$**$Please draw proper diagrams and binary tables and please solve on paper so I can understand better.

Heap: is an implementation strategy, usually applied to trees to describe certain ordering

properties. It is often used to implement priority$-$weighted structures, as it has certain

efficiencies over other approaches. These questions concern Heap as a binary tree, the heap

property, and its efficiencies as a sorting algorithm.

Using a suitable set of diagrams and a brief explanation of the steps between your

diagrams, show how a binary tree would be built for the following sequence of

numbers such that the final tree adheres to the max heap property: $(3,4,14,2,15)$

Using your answer to part $($a$)$ as an example, demonstrate how a heap can be stored

in an array. You should provide a diagram showing the placement of theitems in

the array in relationship to the heap tree, and explain the formulae you'd use to

find a parent, the left child and right child $($if they exist$)$ of any given node in the

array by their indices.

Quantify and compare the performance of heap$-$sorting with another less$-$

efficient list sorting method of your choice and discuss the reasons behind the

performance difference.