Question

I am currently trying to wrap my head around recursion so I picked a c++ textbook and began to read. The first couple of pages in the chapter on recursion were easy to understand but then I got to an item that doesn’t make sense to me.

 int height(node *p)
 {
    if(p==NULL)
       return 0;
    else{
   return 1 + max(height(p->llink),height(p->rlink));

  }

If max gives me the greatest of two values, how does max get its arguments from what height it’s returning.
If anyone could help I would greatly appreciate it…..

Answer 1

To understand recursion you have to think recursively:

• you can understand that an empty tree has height 0
• you can understand that a generic non-empty tree has height 1 + the height of the longest subtree (which can be the one starting from the left or from the right)

Starting from this you can trivially understand the code. If you draw the tree you will see what happens. If you have for example

     A
    / \
   B   C
  / \  
 D   E

• height(A) will return 1 + max(height(B), height(C))
• height(B) will return 1 + max(height(D), height(E))
• height(C) will return 1 + max(height(NULL), height(NULL)) = 1
• height(D) will return 1 + max(height(NULL), height(NULL)) = 1
• height(E) will return 1 + max(height(NULL), height(NULL)) = 1

so

height(A) = 1 + max(height(B), height(C)) =
= 1 + max(1 + max(height(D),height(E)), 1) =
= 1 + max(1 + 1, 1) = 1 + max(2, 1) = 3

(I omitted calls to height(NULL) because they are trivially 0 and otherwise it would have been too much verbose.)