The best way to calculate the height in a binary search tree? (balancing an AVL-tree)

Question

I\'m looking for the best way to calculate a nodes balance in an AVL-tree. I thought I had it working, but after some heavy inserting/updating I can see that it\'s not worki

Answer 1

Well, you can compute the height of a tree with the following recursive function:

int height(struct tree *t) {
    if (t == NULL)
        return 0;
    else
        return max(height(t->left), height(t->right)) + 1;
}

with an appropriate definition of max() and struct tree. You should take the time to figure out why this corresponds to the definition based on path-length that you quote. This function uses zero as the height of the empty tree.

However, for something like an AVL tree, I don't think you actually compute the height each time you need it. Instead, each tree node is augmented with a extra field that remembers the height of the subtree rooted at that node. This field has to be kept up-to-date as the tree is modified by insertions and deletions.

I suspect that, if you compute the height each time instead of caching it within the tree like suggested above, that the AVL tree shape will be correct, but it won't have the expected logarithmic performance.

Answer 2

• Height is easily implemented by recursion, take the maximum of the height of the subtrees plus one.

• The "balance factor of R" refers to the right subtree of the tree which is out of balance, I suppose.

Answer 3

You do not need to calculate tree depths on the fly.

You can maintain them as you perform operations.

Furthermore, you don't actually in fact have to maintain track of depths; you can simply keep track of the difference between the left and right tree depths.

http://www.eternallyconfuzzled.com/tuts/datastructures/jsw_tut_avl.aspx

Just keeping track of the balance factor (difference between left and right subtrees) is I found easier from a programming POV, except that sorting out the balance factor after a rotation is a PITA...