quartz/content/notes/binary-search-tree.md

title	aliases	tags
binary-search-tree	binary search tree, BST	cosc201 datastructure

code

bst-operations

a collection of nodes with one distinguished node called the root

rules:

• the node data contains a key which comes from some ordered type e.g., string
• each node can have at most who children - there are two fixed slots called left child and right child
• the left child node and it descendents are called the left subtree
• the key value at a nodes left child (and all its descendants) must be less than the key of the node
• the key value at a nodes right child (and all its descendants) must be greater than the key of the node
• we do not allow duplicate keys

Notation

• n.key for key
• n.l and n.r for left and right children
• n.p for its parent
• nil for a "not here" marker. e.g., n.r = nil means "n has no right child"

e.g.,

In this example:

• root.p = nil
• root.r = n
• n.p = root
• n.key = emu
• n.l = nil
• n.r.key = rat