Week 3 Web site:

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1 Week 3 Web site: (announcements and resources) Canvas: (modules, assignments, grades) Top Hat join code: X-Team Exercise #1: (in-class Tuesday or Wednesday) Homework: h1 (due before 10pm Fri) Program: p1 peer review (due before 10pm Thursday) Do not complete the rubric Do comment on readability of reviewed code Be constructive (describe what would have improved redability) TAs will be complete grade rubric for each student Report exam conflicts and accommodation requests via: Read: Module 4 before lecture next week THIS WEEK in Lecture: Remaining pages from last Week X-TEAM exercise (Tues or Wed) find your X-team number before class Canvas -> People -> X-Team number Find your X-TEAM group (in lecture) complete the exercise in class and submit photo of completed work to Canvas AVL Trees Next Week Red-Black Trees o insert Git B-Trees insert delete Copyright 2018 Deb Deppeler CS 400 (F18): W3-1

2 Practice III Balancing (revised) insert increases height of sub-tree B left-right rotate at 10-B insert increases height of sub-tree B right-left rotate at 30-B Copyright 2018 Deb Deppeler CS 400 (F18): W3-2

3 AVL AVL: Adelson-Velsky and Landis named after its two Soviet inventors Georgy A-V and Evgenii L "An algorithm for the organization of information" The AVL tree is height-balanced (almost-balanced) Uses the rotations we just learned to maintain H-B Complexity of operations O(H), but what is the height of an almost-balanced AVL tree? AV-L proved that in the worst-case AVL tree is ~ 1.44 log2(n) Implementation Must know the Balance Factor for each node Detect Out Of Balance: when B.F. > 1 Fix: If insert was in left child's left sub-tree, right rotate If insert was in right child's right sub-tree, left rotate If insert was in right child's left sub-tree, right-left rotate If insert was in left child's right sub-tree, left-right rotate How can we know the height of each sub-tree? compute height extra processing on each insert delete store height in node must keep current store height difference - -1,0,1 (or it is out of balance) Copyright 2018 Deb Deppeler CS 400 (F18): W3-3

4 AVL Delete? CS 400 Programming III Copyright 2018 Deb Deppeler CS 400 (F18): W3-4

5 Red-Black Trees (RBT) RBT: Example: Red-Black Tree Properties root property red property black property Red-Black Tree Operations print lookup insert delete Copyright 2018 Deb Deppeler CS 400 (F18): W3-5

6 Inserting into a Red-Black Tree Goal: If T is Empty If T is Non-Empty Which of the properties might be violated as a result of inserting a red leaf node? root property black property red property Non-Empty Case 1: K's parent P is black Copyright 2018 Deb Deppeler CS 400 (F18): W3-6

7 Non-Empty Case 2 Non-Empty Case 2: K's parent P is red Fixing an RBT Tri-Node Restructuring if Recoloring is done if Copyright 2018 Deb Deppeler CS 400 (F18): W3-7

8 Practice 1. Starting with an empty RBT, show the RBT that results from inserting 7 and Redraw the tree from above and then show the result from inserting Redraw the tree from above and then show the result from inserting Redraw the tree from above and then show the result from inserting 1 and Redraw the tree from above and then show the result from inserting 20. Copyright 2018 Deb Deppeler CS 400 (F18): W3-8

9 More Practice! 6. Redraw the tree from the previous page and then show the result from inserting Insert the same list of values into an empty BST: 7, 14, 18, 23, 1, 11, 20, 29 What does this demonstrate about the differences between a BST and RBT? Copyright 2018 Deb Deppeler CS 400 (F18): W3-9

10 More Practice? 8. Show the result from inserting 25 in the RBT below. 9. Redraw the tree from above and then show the result from inserting 27. Copyright 2018 Deb Deppeler CS 400 (F18): W3-10

11 Cascading Fixes Fixing an RBT UPDATED! Recoloring is done if P's sibling S is red Tri-Node Restructuring is done if P's sibling S null Copyright 2018 Deb Deppeler CS 400 (F18): W3-11

12 RBT Complexity print lookup insert Copyright 2018 Deb Deppeler CS 400 (F18): W3-12