For the following questions, you will be

creating various trees using the values in the Array:

A $=[1,3,10,12,55,57,91,98,100]$

$($a$)(3$ points$)$ Draw a Min Heap containing the elements in A with $4$ levels, or state

that it is impossible and explain why.

$($b$)(3$ points$)$ Draw a Max Heap containing the elements in A with $5$ levels, or state

that it is impossible and explain why.

$($c$)(3$ points$)$ Draw a binary search tree containing the elements in A with $4$ levels,

or state that it is impossible and explain why.

$($d$)(3$ points$)$ Draw a binary search tree containing the elements in A with $6$ levels,

or state that it is impossible and explain why.

$($e$)(3$ points$)$ Write the Array that would result from calling Heapify on A to create

a Max Heap. State the exact number of swaps that the algorithm performed $($not

the asymptotic bound$)$