Exercise $1.$

In this exercise, we assume arrays start at index one. Recall that heaps can be seen as binary trees: the root is A$[1],$ the left child of A$[$i$]$ is A$[2$i$],$ and the right child of A$[$i$]$ is A$[2$i$+1].$

$1.$ Which of the following arrays are heap$-$structured as max$-$heaps? Which ones as min$-$heaps?

$($a$)$ A$1=[0,1,2,3,4,5,6,7,8,9]$

$($b$)$ A$2=[9,8,5,6,7,4,3,0,1,2]$

$($c$)$ A$3=[0,1,3,4,5,2,6,7,8,9]$

$2.$ Draw the heap after inserting $5$ into the heap A$4=[0,2,1,3,6,4,8,9,7].$

$3.$ If you insert an element into a heap with $7$ elements, which locations of the array could be altered $($in the course of the insert operation$)?$