RED BLACK TREE & TRIES

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SEARCH STRUCTURES

Red Black Tree  click here

Red Black Tree Algorithm  click here

Tries click here

Red-Black Properties

  1. Every node is either red or black.
  2. Every leaf (NULL pointer) is black.
    ■ Note: this means every “real” node has 2 children
  3. If a node is red, both children are black
    ■ Note: can’t have 2 consecutive reds on a path
  4. Every path from node to descendent leaf contains the same number of black nodes.
  5. The root is always black

RB Trees: Worst-Case Time

  • So we’ve proved that a red-black tree has  O(lg n) height
  • Corollary: These operations take O(lg n) time:
                        ■Minimum(), Maximum()
                        ■Successor(), Predecessor()
                        ■Search()
  • Insert() and Delete():
                        ■Will also take O(lg n) time
                        ■But will need special care since they modify tree

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