Binary search tree BST

1
Binary search tree (BST)

• In BST, for every node v
• Left subtree has keys vs key
• Right subtree has keys vs key
• BST heights
• average O(logn)
• worst case O(n) --- which we want to avoid
• A better balanced BST Red-Black trees
• worst case height 2log2n

2
Red-black tree rules

• Every node is either black or red.
• The root is always black.
• Red nodes parent must be black.
• Every path from the root to a left have the same
  black-height (i.e. same number of black nodes).

3
Why same black height?

• Balance!
• h - black height
• h - height of the tree
• longest path from root to leaf
• __________________________________________________
  ________________________________
• shortest path from root to left

h lt 2h
lt 2
4
Is this a red-black tree?
5
Is this a red-black tree?
new inserted node
6
Is this a red-black tree?
new inserted node
7
Is this a red-black tree?
new inserted node