The height of a rooted tree is the maximum height of any leaf. The length of the unique path from a leaf of the tree to the root is, by definition, the height of that leaf. A rooted tree in which each non-leaf vertex has at most two children is called a binary tree. If each non-leaf vertex has exactly two children, the tree is called a full binary tree.
Consider the following statements. Which of the following is true?
- If a binary tree has $\text{L}$ leaves and height $h$ then $\text{L} \leq 2^h$
- If a binary tree has $\text{L}$ leaves then the maximum value of height $h$ is $\text{L}^{\text{L}}.$
- Given a full binary tree with $\text{L}$ leaves, the maximum height $h = L-1.$
- It is possible to have a binary tree with $35$ leaves and height $100.$
