Count of ways in which N can be represented as sum of Fibonacci numbers without repetition

Given a number N, the task is to find the number of ways in which the integer N can be represented as a sum of Fibonacci numbers without repetition of any Fibonacci number.

#combinatorial #dynamic programming #mathematical #algorithms-dynamic programming #fibonacci #maths

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Buddha Community

Count of ways in which N can be represented as sum of Fibonacci numbers without repetition

Count of ways in which N can be represented as sum of Fibonacci numbers without repetition

Given a number N, the task is to find the number of ways in which the integer N can be represented as a sum of Fibonacci numbers without repetition of any Fibonacci number.

#combinatorial #dynamic programming #mathematical #algorithms-dynamic programming #fibonacci #maths

Brook  Hudson

Brook Hudson

1659074160

Kashmir: A Ruby DSL That Makes Serializing and Caching Objects A Snap

Kashmir is a Ruby DSL that makes serializing and caching objects a snap.

Kashmir allows you to describe representations of Ruby objects. It will generate hashes from these Ruby objects using the representation and dependency tree that you specify.

Kashmir::ActiveRecord will also optimize and try to balance ActiveRecord queries so your application hits the database as little as possible.

Kashmir::Caching builds a dependency tree for complex object representations and caches each level of this tree separately. Kashmir will do so by creating cache views of each level as well as caching a complete tree. The caching engine is smart enough to fill holes in the cache tree with fresh data from your data store.

Combine Kashmir::Caching + Kashmir::ActiveRecord for extra awesomeness.

Example:

For example, a Person with name and age attributes:

  class Person
    include Kashmir
    
    def initialize(name, age)
      @name = name
      @age = age
    end
    
    representations do
      rep :name
      rep :age
    end
  end

could be represented as:

{ name: 'Netto Farah', age: 26 }

Representing an object is as simple as:

  1. Add include Kashmir to the target class.
  2. Whitelist all the fields you want to include in a representation.
# Add fields and methods you want to be visible to Kashmir
representations do
  rep(:name)
  rep(:age)
end
  1. Instantiate an object and #represent it.
# Pass in an array with all the fields you want included
Person.new('Netto Farah', 26).represent([:name, :age]) 
 => {:name=>"Netto Farah", :age=>"26"} 

Installation

Add this line to your application's Gemfile:

gem 'kashmir'

And then execute:

$ bundle

Usage

Kashmir is better described with examples.

Basic Representations

Describing an Object

Only whitelisted fields can be represented by Kashmir. This is done so sensitive fields (like passwords) cannot be accidentally exposed to clients.

class Recipe < OpenStruct
  include Kashmir

  representations do
    rep(:title)
    rep(:preparation_time)
  end
end

Instantiate a Recipe:

recipe = Recipe.new(title: 'Beef Stew', preparation_time: 60)

Kashmir automatically adds a #represent method to every instance of Recipe. #represent takes an Array with all the fields you want as part of your representation.

recipe.represent([:title, :preparation_time])
=> { title: 'Beef Stew', preparation_time: 60 }

Calculated Fields

You can represent any instance variable or method (basically anything that returns true for respond_to?).

class Recipe < OpenStruct
  include Kashmir

  representations do
    rep(:title)
    rep(:num_steps)
  end
  
  def num_steps
    steps.size
  end
end
Recipe.new(title: 'Beef Stew', steps: ['chop', 'cook']).represent([:title, :num_steps])
=> { title: 'Beef Stew', num_steps: 2 }

Nested Representations

You can nest Kashmir objects to represent complex relationships between your objects.

class Recipe < OpenStruct
  include Kashmir

  representations do
    rep(:title)
    rep(:chef)
  end
end

class Chef < OpenStruct
  include Kashmir

  representations do
    base([:name])
  end
end

When you create a representation, nest hashes to create nested representations.

netto = Chef.new(name: 'Netto Farah')
beef_stew = Recipe.new(title: 'Beef Stew', chef: netto)

beef_stew.represent([:title, { :chef => [ :name ] }])
=> {
  :title => "Beef Stew",
  :chef => {
    :name => 'Netto Farah'
  }
}

Not happy with this syntax? Check out Kashmir::DSL or Kashmir::InlineDSL for prettier code.

Base Representations

Are you tired of repeating the same fields over and over? You can create a base representation of your objects, so Kashmir returns basic fields automatically.

class Recipe
  include Kashmir
  
  representations do
    base [:title, :preparation_time]
    rep :num_steps
    rep :chef
  end
end

base(...) takes an array with the fields you want to return on every representation of a given class.

brisket = Recipe.new(title: 'BBQ Brisket', preparation_time: 'a long time')
brisket.represent()
=> { :title => 'BBQ Brisket', :preparation_time => 'a long time' }

Complex Representations

You can nest as many Kashmir objects as you want.

class Recipe < OpenStruct
  include Kashmir

  representations do
    base [:title]
    rep :chef
  end
end

class Chef < OpenStruct
  include Kashmir

  representations do
    base :name
    rep :restaurant
  end
end

class Restaurant < OpenStruct
  include Kashmir

  representations do
    base [:name]
    rep :rating
  end
end
bbq_joint = Restaurant.new(name: "Netto's BBQ Joint", rating: '5 Stars')
netto = Chef.new(name: 'Netto', restaurant: bbq_joint)
brisket = Recipe.new(title: 'BBQ Brisket', chef: netto)

brisket.represent([
  :chef => [
    { :restaurant => [ :rating ] }
  ]
])

=> {
  title: 'BBQ Brisket',
  chef: {
    name: 'Netto',
    restaurant: {
      name: "Netto's BBQ Joint",
      rating: '5 Stars'
    }
  }
}

Collections

Arrays of Kashmir objects work the same way as any other Kashmir representations. Kashmir will augment Array with #represent that will represent every item in the array.

class Ingredient < OpenStruct
  include Kashmir

  representations do
    rep(:name)
    rep(:quantity)
  end
end

class ClassyRecipe < OpenStruct
  include Kashmir

  representations do
    rep(:title)
    rep(:ingredients)
  end
end
omelette = ClassyRecipe.new(title: 'Omelette Du Fromage')
omelette.ingredients = [
  Ingredient.new(name: 'Egg', quantity: 2),
  Ingredient.new(name: 'Cheese', quantity: 'a lot!')
]

Just describe your Array representations like any regular nested representation.

omelette.represent([:title, { 
    :ingredients => [ :name, :quantity ]
  }
])
=> {
  title: 'Omelette Du Fromage',
  ingredients: [
    { name: 'Egg', quantity: 2 },
    { name: 'Cheese', quantity: 'a lot!' }
  ]
}

Kashmir::Dsl

Passing arrays and hashes around can be very tedious and lead to duplication. Kashmir::Dsl allows you to create your own representers/decorators so you can keep your logic in one place and make way more expressive.

class Recipe < OpenStruct
  include Kashmir

  representations do
    rep(:title)
    rep(:num_steps)
  end
end

class RecipeRepresenter
  include Kashmir::Dsl

  prop :title
  prop :num_steps
end

All you need to do is include Kashmir::Dsl in any ruby class. Every call to prop(field_name) will translate directly into just adding an extra field in the representation array.

In this case, RecipeRepresenter will translate directly to [:title, :num_steps].

brisket = Recipe.new(title: 'BBQ Brisket', num_steps: 2)
brisket.represent(RecipePresenter)

=>  { title: 'BBQ Brisket', num_steps: 2 }

Embedded Representers

It is also possible to define nested representers with embed(:property_name, RepresenterClass).

class RecipeWithChefRepresenter
  include Kashmir::Dsl

  prop :title
  embed :chef, ChefRepresenter
end

class ChefRepresenter
  include Kashmir::Dsl
  
  prop :full_name
end

Kashmir will inline these classes and return a raw Kashmir description.

RecipeWithChefRepresenter.definitions == [ :title, { :chef => [ :full_name ] }]
=> true

Representing the objects will work just as before.

chef = Chef.new(first_name: 'Netto', last_name: 'Farah')
brisket = Recipe.new(title: 'BBQ Brisket', chef: chef)

brisket.represent(RecipeWithChefRepresenter)
 
=> {
  title: 'BBQ Brisket',
  chef: {
    full_name: 'Netto Farah'
  }
}

Inline Representers

You don't necessarily need to define a class for every nested representation.

class RecipeWithInlineChefRepresenter
  include Kashmir::Dsl

  prop :title

  inline :chef do
    prop :full_name
  end
end

Using inline(:property_name, &block) will work the same way as embed. Except that you can now define short representations using ruby blocks. Leading us to our next topic.

Kashmir::InlineDsl

Kashmir::InlineDsl sits right in between raw representations and Representers. It reads much better than arrays of hashes and provides the expressiveness of Kashmir::Dsl without all the ceremony.

It works with every feature from Kashmir::Dsl and allows you to define quick inline descriptions for your Kashmir objects.

class Recipe < OpenStruct
  include Kashmir

  representations do
    rep(:title)
    rep(:num_steps)
  end
end

Just call #represent_with(&block) on any Kashmir object and use the Kashmir::Dsl syntax.

brisket = Recipe.new(title: 'BBQ Brisket', num_steps: 2)

brisket.represent_with do
  prop :title
  prop :num_steps
end

=> { title: 'BBQ Brisket', num_steps: 2 }

Nested Inline Representations

You can nest inline representations using inline(:field, &block) the same way we did with Kashmir::Dsl.

class Ingredient < OpenStruct
  include Kashmir

  representations do
    rep(:name)
    rep(:quantity)
  end
end

class ClassyRecipe < OpenStruct
  include Kashmir

  representations do
    rep(:title)
    rep(:ingredients)
  end
end
omelette = ClassyRecipe.new(title: 'Omelette Du Fromage')
omelette.ingredients = [
  Ingredient.new(name: 'Egg', quantity: 2),
  Ingredient.new(name: 'Cheese', quantity: 'a lot!')
]

Just call #represent_with(&block) and start nesting other inline representations.

omelette.represent_with do
  prop :title
  inline :ingredients do
    prop :name
    prop :quantity
  end
end

=> {
  title: 'Omelette Du Fromage',
  ingredients: [
    { name: 'Egg', quantity: 2 },
    { name: 'Cheese', quantity: 'a lot!' }
  ]
}

Inline representations can become lengthy and confusing over time. If you find yourself nesting more than two levels or including more than 3 or 4 fields per level consider creating Representers with Kashmir::Dsl.

Kashmir::ActiveRecord

Kashmir works just as well with ActiveRecord. ActiveRecord::Relations can be used as Kashmir representations just as any other classes.

Kashmir will attempt to preload every ActiveRecord::Relation defined as representations automatically by using ActiveRecord::Associations::Preloader. This will guarantee that you don't run into N+1 queries while representing collections and dependent objects.

Here's an example of how Kashmir will attempt to optimize database queries:

ActiveRecord::Schema.define do
  create_table :recipes, force: true do |t|
    t.column :title, :string
    t.column :num_steps, :integer
    t.column :chef_id, :integer
  end
  
  create_table :chefs, force: true do |t|
    t.column :name, :string
  end
end
module AR
  class Recipe < ActiveRecord::Base
    include Kashmir

    belongs_to :chef

    representations do
      rep :title
      rep :chef
    end
  end

  class Chef < ActiveRecord::Base
    include Kashmir

    has_many :recipes

    representations do
      rep :name
      rep :recipes
    end
  end
end
AR::Chef.all.each do |chef|
  chef.recipes.to_a
end

will generate

SELECT * FROM chefs
SELECT "recipes".* FROM "recipes" WHERE "recipes"."chef_id" = ?
SELECT "recipes".* FROM "recipes" WHERE "recipes"."chef_id" = ?

With Kashmir:

AR::Chef.all.represent([:recipes])
SELECT "chefs".* FROM "chefs"
SELECT "recipes".* FROM "recipes" WHERE "recipes"."chef_id" IN (1, 2)

For more examples, check out: https://github.com/IFTTT/kashmir/blob/master/test/activerecord_tricks_test.rb

Kashmir::Caching (Experimental)

Caching is the best feature in Kashmir. The Kashmir::Caching module will cache every level of the dependency tree Kashmir generates when representing an object.

Dependency Tree

As you can see in the image above, Kashmir will build a dependency tree of the representation. If you have Caching on, Kashmir will:

  • Build a cache key for each individual object (green)
  • Wrap complex dependencies into their on cache key (blue and pink)
  • Wrap the whole representation into one unique cache key (red)

Each layer gets its own cache keys which can be expired at different times. Kashmir will also be able to fill in blanks in the dependency tree and fetch missing objects individually.

Caching is turned off by default, but you can use one of the two available implementations.

You can also build your own custom caching engine by following the NullCaching protocol available at: https://github.com/IFTTT/kashmir/blob/master/lib/kashmir/plugins/null_caching.rb

Enabling Kashmir::Caching

In Memory

Kashmir.init(
  cache_client: Kashmir::Caching::Memory.new
)

With Memcached

require 'kashmir/plugins/memcached_caching'

client = Dalli::Client.new(url, namespace: 'kashmir', compress: true)
default_ttl = 5.minutes

Kashmir.init(
  cache_client: Kashmir::Caching::Memcached.new(client, default_ttl)
)

For more advanced examples, check out: https://github.com/IFTTT/kashmir/blob/master/test/caching_test.rb

Contributing

  1. Fork it ( https://github.com/[my-github-username]/kashmir/fork )
  2. Create your feature branch (git checkout -b my-new-feature)
  3. Commit your changes (git commit -am 'Add some feature')
  4. Push to the branch (git push origin my-new-feature)
  5. Create a new Pull Request

Author: IFTTT
Source code: https://github.com/IFTTT/kashmir
License: MIT license

#ruby  #ruby-on-rails 

Edward Jackson

Edward Jackson

1653377002

PySpark Cheat Sheet: Spark in Python

This PySpark cheat sheet with code samples covers the basics like initializing Spark in Python, loading data, sorting, and repartitioning.

Apache Spark is generally known as a fast, general and open-source engine for big data processing, with built-in modules for streaming, SQL, machine learning and graph processing. It allows you to speed analytic applications up to 100 times faster compared to technologies on the market today. You can interface Spark with Python through "PySpark". This is the Spark Python API exposes the Spark programming model to Python. 

Even though working with Spark will remind you in many ways of working with Pandas DataFrames, you'll also see that it can be tough getting familiar with all the functions that you can use to query, transform, inspect, ... your data. What's more, if you've never worked with any other programming language or if you're new to the field, it might be hard to distinguish between RDD operations.

Let's face it, map() and flatMap() are different enough, but it might still come as a challenge to decide which one you really need when you're faced with them in your analysis. Or what about other functions, like reduce() and reduceByKey()

PySpark cheat sheet

Even though the documentation is very elaborate, it never hurts to have a cheat sheet by your side, especially when you're just getting into it.

This PySpark cheat sheet covers the basics, from initializing Spark and loading your data, to retrieving RDD information, sorting, filtering and sampling your data. But that's not all. You'll also see that topics such as repartitioning, iterating, merging, saving your data and stopping the SparkContext are included in the cheat sheet. 

Note that the examples in the document take small data sets to illustrate the effect of specific functions on your data. In real life data analysis, you'll be using Spark to analyze big data.

PySpark is the Spark Python API that exposes the Spark programming model to Python.

Initializing Spark 

SparkContext 

>>> from pyspark import SparkContext
>>> sc = SparkContext(master = 'local[2]')

Inspect SparkContext 

>>> sc.version #Retrieve SparkContext version
>>> sc.pythonVer #Retrieve Python version
>>> sc.master #Master URL to connect to
>>> str(sc.sparkHome) #Path where Spark is installed on worker nodes
>>> str(sc.sparkUser()) #Retrieve name of the Spark User running SparkContext
>>> sc.appName #Return application name
>>> sc.applicationld #Retrieve application ID
>>> sc.defaultParallelism #Return default level of parallelism
>>> sc.defaultMinPartitions #Default minimum number of partitions for RDDs

Configuration 

>>> from pyspark import SparkConf, SparkContext
>>> conf = (SparkConf()
     .setMaster("local")
     .setAppName("My app")
     . set   ("spark. executor.memory",   "lg"))
>>> sc = SparkContext(conf = conf)

Using the Shell 

In the PySpark shell, a special interpreter-aware SparkContext is already created in the variable called sc.

$ ./bin/spark-shell --master local[2]
$ ./bin/pyspark --master local[s] --py-files code.py

Set which master the context connects to with the --master argument, and add Python .zip..egg or.py files to the

runtime path by passing a comma-separated list to  --py-files.

Loading Data 

Parallelized Collections 

>>> rdd = sc.parallelize([('a',7),('a',2),('b',2)])
>>> rdd2 = sc.parallelize([('a',2),('d',1),('b',1)])
>>> rdd3 = sc.parallelize(range(100))
>>> rdd = sc.parallelize([("a",["x","y","z"]),
               ("b" ["p","r,"])])

External Data 

Read either one text file from HDFS, a local file system or any Hadoop-supported file system URI with textFile(), or read in a directory of text files with wholeTextFiles(). 

>>> textFile = sc.textFile("/my/directory/•.txt")
>>> textFile2 = sc.wholeTextFiles("/my/directory/")

Retrieving RDD Information 

Basic Information 

>>> rdd.getNumPartitions() #List the number of partitions
>>> rdd.count() #Count RDD instances 3
>>> rdd.countByKey() #Count RDD instances by key
defaultdict(<type 'int'>,{'a':2,'b':1})
>>> rdd.countByValue() #Count RDD instances by value
defaultdict(<type 'int'>,{('b',2):1,('a',2):1,('a',7):1})
>>> rdd.collectAsMap() #Return (key,value) pairs as a dictionary
   {'a': 2, 'b': 2}
>>> rdd3.sum() #Sum of RDD elements 4950
>>> sc.parallelize([]).isEmpty() #Check whether RDD is empty
True

Summary 

>>> rdd3.max() #Maximum value of RDD elements 
99
>>> rdd3.min() #Minimum value of RDD elements
0
>>> rdd3.mean() #Mean value of RDD elements 
49.5
>>> rdd3.stdev() #Standard deviation of RDD elements 
28.866070047722118
>>> rdd3.variance() #Compute variance of RDD elements 
833.25
>>> rdd3.histogram(3) #Compute histogram by bins
([0,33,66,99],[33,33,34])
>>> rdd3.stats() #Summary statistics (count, mean, stdev, max & min)

Applying Functions 

#Apply a function to each RFD element
>>> rdd.map(lambda x: x+(x[1],x[0])).collect()
[('a' ,7,7, 'a'),('a' ,2,2, 'a'), ('b' ,2,2, 'b')]
#Apply a function to each RDD element and flatten the result
>>> rdd5 = rdd.flatMap(lambda x: x+(x[1],x[0]))
>>> rdd5.collect()
['a',7 , 7 ,  'a' , 'a' , 2,  2,  'a', 'b', 2 , 2, 'b']
#Apply a flatMap function to each (key,value) pair of rdd4 without changing the keys
>>> rdds.flatMapValues(lambda x: x).collect()
[('a', 'x'), ('a', 'y'), ('a', 'z'),('b', 'p'),('b', 'r')]

Selecting Data

Getting

>>> rdd.collect() #Return a list with all RDD elements 
[('a', 7), ('a', 2), ('b', 2)]
>>> rdd.take(2) #Take first 2 RDD elements 
[('a', 7),  ('a', 2)]
>>> rdd.first() #Take first RDD element
('a', 7)
>>> rdd.top(2) #Take top 2 RDD elements 
[('b', 2), ('a', 7)]

Sampling

>>> rdd3.sample(False, 0.15, 81).collect() #Return sampled subset of rdd3
     [3,4,27,31,40,41,42,43,60,76,79,80,86,97]

Filtering

>>> rdd.filter(lambda x: "a" in x).collect() #Filter the RDD
[('a',7),('a',2)]
>>> rdd5.distinct().collect() #Return distinct RDD values
['a' ,2, 'b',7]
>>> rdd.keys().collect() #Return (key,value) RDD's keys
['a',  'a',  'b']

Iterating 

>>> def g (x): print(x)
>>> rdd.foreach(g) #Apply a function to all RDD elements
('a', 7)
('b', 2)
('a', 2)

Reshaping Data 

Reducing

>>> rdd.reduceByKey(lambda x,y : x+y).collect() #Merge the rdd values for each key
[('a',9),('b',2)]
>>> rdd.reduce(lambda a, b: a+ b) #Merge the rdd values
('a', 7, 'a' , 2 , 'b' , 2)

 

Grouping by

>>> rdd3.groupBy(lambda x: x % 2) #Return RDD of grouped values
          .mapValues(list)
          .collect()
>>> rdd.groupByKey() #Group rdd by key
          .mapValues(list)
          .collect() 
[('a',[7,2]),('b',[2])]

Aggregating

>> seqOp = (lambda x,y: (x[0]+y,x[1]+1))
>>> combOp = (lambda x,y:(x[0]+y[0],x[1]+y[1]))
#Aggregate RDD elements of each partition and then the results
>>> rdd3.aggregate((0,0),seqOp,combOp) 
(4950,100)
#Aggregate values of each RDD key
>>> rdd.aggregateByKey((0,0),seqop,combop).collect() 
     [('a',(9,2)), ('b',(2,1))]
#Aggregate the elements of each partition, and then the results
>>> rdd3.fold(0,add)
     4950
#Merge the values for each key
>>> rdd.foldByKey(0, add).collect()
[('a' ,9), ('b' ,2)]
#Create tuples of RDD elements by applying a function
>>> rdd3.keyBy(lambda x: x+x).collect()

Mathematical Operations 

>>>> rdd.subtract(rdd2).collect() #Return each rdd value not contained in rdd2
[('b' ,2), ('a' ,7)]
#Return each (key,value) pair of rdd2 with no matching key in rdd
>>> rdd2.subtractByKey(rdd).collect()
[('d', 1)1
>>>rdd.cartesian(rdd2).collect() #Return the Cartesian product of rdd and rdd2

Sort 

>>> rdd2.sortBy(lambda x: x[1]).collect() #Sort RDD by given function
[('d',1),('b',1),('a',2)]
>>> rdd2.sortByKey().collect() #Sort (key, value) ROD by key
[('a' ,2), ('b' ,1), ('d' ,1)]

Repartitioning 

>>> rdd.repartition(4) #New RDD with 4 partitions
>>> rdd.coalesce(1) #Decrease the number of partitions in the RDD to 1

Saving 

>>> rdd.saveAsTextFile("rdd.txt")
>>> rdd.saveAsHadoopFile("hdfs:// namenodehost/parent/child",
               'org.apache.hadoop.mapred.TextOutputFormat')

Stopping SparkContext 

>>> sc.stop()

Execution 

$ ./bin/spark-submit examples/src/main/python/pi.py

Have this Cheat Sheet at your fingertips

Original article source at https://www.datacamp.com

#pyspark #cheatsheet #spark #python

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