Question

assume I have a complete binary tree up-to a certain depth d. What would the time complexity be to traverse (pre-order traversal) this tree.

I am confused because I know that the amount of nodes in the tree is 2^d, so therefore the time complexity would be BigO(2^d) ? because the tree is growing exponentially.

But, upon research on the internet, Everyone states that’s traversal is BigO(n) where n is the number of elements (which would be 2^d in this case), not BigO(2^d), what am I missing?

thanks

Answer 1

n is defined as the number of nodes.

2^d is only the number of nodes when every possible node at that depth is full

ie.

     o
   /   \
  o     o
 / \   
o   o

only has 5 nodes when 2^d is 8

A complete binary tree has every node filled except for last row and all of the nodes are filled to the left. You can find the definition on wikipedia

http://en.wikipedia.org/wiki/Binary_tree#Types_of_binary_trees