Skewed Trees relation to Binary Search Tree

Question

I know what Binary search tree is and I know how they work. But what does it take for it to become a skewed tree? What I mean is, do all nodes have to go on one side? or is there any other combination?

Having a tree in this shape (see below) is the only way to make it a skewed tree? If not, what are other possible skewed trees?

Skewed tree example:

Also, I searched but couldn't find a good solid definition of a skewed tree. Does anyone have a good definition?

Answer 1

Figured out a skewed Tree is the worst case of a tree.

` The number of permutations of 1, 2, ... n = n!

The number of BST Shapes: (1/n+1)(2n!/n!n!)

The number of skewed trees of 1, 2, ....n = 2^(n-1)

` Here is an example I was shown: http://i61.tinypic.com/4gji9u.png

Answer 2

A good definition for a skew tree is a binary tree such that all the nodes except one have one and only one child. (The remaining node has no children.) Another good definition is a binary tree of n nodes such that its depth is n-1.

Answer 3

A binary tree, which is dominated solely by left child nodes or right child nodes, is called a skewed binary tree, more specifically left skewed binary tree, or right skewed binary tree.