Discuss an algorithm to traverse a tree, depth first.

Write a function that takes as input a binary tree, and returns the length of the longest path.

For example, in this binary tree:

    1
   / \
  2   3
     /
    5

the answer is 2, since the path from vertex 1 to vertex 5 involves two edge traversals.

Write function that takes a binary tree and efficiently returns the Nth smallest element.

For example, if N=4, and the tree looks like:

    3
   / \
  2   5
 /   / \
1   4   6

The function should return 4.

Write a function that takes as input a binary tree, and prints out each level of the tree on a newline. For example:

    a
   / \
  b   c
 /   / \
d   e   f

will output:

a
b c
d e f