A Robot path problem – SydJS June 2012 by Filippo Vitale Published June 20, 2012 in Programming A Robot path problem helped me realise I still love JavaScript Project Euler 208 – https://projecteuler.net/problem=208

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