Red-Black Trees

Binary Search Tree operations are O(h), not O(lgn).

If we can keep the tree balanced, the operations will be O(lgn).

This is the goal of Red-Black trees.

• Internal Node
  
  
  
  NIL children are leaves
  color $\in$ {Red, Black}
• Leaf Node: NIL
  Leaf nodes are sentinels (dummy objects), and the color is always Black.

By constraining colors of nodes along paths from root to leaf, RB trees ensure no path is more than twice as long as any other (the tree is balanced).