Finding the max value in a heap (Scheme)

Question

I'm trying to return a function that returns the maximum value in a heap (where the heap goes from min on top to max on the bottom). I understand how I could do something similar to this in BST. But I don't know how I would do this in a heap because I don't completely understand the organization for heaps. In a BST I would just keep going to the left until I get to the end. But if I keep going towards the bottom of a heap, there's a chance that the maximum value is on the other subtree. (Not sure if that made complete sense). Any help in how to approach this would be appreciated. Thanks in advance.

*edit

So I thought of a different way to approach this but it's not correct. Basically after coming to the conclusion that heaps are just a bunch of nested lists, I made a code that makes the heap into one list and uses another helper function that gets the max value. But how would I approach this by actually going through and looking at each individual node?

Answer 1

Right, in a min-heap each node is only guaranteed to be greater than it's parent. A full walk will give a solution, but you can be a little smarter by realizing the maximum will be in a singleton tree at the bottom of the structure. You can also use let to force evaluation of the leftmost tree first. Assuming a binary structure for the heap.

(define (max-heap min-heap)
  ((empty-heap? min-heap)
   (error "empty heap has no maximum")
  ((singleton? min-heap)
   (node min-heap))
  ((empty-heap? (left-heap min-heap))
   (max-heap (right-heap min-heap)))
  ((empty-heap? (right-heap min-heap))
   (max-heap (left-heap min-heap)))
  (else 
   (let ((left-max (max-heap (left-heap min-heap))))
     (let ((right-max (max-heap (right-heap))))
       (if (> left-max right-max) left-max right-max))))))

You still have to walk the whole tree, but you only need to do it once. And your stack is only ever as big as the depth of the heap.