one way to solve the problem 411 in clojure
TRANSCRIPT
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clj-syd pep-411"It was nice to meet you at the first clj-syd hack night"
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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"
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(hack-night (nth clj-syd 10))
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Problem 411
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Problem 411 outline
Generate2D Grid
of Stations
Calculatelongest
uphill path
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Problem 411 longest uphill path
longestpath = 5
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Problem 411 longest uphill path
n x n
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Problem 411 longest uphill path
n=22
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Problem 411 station generation
(x, y) = (2i mod n, 3i mod n)i = [0..2n]
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Problem 411 station generation
n = 2244 stations (2n)11 distinct stations
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Problem 411 30 instances
k = [1..30] n = k5
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Problem 411 30 instances
k = [1..30] n = k5
Σ solve(n)
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Problem 411 30 instances
k = [1..30] n = k5
Σ solve(n)
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Problem 411 n = k5
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Dynamic Programming Approach
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Naïve Algorithm generate stations
basei mod n(Modular Exponentiation)
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Naïve Algorithm generate stations
(x, y) = (2i mod n, 3i mod n)i = [0..2n]
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Naïve Algorithm generate stations
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Naïve Algorithm generate stations
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Naïve Algorithm dynamic programming
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Naïve Algorithm dynamic programming
max
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Naïve Algorithm dynamic programming
1+max*subproblem
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Naïve Algorithm dynamic programming
1+max*subproblem
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Naïve Algorithm dynamic programming
0
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Naïve Algorithm correct (but slow)
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Naïve Algorithm correct (but slow)
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Naïve Algorithm correct (but slow)
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Improvements:Station Generation
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Station Generation avoid repetitions
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Station Generation avoid repetitions
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Station Generation avoid repetitions
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Station Generation avoid repetitions
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Station Generation improve modpow
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Station Generation improve modpow
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Improvements:Station Generation
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Improvements:Station Generation
Data Structure
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QuadTree
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QuadTree
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Point QuadTree
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*QuadTree
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SortedMap ofSortedSets DS
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SortedMap of SortedSet group by Y coord
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SortedMap of SortedSet group by Y coord
y=1
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SortedMap of SortedSet group by Y coord
y=3
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SortedMap of SortedSet group by Y coord
y=15
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SortedMap of SortedSet group by Y coord
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SortedMap of SortedSet group by Y coord
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SortedMap of SortedSet group by Y coord
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SortedMap of SortedSet group by Y coord
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SortedMap of SortedSet group by Y coord
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SortedMap of SortedSet group by Y coord
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SortedMap ofSortedSets DS
Now what ?!?!?
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SortedMap of SortedSet now what?!?!
same problem but 1D only... any leverage?
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SortedMap of SortedSet Patience Sorting
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SortedMap of SortedSet Patience Sorting
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SortedMap of SortedSet Patience Sorting
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SortedMap of SortedSet now what?!?!
.....
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SortedMap of SortedSet now what?!?!
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SortedMap of SortedSet now what?!?!
WTF ??!?!?!
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SortedMap of SortedSet Patience Sorting
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SortedMap of SortedSet Patience Sorting
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SortedMap of SortedSet Patience Sorting
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SortedMap of SortedSet Patience Sorting
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SortedMap of SortedSet Patience Sorting
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SortedMap of SortedSet Patience Sorting
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SortedMap of SortedSet Patience Sorting
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SortedMap of SortedSet Patience Sorting
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SortedMap of SortedSet Patience Sorting
[1 3 5 8 10][1 4 5 8 10][1 4 6 8 10]
...
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SortedMap ofSortedSets DS
Patience Algorithm ?
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SortedMap of SortedSet Patience
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SortedMap of SortedSet Patience
3
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SortedMap of SortedSet Patience
4
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SortedMap of SortedSet Patience Sorting
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SortedMap of SortedSet Patience
4
[1 10 12] --> [1 2 12] --> [1 2 12 20]
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SortedMap of SortedSet Patience
4
[1 10 12] --> [1 2 12] --> [1 2 12 20]
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SortedMap of SortedSet Patience
4
[1 2 12 20] --> [1 2 8 20] --> [1 2 8 14]
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SortedMap of SortedSet Patience
4
[1 2 8 14] --> [1 2 4 14] --> [ ? ? ? ]
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SortedMap of SortedSet Patience
5
[1 2 8 14] --> [1 2 4 14] --> [1 2 4 14 18]
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SortedMap of SortedSet Patience
5
[1 2 8 14] --> [1 2 4 14] --> [1 2 4 14 18]
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SortedMap of SortedSet Patience
5
[1 2 4 14 18] --> [1 2 4 6 18] --> [1 2 4 6 16]
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Patience AlgorithmPython to the Rescue
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Patience AlgorithmPython to the Rescue
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SortedMap of SortedSet Py to the rescue
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SortedMap of SortedSet Py to the rescue
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SortedMap of SortedSet Py to the rescue
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SortedMap of SortedSet Py to the rescue
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SortedMap of SortedSet Py to the rescue
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SortedMap of SortedSet Py to the rescue
http://hg.python.org/cpython/file/2.7/Lib/bisect.py
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SortedMap of SortedSet Py to the rescue
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SortedMap of SortedSet Py to the rescue
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SortedMap of SortedSet Py to the rescue
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SortedMap of SortedSet Py to the rescue
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SortedMap of SortedSet Py to the rescue
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SortedMap of SortedSet Py to the rescue
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SortedMap of SortedSet Py to the rescue
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LIS in 1D is easy...What about our 2D DS?
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SortedMap of SortedSet LIS on our DS
[1 2 4 6 16]
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SortedMap of SortedSet LIS on our DS
[1 2 4 6 16]
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SortedMap of SortedSet LIS on our DS
[1 2 4 6 16]
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SortedMap of SortedSet LIS on our DS
[1 2 4 6 16]
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SortedMap of SortedSet LIS on our DS
[1 2 4 6 16]
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DS as a SortedSet
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DS as a SortedSet Full Scale?
k=30 --> n=305 --> 24,300,000
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DS as a SortedSet Full Scale?
k=30 --> n=305 --> 24,300,000
Everything --> "mod n"
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DS as a SortedSet Full Scale?
k=30 --> n=305 --> 24,300,000
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DS as a SortedSet XY combined
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DS as a SortedSet XY combined
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DS as a SortedSet XY combined
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DS as a SortedSet Stations-Y
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Here be Dragons
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Here be Dragons
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Optimisations innermost loops
"If a tree falls in a forest and no one is around to hear it, does it make a sound?"
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Optimisations innermost loops
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map - pmap - r/map
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*map you multicore, uh?
map
pmap
r/map
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*map you multicore, uh?
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*map you multicore, uh?
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what's next?
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What's next? chunked-seq
http://goo.gl/Peym4
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What's next? chunked-seq
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What's next? 1) measure 2) optimise
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What's next? 1) measure 2) optimise
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Questions?
Twitter @filippovitale BitBucket: filippovitale
GitHub: filippovitale
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Thank you!
Twitter @filippovitale BitBucket / GitHub: filippovitale
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f in