one way to solve the problem 411 in clojure

clj-syd pep-411"It was nice to meet you at the first clj-syd hack night"

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"

(hack-night (nth clj-syd 10))

Problem 411

Problem 411 outline

Generate2D Grid

of Stations

Calculatelongest

uphill path

Problem 411 longest uphill path

longestpath = 5


n x n


n=22

Problem 411 station generation

(x, y) = (2i mod n, 3i mod n)i = [0..2n]

Problem 411 station generation

n = 2244 stations (2n)11 distinct stations

Problem 411 30 instances

k = [1..30] n = k5

Problem 411 30 instances

k = [1..30] n = k5

Σ solve(n)

Problem 411 n = k5

Dynamic Programming Approach

Naïve Algorithm generate stations

basei mod n(Modular Exponentiation)


(x, y) = (2i mod n, 3i mod n)i = [0..2n]

Naïve Algorithm dynamic programming


max


1+max*subproblem


0

Naïve Algorithm correct (but slow)

Improvements:Station Generation

Station Generation avoid repetitions

Station Generation improve modpow


Data Structure

QuadTree

Point QuadTree

*QuadTree

SortedMap ofSortedSets DS

SortedMap of SortedSet group by Y coord


y=1


y=3


y=15


Now what ?!?!?

SortedMap of SortedSet now what?!?!

same problem but 1D only... any leverage?

SortedMap of SortedSet Patience Sorting


.....


WTF ??!?!?!


[1 3 5 8 10][1 4 5 8 10][1 4 6 8 10]

...


Patience Algorithm ?

SortedMap of SortedSet Patience


3


4


4

[1 10 12] --> [1 2 12] --> [1 2 12 20]


4

[1 2 12 20] --> [1 2 8 20] --> [1 2 8 14]


4

[1 2 8 14] --> [1 2 4 14] --> [ ? ? ? ]


5

[1 2 8 14] --> [1 2 4 14] --> [1 2 4 14 18]


5

[1 2 4 14 18] --> [1 2 4 6 18] --> [1 2 4 6 16]

Patience AlgorithmPython to the Rescue

SortedMap of SortedSet Py to the rescue


http://hg.python.org/cpython/file/2.7/Lib/bisect.py

LIS in 1D is easy...What about our 2D DS?

SortedMap of SortedSet LIS on our DS

[1 2 4 6 16]

DS as a SortedSet

DS as a SortedSet Full Scale?

k=30 --> n=305 --> 24,300,000


k=30 --> n=305 --> 24,300,000

Everything --> "mod n"


k=30 --> n=305 --> 24,300,000

DS as a SortedSet XY combined

DS as a SortedSet Stations-Y

Here be Dragons

Optimisations innermost loops

"If a tree falls in a forest and no one is around to hear it, does it make a sound?"

Optimisations innermost loops

map - pmap - r/map

*map you multicore, uh?

map

pmap

r/map

*map you multicore, uh?

what's next?

What's next? chunked-seq

http://goo.gl/Peym4

What's next? chunked-seq

What's next? 1) measure 2) optimise

Questions?

Twitter @filippovitale BitBucket: filippovitale

GitHub: filippovitale

Thank you!

Twitter @filippovitale BitBucket / GitHub: filippovitale

one way to solve the problem 411 in clojure

Presentations & Public Speaking

sortedmapofsortedset

mod n i

problem411stationgeneration

k5 solven

cljsyd hack night

problem411stationgeneration

distinct stations

longest uphillpath