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Insertion ․Every insertion takes place at a leaf; this changes a black NIL pointer to a node with two black NIL pointers. ․To preserve the black height of the tree, the new node is set to red. If the new parent is black, then we are done; otherwise, we must restructure (Property 4 violation)!! ․How to fix two reds in a row? Check uncle's color! If the uncle is red, reversing the relatives' colors either solves the problem or pushes it one-level higher. Unit 3 Spring 2013 14
Insertion: Black Uncle ․How to fix two reds in a row? Check uncle's color! If the uncle is black (all nodes around the new node and its parent must be black), rotate right about the grandparent. Change some nodes' colors to make the black height the same as before. Unit 3 Spring 2013 15
Page 1 and 2: Unit 3: Data Structures on Trees
Page 3 and 4: Tree Search ․Operations Search ca
Page 5 and 6: Tree Insertion ․Insert z into tre
Page 7 and 8: Deleting z in a Binary Search Tree
Page 9 and 10: Balanced Search Trees: Red-Black Tr
Page 11 and 12: Black Height (cont'd) ․Let h be t
Page 13: Left Rotation Left-Rotate(T, x) 1.
Page 17 and 18: RB-Tree Insertion Fixup RB-Insert-F
Page 19 and 20: Deleting z in an RB-Tree T.nil q z
Page 21 and 22: RB-Tree Deletion (cont’d) RB-Dele
Page 23 and 24: Four Cases for Color Fixup ․ Case
Page 25 and 26: Case 2 for Color Fixup ․Case 2: x
Page 27 and 28: Case 4 for Color Fixup ․Case 4: x
Page 29: Conclusion: Red-Black Trees ․Red-

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