Figure $1$A binary search tree for Questions $1-3$

By using the binary tree in Figure $1$;

$($a$)$ List the root node of the tree.

$($b$)$ List the leaf node$($s$)$ of the tree.

$($c$)$ Find the height of the tree.

$($d$)$ Find the level of the node with info $80$

$($e$)$ List the path from the node with info $60$ to the node with info $35$ Question $2(25$ pts$)$:

By using the binary tree in Figure $1$;

$($a$)$ List the nodes that are visited by the function insert to insert $87$ into the tree in Figure $1.$

$($b$)$ What is the height of the tree after inserting $87?$

$($c$)$ Redraw the tree after inserting $87.$

$($d$)$ List the nodes that are visited by the function insert to insert $79$ into the tree in Figure $1.$

$($e$)$ What is the height of the tree after inserting $79?$

$($f$)$ Redraw the tree after inserting $79.$ Question $3(25$ pts$)$:

By using the binary tree in Figure $1$;

$($a$)$ What is the height of the tree after deleting $35$ from the tree in Figure $1?$

$($b$)$ Redraw the tree after deleting $35$ from the tree in Figure $1.$

$($c$)$ What is the height of the tree after deleting $72$ from the tree in Figure $1?$

$($d$)$ Redraw the tree after deleting $72$ from the tree in Figure $1.$

$($e$)$ What is the height of the tree after deleting $82$ from the tree in Figure $1?$

$($f$)$ Redraw the tree after deleting $82$ from the tree in Figure $1.$