Build a binary search tree for the following words, sorted alphabetically: gaffe, rebellion, fool, elaborate, spread, joke, freedom, stroke, guideline, and aware. Add words to this tree in the order in which they are listed.

$($a$)$ How many comparisons are needed to locate spread in this tree, starting from the top?

$($b$)$ How many comparisons are needed to add the word thorough to this tree?

$($c$)$ What is the parent of the node labeled elaborate?