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Case 1 for Color Fixup ․Case 1: The doubly black node x has a red sibling w. ․One left rotation around x.p and constant # of color changes are done. ․The # of black nodes in each path is preserved. ․Converts into case 2, 3, or 4. Unit 3 Spring 2013 24
Case 2 for Color Fixup ․Case 2: x has a black sibling and two black nephews. ․Take off one black from x and its sibling, push one black up to x.p, and repeat the while loop with x.p as the new node x. ․The # of black nodes in each path is preserved. ․Perform constant # of color changes and repeat at most O(h) times. (No rotation!!) B Unit 3 Spring 2013 25
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 and 14: Left Rotation Left-Rotate(T, x) 1.
Page 15 and 16: Insertion: Black Uncle ․How to fi
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: Four Cases for Color Fixup ․ Case
Page 27 and 28: Case 4 for Color Fixup ․Case 4: x
Page 29: Conclusion: Red-Black Trees ․Red-

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