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Beyond the language the importance of algorithms in programming Simone Carle3 / / @weppos

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Beyond the language An introduc:on to algorithms Simone Carle3 / / @weppos

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algorithm |ˈalgərɪð(ə)m| a process or set of rules to be followed in calculations or other problem-solving operations, especially by a computer.

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algorithm |ˈalgərɪð(ə)m| a word used by programmers
 when they don't want to explain what they did.

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An Algorithm is not a Program A program can be viewed as an elaborate algorithm.

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An Algorithm is not a Program Computer programs contain algorithms that detail the specific instruc:ons a computer should perform, in a specific order, to execute a specific task.

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As a you use a to implement to write programmer, programming language algorithms programs.

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bombardino

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bombardino |\_(ツ)_/¯| The Bombardino is a popular winter drink in Italy, especially in the ski resorts. It is made with warm zabaglione (egg-based liqueur), brandy, and topped with a generous amount of whipped cream.

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The Problem • Outside is very cold in Sandusky • You want to warm up with some Bombardino • One Bombardino is poisoned and it weighs a liFle bit more than the others • The only way for you to find the poisoned one is to weigh the Bombardino • Each :me you weigh a Bombardino you waste precious :me • You want to drink as much Bombardino as you can, ideally without drinking the poisoned one and before all the good Bombardino are gone

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The formalized Problem Problem Instance Computa?on model Algorithm Goal Find the heaviest item among n items. n items including the item we want to find. Scale. Each weight taken has a fixed cost. Weighing strategy. We want an algorithm that finds the heaviest item in the collec:on. The algorithm should be correct and efficient.

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The simplest algorithm

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The simplest algorithm Take the first item and compare it to all the other items in the collec:on.

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The simplest algorithm

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The simplest algorithm

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The simplest algorithm 1

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The simplest algorithm 2

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The simplest algorithm 3

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The simplest algorithm 4

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The simplest algorithm 5

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The simplest algorithm 6

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The simplest algorithm Correct? Efficient?

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The simplest algorithm Correct? Efficient? YES

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The simplest algorithm Correct? Efficient? YES

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Cost of an algorithm

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For simplicity, let's define the cost of an algorithm as an es:ma:on of the resources needed by an algorithm to solve a computa:on problem.

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The lower the cost, the higher the efficiency of the algorithm.

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The Big-O nota:on is used to classify the cost of an algorithm rela:ve to changes in input size.

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Big-O nota:on is a way to measure the complexity of the algorithm in the worst-case scenario.

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Big-O Complexity Big-O n = 2 n = 10 n = 20 constant O(1) 1 1 1 logarithmic O(log2n) 1 ~ 3,3 ~ 4,3 linear O(n) 2 10 20 quadra?c O(n2) 4 100 400 exponen?al O(2n) 4 1.024 1.048.576 bigocheatsheet.com

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1st algorithm: "one vs all" Take the first item and compare it to all the other items in the collec:on.

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1st algorithm Correct? Cost? Big-O? Efficient? YES n O(n) It depends…

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2nd algorithm "each pair" Compare a pair of items at :me.

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2nd algorithm

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2nd algorithm 1

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2nd algorithm 2

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2nd algorithm 3

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2nd algorithm 4

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2nd algorithm Correct? Cost? Big-O? Efficient? YES n/2 O(n) It depends…

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3rd algorithm: "divide et pesa" Split the collec:on of items in two sets with the same number of items, and weigh them. Keep the heaviest set and discard drink the other.

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3rd algorithm 1

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3rd algorithm 2

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3rd algorithm 3

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3rd algorithm Correct? Cost? Big-O? Efficient? YES log2n O(log n) It depends…

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4th algorithm: "divide /3 et pesa" Split the collec:on of items in 3 sets, and weigh the ones with the same number of elements.

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4th algorithm 1

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4th algorithm 1

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4th algorithm 2

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4th algorithm Correct? Cost? Big-O? Efficient? YES log3n O(log n) YES

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Language vs Algorithm Shouldn't I simply use a faster language?

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n 10 100 1.000 10.000 1st 9m 1h 39m 16h 6d 2nd 5m 50m 8h 3,5d 3rd 3m 6m 9m 13m 4th 3m 5m 7m 9m

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Data Structures Ruby Hash Table

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rubyists = {} # insert rubyists[:weppos] = "Simone Carletti" rubyists[:jodosha] = "Luca Guidi" rubyists[:john] = "John Doe" # delete rubyists.delete(:john) # search rubyists[:weppos] # => "Simone Carletti"

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all opera:ons should cost O(1) In an ideal world

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Linked list key1: "value1" key2: "value2" key3: "value3"

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Linked list key1: "value1" key2: "value2" key3: "value3" search costs O(n)

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search in Ruby 2.3 0 0,002 0,003 0,005 0,006 4 16 64 256 1024 4096 16384 10k itera?ons First Key Last Key 4 0,00305 0,00282 8 0,00417 0,00318 16 0,00391 0,00359 32 0,00476 0,00399 64 0,00335 0,00275 128 0,00447 0,00366 256 0,00435 0,00342 512 0,00325 0,00439 1024 0,00317 0,00300 2048 0,00413 0,00334 4096 0,00490 0,00370 8192 0,00342 0,00452 16384 0,00522 0,00302 32768 0,00367 0,00408

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Hash Table in Ruby 16 num_bins #define ST_DEFAULT_MAX_DENSITY 5 #define ST_DEFAULT_INIT_TABLE_SIZE 16 #define ST_DEFAULT_PACKED_TABLE_SIZE 18

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Hash Table in Ruby 16 whatever[:key1] = "value"

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Hash Table in Ruby 16 whatever[:key1] = "value" :key1.hash # => 707933195402600884 707933195402600884 % 16 # => 4

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Hash Table in Ruby 16 whatever[:key1] = "value" key1

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Hash Table in Ruby 16 whatever[:key1] = "value" whatever[:key2] = "value" key1 key2

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Hash Table in Ruby 16 whatever[:key1] = "value" whatever[:key2] = "value" whatever[:key3] = "value" key3 key2 key1

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Hash Table in Ruby 16 whatever[:key1] = "value" whatever[:key2] = "value" whatever[:key3] = "value" ... whatever[:keyN] = "value" key3 key2 key1 #define ST_DEFAULT_MAX_DENSITY 5 #define ST_DEFAULT_INIT_TABLE_SIZE 16 #define ST_DEFAULT_PACKED_TABLE_SIZE 18

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Hash Table in Ruby 17 key3 key2 key1

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Hash Table in Ruby 17 static void rehash(register st_table *table) { ... } key3 key2 key1

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Hash Table in Ruby 17 static void rehash(register st_table *table) { ... } key3 key2 key1

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Hash Table in Ruby 17 # search whatever[:keyX] keyX

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Hash Table in Ruby 17 # search whatever[:keyX] :keyX.hash # => 2149668665177381993 2149668665177381993 % 17 # => 8 keyX

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Hash Table in Ruby 8 17 # search whatever[:keyX] :keyX.hash # => 2149668665177381993 2149668665177381993 % 17 # => 8 keyX

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Object#hash class BadKey def hash 3 end end class GoodKey end

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Lookup :me with BadKey 10k itera?ons First Key Last Key 4 0,00362 0,00580 8 0,00587 0,00397 16 0,00851 0,00442 32 0,01820 0,00300 64 0,02397 0,00295 128 0,05332 0,00348 256 0,09378 0,00476 512 0,20330 0,00294 1024 0,41460 0,00297 2048 0,92197 0,00453 4096 1,58056 0,00289 8192 3,32300 0,00306 16384 6,66864 0,00414 32768 14,44931 0,00324 Lookup :me with GoodKey 10k itera?ons First Key Last Key 4 0,00305 0,00282 8 0,00417 0,00318 16 0,00391 0,00359 32 0,00476 0,00399 64 0,00335 0,00275 128 0,00447 0,00366 256 0,00435 0,00342 512 0,00325 0,00439 1024 0,00317 0,00300 2048 0,00413 0,00334 4096 0,00490 0,00370 8192 0,00342 0,00452 16384 0,00522 0,00302 32768 0,00367 0,00408 4 8 16 32 64 128 256 512 1024 2048 4096 8192 16384 32768 Good Key Bad Key

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a good

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Thanks to Prof. Luciano Gualà Department of Mathema:cs
 the University of Rome "Tor Vergata" Pat Shaughnessy Author of Ruby Under a Microscope

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Photos hFps:/ /www.flickr.com/photos/stevefrazier/21397889609/

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Thanks! DNSimple dnsimple.com @dnsimple Simone Carleb simonecarle3.com @weppos hFps:/ /dnsimple.com/codemash