Build a binary search tree for the following numbers, sorted by value: $15,29,9,11,2,31,18,3,14,$ and $6.$

Add numbers to this tree in the order in which they are listed.

$($a$)$ How many comparisons are needed to locate $11$ in this tree, starting from the top?

$($b$)$ How many comparisons are needed to add $17$ to this tree?

$($c$)$ What is the parent of the node labeled $2?$

$($d$)$ What are the children of the node labeled $29?$

$15$

$29$

$9$

$11$

$2$

$31$

$18$

$3$

$14$

$6$