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Red-Black Tree Neil Tang 02/04/2010

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1 Red-Black Tree Neil Tang 02/04/2010
CS223 Advanced Data Structures and Algorithms

2 CS223 Advanced Data Structures and Algorithms
Class Overview Definition Tree height Rotation and color flip Insert CS223 Advanced Data Structures and Algorithms

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Definition A red-black tree is a special binary search tree in which every node is either red or black; the root is black; if a node is red, then both its children are black; every simple path from a node to a null reference contains the same number of black nodes. CS223 Advanced Data Structures and Algorithms

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Definition CS223 Advanced Data Structures and Algorithms

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Height Theorem: A red-black tree with N nodes has height at most 2log(N+1). (pp.274 Cormen’s book) Experiments suggests that the average red-black tree is about as deep as an average AVL tree. The rotation happens less frequently. CS223 Advanced Data Structures and Algorithms

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An Example CS223 Advanced Data Structures and Algorithms

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Insertion Always color the new node to be inserted red. Remember that the new node will always be a leaf node right after insertion. If its parent is black, done! If its parent is red, perform a single (double) rotation! CS223 Advanced Data Structures and Algorithms

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Rotation if S is Black CS223 Advanced Data Structures and Algorithms

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Color Flip if S is red CS223 Advanced Data Structures and Algorithms

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Example: Insert 45 CS223 Advanced Data Structures and Algorithms

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Insert CS223 Advanced Data Structures and Algorithms

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Insert CS223 Advanced Data Structures and Algorithms

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Insert CS223 Advanced Data Structures and Algorithms

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