the node with index i """
    return 2*i + 2


class Heap:
    
    def __init__(self):
        self.array = []
        
    def set_test_case(self):
        # a valid heap that we can play with;
        # same numbers as in the pythonds material.
        #        5
        #     9     11
        #   14  18
        self.array = [5, 9, 11, 14, 18]

def main():
    heap = Heap()
    heap.set_test_case()

if __name__ == "__main__":
    import doctest
    doctest.testmod()
    main()