Binary Search Trees

Question

This is some code found on wikipedia regarding BST :

# 'node' refers to the parent-node in this case
 def search_binary_tree(node, key):
     if node is None:
         return None  # key not found
     if key < node.key:
         return search_binary_tree(node.leftChild, key)
     elif key > node.key:
         return search_binary_tree(node.rightChild, key)
     else:  # key is equal to node key
         return node.value  # found key

Now here's a Binary Tree :

       10
    5        12
  3   8    9   14
     4 11  

If I am searching for 11, and I follow the algorithm up there, I start with 10, I go right to 12, and then left to 9. And I reach the end of the tree without finding 11. But 11 exists in my tree, it's just on the other side.

Can you please explain what are the restrictions in a Binary Tree for this algorithm to work on my tree ?

Thanks.

Answer 1

It's just because your tree is not a binary search tree: it is not ordered correctly. The BST is build as described in the algorithm actually. For instance in your tree: the node '9' is not at the right position because as 9 < 10 it should be under the left branch of your root node '10'. Same for '14' and '11' which should be on the right branch.

for instance a BST could sth like this:

    10
  5    11
3   8    12
          14