Red black trees presentation
Download as PPT, PDF1 like2,431 views
Red-black trees are binary search trees where each node is colored red or black. They provide O(log N) operations by ensuring that every path from root to leaf contains the same number of black nodes. They can be viewed as representations of 2-3-4 trees, where each black node corresponds to a node in the 2-3 tree and each red node is placed in the same node as its black parent. Inserting a new node may cause a "double red" violation, requiring restructuring by rotations or recoloring to maintain the red-black properties.
Red black trees presentation
- 1. Red-Black Trees Niño Guerrero Dexter Paul Gumahad Rene Madera Reymart Pagente Data Structure || JRMSU Computer Science
- 2. Red-Black Trees • A Red-Black tree is a binary search tree with these traits: – Every node is either red or black. – The root is always black. – If a node is red, its children must be black. – Every path from any node to a null must have the same number of black nodes. • Operations on Red-Black trees are O(log N). Data Structure || JRMSU Computer Science
- 3. Red-Black tree c a f b d g e Data Structure || JRMSU Computer Science
- 4. Red-Black Trees • Red-black trees can be thought of as binary tree representations of a 2-3-4 tree. • A 2-3-4 tree is a B-tree of degree 4. • This means each internal node has either 2, 3, or 4 children. • The next slide illustrates this. Data Structure || JRMSU Computer Science
- 5. 2-3-4 tree c a b f d e Data Structure || JRMSU Computer Science g
- 6. How the Trees Relate c c a f d e f a b d b g g e Each black node represents a node in the 2-3-4 tree. Each red node is in the same node with its black parent. This explains why every path has the same number of black nodes. Data Structure || JRMSU Computer Science
- 7. Mappings a a b a or a b a b b a b c a Data Structure || JRMSU Computer Science c
- 8. Inserting into a Red-Black Tree • An inserted node is placed as in a binary search tree as a red node, unless it is the root. • If the parent of the new node is also red, called a “double red”, the tree will have to be adjusted, since a red child must have a black parent. Data Structure || JRMSU Computer Science
- 9. Two Cases 1. a u w c b 2. a Inserting node z causes double red, and z’s parent has black sibling w. This occurs when a 4-node is malformed: must restructure. v z u c w b z v Inserting node z causes double red, and z’s parent has red sibling w. This occurs when a 4-node overflows: must recolor. Note: these are partial trees so not all Data Structure || JRMSU Computer subtrees are shown. of their Science
- 10. Restructuring a c w c w a b a w c b b c b Double rotation w a Single rotation b The malformed 4-node is now a well-formed 4-node. a c Data Structure || JRMSU Computer Science Parent is black, children are red.
- 11. Recoloring b b w d a w d a c c b w a b c w a d Note: since b is now red, this can cause a double red with b’s parent. If so, the two cases are considered again for Science its parent. Data Structure || JRMSU Computer b and c d
- 12. Example e e e h h k 1. Insert e 2. Insert h h h e k e 3. Insert k, h has null (black) sibling h e k n 4. Restructure 5. Insert n, k has red sibling Data Structure || JRMSU Computer Science k n 6. Recolor (root left black)
- 13. End Data Structure || JRMSU Computer Science