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CS61B Textbook
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DISCLAIMER
1. Introduction
2. Lists
3. Testing
4. Inheritance, Implements
5. Generics and Autoboxing
7. Packages and Access Control
9. Extends, Casting, Higher Order Functions
11. Subtype Polymorphism, Comparators, Comparable
12. Exceptions, Iterators, Object Methods
13. Asymptotics I
14. Disjoint Sets
15. Asymptotics II
16. ADTs and BSTs
17. B-Trees
17.1 BST Performance
17.2 Big O vs. Worst Case
17.3 B-Tree Operations
17.4 B-Tree Invariants
17.5 B-Tree Performance
17.6 Summary
17.7 Exercises
18. Red Black Trees
19. Hashing I
20. Hashing II
21. Heaps and Priority Queues
22. Tree Traversals and Graphs
23. Graph Traversals and Implementations
24. Shortest Paths
25. Minimum Spanning Trees
26. Prefix Operations and Tries
27. Software Engineering I
28. Reductions and Decomposition
29. Basic Sorts
30. Quicksort
31. Software Engineering II
32. More Quick Sort, Sorting Summary
33. Software Engineering III
34. Sorting and Algorithmic Bounds
35. Radix Sorts
36. Sorting and Data Structures Conclusion
37. Software Engineering IV
38. Compression and Complexity
39. Compression, Complexity, P = NP
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17.4 B-Tree Invariants
B-Tree Invariants
Because of the way B-Trees are constructed, they have two invariants:
1.
All leaves are the same distance from the root.
2.
A non-leaf node with k items must have exactly k + 1 children.
These two invariants guarantee a "bushy" tree with
log
N
\log N
lo
g
N
height.
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17.5 B-Tree Performance
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