The document discusses various immutable data structures including stacks, trees, vector tries, hash array mapped tries (HAMTs), log-structured merge trees (LSM-Trees), and their applications in programming and databases like Git. It provides code examples of implementing immutable data structures in Java to demonstrate how they can be used to make code thread-safe and avoid issues like null pointer exceptions.

1. Immutable Data Structures
Eric Fu
2018-06-15

2. Agenda
• Stack
• Tree
• Vector Trie
• HAMT
• Git
• LSM-Tree
• Practice

3. Immutable Stack
A Clean Example for Starters

4. CopyOnWriteArrayList ?

5. Stack

6. Stack

7. Stack

8. Stack

9. Immutable Tree

10. Tree

11. Tree

12. RB-Tree

13. RB-Tree

14. Vector Trie
Immutable Array List

15. Trie
Also called:
• Dictionary tree
• Radix tree
• Prefix tree
• Digital search tree

16. Trie (compressed)
• With prefix only
"A", "to", "tea", "ted"
"ten", "i", "in", "inn"

17. Vector Trie

18. Vector Trie (Mutable)

19. Vector Trie - Update

20. Vector Trie - Push

21. Vector Trie – Push (1/3)

22. Vector Trie – Push (2/3)

23. Vector Trie – Push (3/3)

24. Vector Trie – Pop (1/3)

25. Vector Trie – Pop (2/3)

26. Vector Trie – Pop (3/3)

27. Complexity
• Mostly....

28. Go Efficient
• More branches

29. Go Efficient
• More branches
• Align to binary bits

30. Go Efficient
• More branches – 32
• Align to binary bits – 5 bits

31. Hash Array Mapped Trie (HAMT)
Immutable Hash Table

32. Rethink Vector Trie
• Must the index be continuous (0, 1, 2...) ?
• Actually not!
• Furthermore: hash(anything) -> integer

33. HAMT - Naive
• Contains {0x00, 0xff}

34. HAMT – Bitmap Compressed
• Compress each node with bitmap

35. HAMT - Pruned
• Leave out unnecessary nodes

36. Some Real-world Examples

37. Git

38. How Git works?
• Git stored all versions of all directories and files
• A Git commit is a snapshot of root directory
• A Git branch/tag is a reference to some commit

52. That's it!

53. Log-Structured Merge-Tree (LSM-
Tree)

59. More Trees

60. Insights
• Modify in memory
• Read merged results
• Newly merged blocks are appended

61. Modern LSM-Tree Implements
• Memtable
• Immutable Memtable
• Level 0 (overlapped)
• Level 1
• Level 2
• ....
Memory
Disk
Write
Read
61

62. Immutable in Practice
In Java

63. A Familiar Example
• Java's string vs. CPP's string

64. Easy to understand
• Same name, same value
Mutable Request
Immutable Request:

65. Always thread-safe

66. Always thread-safe
• Immutable to programming as MVCC to database
• Lock or Snapshot

67. Other Pros
• Friendly for caching
• Atomic Failure
• Avoid null-pointer exception

68. Java Example 1

69. Java Example 2
• Requirement: cache the results of factorizing
• Two variable with setter?
• Two atomic variable?

70. Java Example 2 (cont.)

71. Java Example 2 (cont.)

72. Thanks!
Q&A