$16$

$14$

$10$

$89$

$7$

$65$

$12$

$114$

$37.43.$ Answer the following questions based on this tree:

$37.$ Write the complete binary tree as an array.

$($a$)1614121078965114$

$($b$)1614121071148965$

$($c$)1614108976512114$

$($d$)8910657141141216$

$38.$ If the element $18$ is added to the heap, what elements will it be swapped with to fix

the heap?

$($a$)11,12,16$

$($b$)5,7,14,16$

$($c$)11,12$

$($d$)8,10,14$

$3$

Name: $1$ MULTIPLE CHOICE

$39.$ If the heap is popped, which element will be removed and returned?

$($a$)16$

$($b$)8$

$($c$)5$

$($d$)4$

$40.$ If the heap is popped, which swaps will happen to fix the heap?

$($a$)16->5,5->12->4$

$($b$)16->14->10->9$

$($c$)16->5,5->14->10->9$

$($d$)16->12->11$

$41.$ How long does it take to add an element to a heap?

$($a$)$ O$($log n$)$

$($b$)$ O$($n

$2$

$)$

$($c$)$ O$(1)$

$($d$)$ O$($n log n$)$

$($e$)$ O$($n$)$

$42.$ How long does it take to access the maximum element in a heap?

$($a$)$ O$($log n$)$

$($b$)$ O$($n

$2$

$)$

$($c$)$ O$(1)$

$($d$)$ O$($n log n$)$

$($e$)$ O$($n$)$

$43.$ How long does it take to pop a heap?

$($a$)$ O$($log n$)$

$($b$)$ O$($n

$2$

$)$

$($c$)$ O$(1)$

$($d$)$ O$($n log n$)$

$($e$)$ O$($n$)$