Question $4$: You are given a min$-$heap $A[1$dotsn$]$ and a variable largest that stores the

largest number in this min$-$heap.

In class, we have seen algorithms InSERT$(A,x)($which adds the number $x$ to the min$-$

heap and restores the heap property$)$ and ExTRACTMin$(A)($which removes the smallest

number from the heap and restores the heap property$).$

Explain, in a few sentences, how these two algorithms can be modified such that the

value of largest is correctly maintained. The running times of the two modified algorithms

must still be $O(logn).$