Please solve this ASAPPART $1-$ An extended max heap operation

A max heap is useful to implement another data structure Priority Queue, where you can always

have the highest priority value at the root of the heap, so that the system can easily gain access

to the most imminent task at a time.

In case we want to force the system to handle a certain task sooner, we might need to increase

a certain priority value inside the max heap while still maintaining the max heap property. For

this reason we may introduce the Heap$-$Increase routine, which is defined as:

Heap$-$Increase $($A$,$ i$,$ k$)$

Given a max heap array $A($of size n$),$ Heap$-$Increase $($A$,$ i$,$ k$)$ increases $A[i]$ by $k.$

A$.$ How would you heapify the now changed heap array after A$[$i$]$ is increased? How would

you mitigate potential max$-$heap violations? To answer this question, you may either $-$

Show your implementation of Heap$-$Increase using the following pseudocode

template;

or explain the mechanism in plain English, in no more than $4$ full sentences. $(6$pts$)$

Hint: Recall the strict premise in order to apply Max$-$Heapify and how we do Build$-$Heap

from ground up$.$

B$.$ And what is the Big$-$O$-$of$-$n time complexity of your Heap$-$Increase routine?

$(4$pt$)$ Hint: There are two acceptable answers, depending on how you implement it in $A.$

Heap$-$Increase$($A$,$ i$,$ k$)$

A$[$i$]=$ A$[$i$]+$ k; $//$assuming k is always positive

$//$ And then?