For this question, we will use the heap-supporting functions as seen in the lecture slides as building blocks for this assignment to build a new heap implementation. The heap implementation shown in the lecture slides is an example of a min-heap, in which the smallest element is at the root and all elements in child trees are larger than the value at the root. We can also construct max-heap data structures in which the largest element in the heap is at the root and all elements in child trees are smaller than the root.

The objective is to define SCHEME functions to manipulate a heap which:

1. maintain a binary tree as a heap,

2. use a generic (first order) order relation,

3. provides functions which can determine if a heap is empty? as well as heap-insert, heap-remove, and combine-heaps

(a) Define a SCHEME procedure, named (heap-insert f x H), which adds element x to heap H using the first-order relation f to determine which element belongs at the root of each (sub)tree.
For instance, if we wanted the same behavior as the heaps in the lecture slides (min-heap), we would use the "less than" function as our first-order relation:

(heap-insert < 100 (heap-insert < 10 (list))) (10 () (100 () ()))

If, instead, we wanted a max-heap implementation, where the largest element is at the root of the heap, we would use the "greater than" function as our first-order relation.

(heap-insert > 100 (heap-insert > 10 (list))) (100 () (10 () ()))

Note, you must use the same first-order relation for all of the heap procedures applied to a particular heap structure

HELPER FUNCTIONS

(define (create-heap value left right)
(list value left right))
(define (heap-root H) (car H))
(define (left T) (cadr T))
(define (right T) (caddr T))

(define (heap-insert f x H)
...)