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Rotations ․Left/right rotations: The basic restructuring step for binary search trees. ․Rotation is a local operation changing O(1) pointers. ․In-order property preservation: An in-order search tree before a rotation stays an in-order one. In-order: The property of a binary search tree still holds!! Unit 3 Spring 2013 12
Left Rotation Left-Rotate(T, x) 1. y = x.right // Set y 2. x.right = y.left // Turn y's left subtree into x's right subtree 3. if y.left T.nil 4. y.left.p = x 5. y.p = x.p // Link x's parent to y 6. if x.p == T.nil 7. T.root = y 8. elseif x == x.p.left // x is a left child 9. x.p.left = y 10. else x.p.right = y 11. y.left = x // Put x on y's left 12. x.p = y Unit 3 Spring 2013 13
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: Black Height (cont'd) ․Let h be t
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 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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