Red-black Tree: Difference between revisions

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# There are never 2 red nodes in a row (a red node has only black children).
# There are never 2 red nodes in a row (a red node has only black children).
# Every path taken from root to a NULL pointer has the same number of black nodes.
# Every path taken from root to a NULL pointer has the same number of black nodes.
These invariants are in addition to the fact that the red-black tree is a binary search tree, so it has the [[Binary_Search_Trees#Binary_Search_Tree_Property|Binary Search Tree Property]]
These invariants are in addition to the fact that the red-black tree is a binary search tree, so it has the [[Binary_Search_Trees#Binary_Search_Tree_Property|Binary Search Tree Property]].

Revision as of 05:00, 13 October 2021

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Overview

Red-black trees had been invented by Bayer (1972) and Guibas, Sedgewick (1978). They are a type of binary search tree that self-balances on insertion and deletion, thus maintaining its height to a minimum, which leads to efficient operations. Almost all binary search tree operations have a running time bounded by the tree height, and in this case the tree height stays constant at log n, yielding O(log n) operations.

Red-Black Tree Invariants

  1. Each node is either red or black.
  2. The root is always black.
  3. There are never 2 red nodes in a row (a red node has only black children).
  4. Every path taken from root to a NULL pointer has the same number of black nodes.

These invariants are in addition to the fact that the red-black tree is a binary search tree, so it has the Binary Search Tree Property.