Purely Functional Data Structures

A look at numerous data structures in purely functional setting. Based on the work of Chris Okasaki. Also a brief study of amortized analysis.

Related haskell code: https://github.com/tejasbubane/functional-data-structures

Transcript

1. PURELY FUNCTIONAL DATA STRUCTURES BASED ON THE WORK OF CHRIS OKASAKI BY TEJAS BUBANE BANGALORE FUNCTIONAL PROGRAMMING MEETUP https://github.com/tejasbubane/functional-data-structures
2. PURELY FUNCTIONAL ?? ▸Immutable ▸Persistent
3. LINKED LIST data List a = Nil | Cons a (List a)
4. STRUCTURAL SHARING xs ++ ys update xs 2 7
5. QUEUE data Queue a = Queue [a] [a] FIFO
6. BINARY SEARCH TREES data Tree a = Empty | Node (Tree a) a (Tree a) log n
7. PATH COPYING insert ‘e’ xs
8. SKEWED BINARY SEARCH TREES ▸ Depth ~ O(n) ▸ Linear Search Time
9. RED-BLACK TREES data Color = Red | Black data RBTree a = Empty | Node Color (RBTree a) a (RBTree a)
10. RED-BLACK TREES ▸No red node has red child ▸Every path from root to empty node contains same number of black nodes
11. RED-BLACK TREES - INSERTION
12. TRIES
13. ANALYSIS
14. AMORTIZED ANALYSIS data Queue a = Queue [a] [a] check :: [a] -> [a] -> Queue a check [] r = Queue (reverse r) [] check f r = Queue f r Take slowest cost and distribute over faster ones
15. LAZINESS ▸ Evaluate on demand - Thunks ▸ Memoize results
16. BANKERS QUEUES check :: Queue a -> Queue a check q@(Queue lenf fs lenr rs) | lenf <= lenr = Queue (lenf + lenr) (fs ++ reverse rs) 0 [] | otherwise = q No pattern-matching on lists (fs & rs) so no evaluation.
17. THANKS !! QUESTIONS