One way to solve the Problem 411 in Clojure – Clj-Syd May 2013

During the first clj-syd hack night we all discussed possible approaches on solving the ProjectEuler problem 411 and we started solving it.

After few weeks I finally solved it and this is how I did it.

Transcript

1. clj-syd pep-411 "It was nice to meet you at the first clj-syd hack night"
2. clj-syd pep-411 "It was nice to meet you at the first clj-syd hack night" aka "One way to solve the Problem 411 in Clojure"
3. (hack-night (nth clj-syd 10))
4. Problem 411
5. Problem 411 outline Generate 2D Grid of Stations Calculate longest uphill path
6. Problem 411 longest uphill path longest path = 5
7. Problem 411 longest uphill path n x n
8. Problem 411 longest uphill path n=22
9. Problem 411 station generation (x, y) = (2i mod n, 3i mod n) i = [0..2n]
10. Problem 411 station generation n = 22 44 stations (2n) 11 distinct stations
11. Problem 411 30 instances k = [1..30] n = k5
12. Problem 411 30 instances k = [1..30] n = k5 Σ solve(n)
13. Problem 411 30 instances k = [1..30] n = k5 Σ solve(n)
14. Problem 411 n = k5
15. Dynamic Programming Approach
16. Naïve Algorithm generate stations basei mod n (Modular Exponentiation)
17. Naïve Algorithm generate stations (x, y) = (2i mod n, 3i mod n) i = [0..2n]
18. Naïve Algorithm generate stations
19. Naïve Algorithm generate stations
20. Naïve Algorithm dynamic programming
21. Naïve Algorithm dynamic programming max
22. Naïve Algorithm dynamic programming 1+max *subproblem
23. Naïve Algorithm dynamic programming 1+max *subproblem
24. Naïve Algorithm dynamic programming 0
25. Naïve Algorithm correct (but slow)
26. Naïve Algorithm correct (but slow)
27. Naïve Algorithm correct (but slow)
28. Improvements: Station Generation
29. Station Generation avoid repetitions
30. Station Generation avoid repetitions
31. Station Generation avoid repetitions
32. Station Generation avoid repetitions
33. Station Generation improve modpow
34. Station Generation improve modpow
35. Improvements: Station Generation
36. Improvements: Station Generation Data Structure
37. QuadTree
38. QuadTree
39. Point QuadTree
41. *QuadTree
42. SortedMap of SortedSets DS
43. SortedMap of SortedSet group by Y coord
44. SortedMap of SortedSet group by Y coord y=1
45. SortedMap of SortedSet group by Y coord y=3
46. SortedMap of SortedSet group by Y coord y=15
47. SortedMap of SortedSet group by Y coord
48. SortedMap of SortedSet group by Y coord
49. SortedMap of SortedSet group by Y coord
50. SortedMap of SortedSet group by Y coord
51. SortedMap of SortedSet group by Y coord
52. SortedMap of SortedSet group by Y coord
53. SortedMap of SortedSets DS Now what ?!?!?
54. SortedMap of SortedSet now what?!?! same problem but 1D only... any leverage?
55. SortedMap of SortedSet Patience Sorting
56. SortedMap of SortedSet Patience Sorting
57. SortedMap of SortedSet Patience Sorting
58. SortedMap of SortedSet now what?!?! .....
59. SortedMap of SortedSet now what?!?!
60. SortedMap of SortedSet now what?!?! WTF ??!?!?!
61. SortedMap of SortedSet Patience Sorting
62. SortedMap of SortedSet Patience Sorting
63. SortedMap of SortedSet Patience Sorting
64. SortedMap of SortedSet Patience Sorting
65. SortedMap of SortedSet Patience Sorting
66. SortedMap of SortedSet Patience Sorting
67. SortedMap of SortedSet Patience Sorting
68. SortedMap of SortedSet Patience Sorting
69. SortedMap of SortedSet Patience Sorting [1 3 5 8 10] [1 4 5 8 10] [1 4 6 8 10] ...
70. SortedMap of SortedSets DS Patience Algorithm ?
71. SortedMap of SortedSet Patience
72. SortedMap of SortedSet Patience 3
73. SortedMap of SortedSet Patience 4
74. SortedMap of SortedSet Patience Sorting
75. SortedMap of SortedSet Patience 4 [1 10 12] --> [1 2 12] --> [1 2 12 20]
76. SortedMap of SortedSet Patience 4 [1 10 12] --> [1 2 12] --> [1 2 12 20]
77. SortedMap of SortedSet Patience 4 [1 2 12 20] --> [1 2 8 20] --> [1 2 8 14]
78. SortedMap of SortedSet Patience 4 [1 2 8 14] --> [1 2 4 14] --> [ ? ? ? ]
79. SortedMap of SortedSet Patience 5 [1 2 8 14] --> [1 2 4 14] --> [1 2 4 14 18]
80. SortedMap of SortedSet Patience 5 [1 2 8 14] --> [1 2 4 14] --> [1 2 4 14 18]
81. SortedMap of SortedSet Patience 5 [1 2 4 14 18] --> [1 2 4 6 18] --> [1 2 4 6 16]
82. Patience Algorithm Python to the Rescue
83. Patience Algorithm Python to the Rescue
84. SortedMap of SortedSet Py to the rescue
85. SortedMap of SortedSet Py to the rescue
86. SortedMap of SortedSet Py to the rescue
87. SortedMap of SortedSet Py to the rescue
88. SortedMap of SortedSet Py to the rescue
89. SortedMap of SortedSet Py to the rescue http://hg.python.org/cpython/file/2.7/Lib/bisect.py
90. SortedMap of SortedSet Py to the rescue
91. SortedMap of SortedSet Py to the rescue
92. SortedMap of SortedSet Py to the rescue
93. SortedMap of SortedSet Py to the rescue
94. SortedMap of SortedSet Py to the rescue
95. SortedMap of SortedSet Py to the rescue
96. SortedMap of SortedSet Py to the rescue
97. LIS in 1D is easy... What about our 2D DS?
98. SortedMap of SortedSet LIS on our DS [1 2 4 6 16]
99. SortedMap of SortedSet LIS on our DS [1 2 4 6 16]
100. SortedMap of SortedSet LIS on our DS [1 2 4 6 16]
101. SortedMap of SortedSet LIS on our DS [1 2 4 6 16]
102. SortedMap of SortedSet LIS on our DS [1 2 4 6 16]
103. DS as a SortedSet
104. DS as a SortedSet Full Scale? k=30 --> n=305 --> 24,300,000
105. DS as a SortedSet Full Scale? k=30 --> n=305 --> 24,300,000 Everything --> "mod n"
106. DS as a SortedSet Full Scale? k=30 --> n=305 --> 24,300,000
107. DS as a SortedSet XY combined
108. DS as a SortedSet XY combined
109. DS as a SortedSet XY combined
110. DS as a SortedSet Stations-Y
111. Here be Dragons
112. Here be Dragons
113. Optimisations innermost loops "If a tree falls in a forest and no one is around to hear it, does it make a sound?"
114. Optimisations innermost loops
115. map - pmap - r/map
116. *map you multicore, uh? map pmap r/map
117. *map you multicore, uh?
118. *map you multicore, uh?
119. what's next?
120. What's next? chunked-seq http://goo.gl/Peym4
121. What's next? chunked-seq
122. What's next? 1) measure 2) optimise
123. What's next? 1) measure 2) optimise
124. Questions? Twitter @filippovitale BitBucket: filippovitale GitHub: filippovitale
125. Thank you! Twitter @filippovitale BitBucket / GitHub: filippovitale
126. f in