Construct heuristic functions and apply a) simple hill climbing b)
steepest-ascent hill climbing to 3 problems
Tower of Hanoi, Monkey and Bananas, Missionaries and Cannibals. 
Show search trees and explain how your functions help to reduce
search. Do they really work? If your functions do not work properly
explain what happened.

It sounds like you are looking for an implementation of these
functions. I'd do this (it's actually quite an interesting problems)
but it's a little more work than a $2.00 question usually entails,
(for me probably a $20.00 question although others might have
different opnions) for a Java implementation, especially since I'd
need to write code to display the search trees.

In Scheme/Lisp?