Representing Binary Trees
Recall that a binary tree is a rooted tree wherein no node has more than two children. Additionally, every child is either a _left_child_ or a _right_child_ of its parent, even if its parent has only one child.

In the most popular binary tree representation, each tree node has three references to neighboring tree nodes: a "parent" reference, and "left" and "right" references for the two children. (For some algorithms, the "parent" references are unnecessary.) Each node also has an "item" reference.

BINARY SEARCH TREES
An _ordered_dictionary_ is a dictionary in which the keys have a total order, just like in a heap. You can insert, find, and remove entries, just as with a hash table. But unlike a hash table, you can quickly find the entry with minimum or maximum key, or the entry nearest another entry in the total order.
An ordered dictionary does anything a dictionary or binary heap can do and more, albeit more slowly.
The simplest implementation of an ordered dictionary is a binary search tree, wherein entries are maintained in a (somewhat) sorted order. The _left_subtree_ of a node is the subtree rooted at the node's left child; _right_subtree_ is defined similarly. A binary search tree satisfies the _binary_search_tree_invariant_: for any node X, every key in the left subtree of X is less than or equal to X's key, and every key in the right subtree of X is greater than or equal to X's key.
When a node has only one child, that child is either a left child or a right child, depending on whether its key is smaller or larger than its parent's key. (A key equal to the parent's key can go into either subtree.) An inorder traversal of a binary search tree visits the nodes in sorted order.