Lecture 20: Screw that, I want It All

1. CSC 213 – Large Scale Programming Lecture 20:Screw that, I want It All

2. Implementing Map with a Tree • Accessing root much faster than going to leaves • In real-world, should place important data near root • Which key best at root of Tree of NHL teams?

3. Implementing Map with a Tree • Accessing root much faster than going to leaves • In real-world, should place important data near root • Which key best at root of Tree of NHL teams? • BST: Key for Entry added first

4. Implementing Map with a Tree • Accessing root much faster than going to leaves • In real-world, should place important data near root • Which key best at root of Tree of NHL teams? • BST: Key for Entry added first • AVLTree:RandomEntry near midpoint

5. Implementing Map with a Tree • Accessing root much faster than going to leaves • In real-world, should place important data near root • Which key best at root of Tree of NHL teams? • BST: Key for Entry added first • AVLTree:RandomEntry near midpoint • SplayTree:Most recently used key

6. Building a SplayTree • Another approach which builds upon BST • Not anAVLTree, however, but a new BST subclass

7. Concept Behind SplayTree • Splay trees do NOT maintain balance • Recently used nodes clustered near top of BST • Most recently accessed nodes take O(1) time • Other nodes may need O(n) time to find, however

8. Concept Behind SplayTree • Splay trees do NOT maintain balance • Recently used nodes clustered near top of BST • Most recently accessed nodes take O(1) time • Other nodes may need O(n) time to find, however

9. SplayTree Complexity • Without balancing, keeps BST'sO(n) complexity • Worst-case performance is like all unbalanced trees • But splaying gives expected O(logn) complexity • Averages complexity of O(1) & O(n) operations • If work concentrated on small subset, time is faster • Worst-case hard to create without knowing tree

10. Be Kind: Splay Your Tree • Assumes nodes reused soon after initial use • At end of each method, moves node up to root • Using node now O(1) and will only slowly drop in tree • Splay tree with each find, insert& remove • AVL-like restructuring to reorganize nodes in tree • But continues rotations until node becomes root

11. How To Splay

12. How To Splay • Uses trinode restructuringbut not like AVL does • Not balancing: selects node, parent, & grandparent • Always move node to root of subtree when splaying • When splaying, new types restructures also exist • Node & parent always used in these rotations • Rotations will also use grandparent, if it exists • Moving node to tree root is goal of splaying • May get a balanced tree, but WANT IT ALL, ASAP

13. When To Use Splay Tree • What applications are good for a splay tree? • Where would splay trees be a BAD IDEA?

14. Splay Node Rotations • Uses different nodes than previous rotations • AVLTreemoves node down to balance tree's tao • Can now be greedy: make it SplayTree's root

15. Splay Node Rotations • Uses different nodes than previous rotations • AVLTreemoves node down to balance tree's tao • Can now be greedy: make it SplayTree's root AVLTree

16. Splay Node Rotations • Uses different nodes than previous rotations • AVLTreemoves node down to balance tree's tao • Can now be greedy: make it SplayTree's root AVLTree SplayTree

17. Zig-Zag When Splaying a Tree • When node median of parent & grandparent • Just like in AVL tree, perform trinode restructuring • Use 7(+1) variables to set node's parent & children node grandparent grandparent parent parent T1 node T1 T2 T3 T4 T4 T2 T3

18. Zig-Zig When Splaying a Tree • When node, parent, & grandparent in a line • Rotation differs from AVL tree's trinode restructure grandparent parent T1 node T2 T4 T3

19. Zig-Zig When Splaying a Tree • When node, parent, & grandparent in a line • Rotation differs from AVL tree's trinode restructure • Greed is very good: splay node to subtree root node grandparent parent parent T1 T4 node grandparent T2 T3 T4 T1 T2 T3

20. SplayingRight Child Of Root • Simplest process is when parent is the root • Single rotation completes splaying process • Splaying does not stop until you reach the top • Rotation not always used, may only need restructures root node T1 T3 T2

21. SplayingRight Child Of Root • Simplest process is when parent is the root • Single rotation completes splaying process • Splaying does not stop until you reach the top • Rotation not always used, may only need restructures root node T1 T3 T2

22. SplayingRight Child Of Root • Simplest process is when parent is the root • Single rotation completes splaying process • Splaying does not stop until you reach the top • Rotation not always used, may only need restructures node root root node T1 T3 T1 T2 T3 T2

23. SplayingLeft Child Of Root • Simplest process is when parent is the root • Single rotation completes splaying process • Splaying does not stop until you reach the top • Rotation not always used, may only need restructures root node node root T1 T3 T3 T1 T2 T2

24. Which Node Gets Splayed?

25. Which Node Gets Splayed? • Only internal nodes can be splayed • When operation end with leaf, splay its parent

26. For Next Lecture • Weekly assignment available to test skills • Assignment due at regular time next Tuesday • Lab project phase #2 due tomorrow as well • When group ready to submit, send me e-mail • Midterm #1 in class on Friday • Open-book, open-note exam (as usual) • Use any lecture’s slides IF you have notes on them • No computers, calculators, or friends, however