Question

This has already been discussed here, but I have an implementation below (which was never discussed in the thread),

public boolean isBalanced(BSTNode node) {
    if(maxHeight() > (int)(Math.log(size())/Math.log(2)) + 1) 
        return false;
    else
        return true;
}

where maxHeight() returns the maximum height of the tree. Basically I am checking if maxHeight > log(n), where n is the number of elements in the tree. Is this a correct solution?

Answer 1

This solution is not correct. A balanced tree is balanced if its height is O(lg(n)), thus it (the height) needs to be smaller then c*lg(n) – for some CONSTANT c. Your solution assumes this constant is 1.

Note that only a complete tree is of height lg(n) exactly.

Look for example on a Fibonacci tree, which is a balanced tree (and is actually the worst case for an AVL tree). However – its height is larger then lgn (~1.44*lg(n)), and the suggested algorithm will return a fibonacci tree is not balanced.