A Robot path problem – SydJS June 2012

A Robot path problem helped me realise I still love JavaScript
Project Euler 208 – https://projecteuler.net/problem=208

Transcript

1. A Robot path problem helped me realise I still love JavaScript
2. Water-Cooler Talk
3. Project Euler
4. One-minute Rule "My program takes days to get to the answer!" Each problem has been designed according to a "one-minute rule", which means that although it may take several hours to design a successful algorithm with more difficult problems, an efficient implementation will allow a solution to be obtained on a modestly powered computer in less than one minute.
5. Which programming language? http://shootout.alioth.debian.org/u64/which-programming-languages-are-fastest.php
6. http://xkcd.com/568/
8. Project Euler - Problem 208
9. Project Euler - Problem 208 A robot moves in a series of one-fifth circular arcs (72°)
10. Project Euler - Problem 208 A robot moves in a series of one-fifth circular arcs (72°) with a free choice of ▪ a clockwise or ▪ an anti-clockwise arc for each step but no turning on the spot.
11. Project Euler - Problem 208 One of 70932 possible closed paths of 25 arcs
12. Project Euler - Problem 208 Given that the robot starts facing North: How many journeys of 70 arcs in length can it take that return it, after the final arc, to its starting position? (Any arc may be traversed multiple times) http://projecteuler.net/problem=208
14. Move left, move right 5 possible moves:
15. Move left, move right How many closed path? 5 possible moves:
16. Move left, move right 5 possible moves:
17. N levels http://www.wolframalpha.com/input/?i=binary+tree+5
18. 70 levels Number of grains of sand on earth! http://www.wolframalpha.com/input/?i=2%5E71
20. The plane
21. The plane
22. Sample elements
23. Default coordinates
24. Plane centered
25. Positive up and right
26. CSS code http://jsbin.com/evinum/edit#html,live http://jsfiddle.net/filippovitale/3z7Ln/embedded/
28. Arc left, Arc right
29. Arc left, Arc right
30. Arc left, Arc right
31. Arc left, Arc right Basically we add:
32. Arc left, Arc right Basically we add: http://jsbin.com/abaxoy/edit#preview
34. Move left, move right Model: • Move = { L, R } • StateI = ( x, y, heading ) StateI
35. Move left, move right Model: • Move = { L, R } • StateI = ( x, y, heading ) • StateII = ( lx, ly, rx, ry ) StateI StateII
36. Move left, move right
37. Move left, move right
38. Move left, move right
39. Move left, move right
40. Move left, move right
41. Move left, move right
42. Move left, move right How can we rotate a point on a plane? http://www.wolframalpha.com/input/?i=%7B100%2C+0%7D+72%C2%B0+rotation
43. Move left, move right How can we rotate a point on a plane? http://www.wolframalpha.com/input/?i=%7B100%2C+0%7D+72%C2%B0+rotation http://www.wolframalpha.com/input/?i=with+center+%7B-50%2C0%7D+rotate+72+deg+%7B50%2C0%7D
44. Move left, move right http://www.wolframalpha.com/input/?i=%7B100%2C+0%7D+72%C2%B0+rotation
45. Move left, move right
46. Move left, move right
47. Move left, move right
48. Move left, move right http://jsbin.com/anijuc/edit#preview ~0.000001
50. Brute force (naïve method)
51. Brute force (naïve method) http://jsbin.com/ejebip/edit#preview
53. ABCDE Model A B C D E 0 1 2 3 4
54. ABCDE Model A B C D E 0 1 2 3 4 heading 0 1 2 3 4
55. ABCDE Model A B C D E 0 1 2 3 4 heading counter 0 1 2 3 4 http://jsbin.com/oyifem/edit#preview
57. A way to solve this problem
58. A way to solve this problem
59. A way to solve this problem
60. A way to solve this problem
61. A way to solve this problem
62. A way to solve this problem MaxDistance!
63. A way to solve this problem
64. A way to solve this problem ClosedPath!
65. A way to solve this problem
66. A way to solve this problem
67. A way to solve this problem
68. A way to solve this problem http://jsfiddle.net/filippovitale/hS9KS/embedded/result/ http://underscorejs.org/ + CoffeConsole
70. Conclusion ~2 seconds ??? seconds
71. Conclusion ~2 seconds ~20 seconds
72. Conclusion ~2 seconds ~20 seconds ~89 seconds
73. Questions? twitter / bitbucket / github @filippovitale
74. A Robot path problem helped me realise I still love JavaScript