$3$ a$)$ Code count, height, and sum methods for a binary search tree node. Sum adds up all the values in the tree.

b$)$ To efficiently search a binary search tree what must be true about that binary search tree? Explain why this is so$.$ List the steps used to get a Binary Search Tree in this form. $($You can write code if you prefer.$)$

$4)$ a$)$ Given the following list of inputs: $(58,42,21,74,82,78,68,87)$

Trace the heapsort algorithm for a heap. Do this trace in array form.

b$)$ Write the sort method for a heapsort and write any methods called directly from your sort method.