How I won the APL Problem Solving Competition

1. HowI won the APL Problem SolvingCompetition Emil Bremer Orloff Dyalog’14 Eastbourne, UK

2. Whatwillthisbeabout ”Emil will describe his experiences of Dyalog and tell us how he managed to master enough of it to win the competition.”

3. Whatwillthisbeabout • Aboutme • Relation to APL • The competition

4. Aboutme • Studying Computer Science at Aarhus University

5. Aboutme • Studying Computer Science at Aarhus University

6. Aboutme • Studying Computer Science at Aarhus University • 4 yearsintomymaster’sdegree

7. Aboutme • Studying Computer Science at Aarhus University • 4 yearsintomymaster’sdegree • Specialized in Cryptography and programminglanguages • Programmingexperience in: Java, Ocaml, SML, C, Coq, (Matlab)

8. My firstencounterwith APL

9. My firstencounterwith APL • 2011: mydepartmentshared a link to the DyalogCompetition

10. My firstencounterwith APL • 2011: mydepartmentshared a link to the DyalogCompetition • A horrible mess of funnycharacters!

11. My firstencounterwith APL • 2011: mydepartmentshared a link to the DyalogCompetition • A horrible mess of funnycharacters! • Becameinteressted due to the nature of the language – had to useanother approach • Didn’t have time to learn

12. Fastforward  2014 • Last chance to compete as a student

13. Fastforward  2014 • Last chance to compete as a student • Legrand’s book

14. The Competition • Phase 1 • 10 problems solvedusingdfns • Herefollows a couple of my solutions

15. Problem 5 - MirrorMirror • Tellif a given strings is a palidrome

16. Problem 5 - MirrorMirror • Tellif a given strings is a palidrome • Naïve: {⍵≡⌽⍵}

17. Problem 5 - MirrorMirror • Tellif a given strings is a palidrome • Naïve: {⍵≡⌽⍵} • Unfortunatelyonly letters are relevant

18. Problem 5 - MirrorMirror • Tellif a given strings is a palidrome • Naïve: {⍵≡⌽⍵} • Unfortunatelyonly letters arerelevant • {{⍵≡⌽⍵}(⍵∊'abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ')/⍵}

19. Problem 8 - Go the distance • Find the distance betweentwo points in n-dimensional space

20. Problem 8 - Go the distance • Find the distance betweentwo points in n-dimensional space • {(+/(⍵-⍺)*2)*0.5}

21. Part II • Consisted of 3 problem sets • Eachcontaining 3 parts (easy, medium, hard)

22. Part II • Consisted of 3 problem sets • Eachcontaining 3 parts (easy, medium, hard) • Bioinformatics • Cryptography • Recreation and games

23. Part II • Consisted of 3 problem sets • Eachcontaining 3 parts (easy, medium, hard) • Bioinformatics(easy, medium, hard) • Cryptography(easy, hard) • Recreation and Games (hard)

24. Bioinformatics • K-mercounting • Most frequentk-mers • Clumpfinding • Approximatepatternmatching • Sharedk-mers • Longestsharedsubstring • Shortestnon-sharedsubstring • Edit distance

25. Bioinformatics • K-mercounting • Most frequentk-mers • Clumpfinding • Approximatepatternmatching • Sharedk-mers • Longestsharedsubstring • Shortestnon-sharedsubstring • Edit distance

26. Bioinformatics • K-mercounting • Most frequentk-mers • Clumpfinding • Approximatepatternmatching • Sharedk-mers • Longestsharedsubstring • Shortestnon-sharedsubstring • Edit distance Substrings and ⍷

27. Substring • Created a helperfunctionthatcouldcreate all substrings of a given length

28. Substring • Created a helperfunctionthatcouldcreate all substrings of a given length • Create all relevant indexes

29. Substring • Created a helperfunctionthatcouldcreate all substrings of a given length • Creating all relevant indexes

30. Substring • Created a helperfunctionthatcouldcreate all substrings of a given length • Creating all relevant indexes • UseN-Wisereduce! {⍵>⍴⍺:'' ⍵,/⍺} • Changedshortlybefore deadline

31. Bioinformatics • K-mercounting • Most frequentk-mers • Clumpfinding • Approximatepatternmatching • Sharedk-mers • Longestsharedsubstring • Shortestnon-sharedsubstring • Edit distance Substrings And ⍷

32. Edit distance • Given twostrings find the minimal editsthatbrings the first to the second • An edit: • Insert a character • Delete a character

33. Edit distance • Generate a matrix that gives the editdistancebetween the substrings

34. Edit distance • Generate a matrix that gives the editdistancebetween the substrings

35. Edit distance • Generate a matrix that gives the editdistancebetween the substrings Firstrow and first column arealways the same

36. Edit distance • Each element in table is given by • 0+value to NW if the characters match • 1+the minimum value to the W, NW or N if the characters does not match

37. Edit distance • Each element in table is given by • 0+value to NW if the characters match • 1+the minimum value to the W, NW or N if the characters does not match • Which is min(cost+NW, 1+W, 1+N)

38. Edit distance firstRow←(⍳1+⍴t)-1

39. Edit distance firstRow←(⍳1+⍴t)-1 nextRow←{ {(⍺+1)⌊⍵}\(1+⍵)⌊(1+⊃⍵),(¯1↓⍵)+⍺≠t }

40. Edit distance firstRow←(⍳1+⍴t)-1 nextRow←{ {(⍺+1)⌊⍵}\(1+⍵)⌊(1+⊃⍵),(¯1↓⍵)+⍺≠t } lastRow←⊃nextRow/(⌽s),⊂firstRow ed←⊃⌽lastRow

41. Edit distance firstRow←(⍳1+⍴t)-1 nextRow←{ {(⍺+1)⌊⍵}\(1+⍵)⌊(1+⊃⍵),(¯1↓⍵)+⍺≠t } lastRow←⊃nextRow/(⌽s),⊂firstRow ed←⊃⌽lastRow

42. Whatwasactuallydelivered

43. Cryptography • Viginèrecipher • Book cipher variation • Playfaircipher

44. Cryptography • Viginèrecipher • Book cipher variation • Playfaircipher

45. Recreation and Games • Word search • Scrabble • Bridge

46. Recreation and Games • Word search • Scrabble • Bridge

47. Questions?