Calculating Combinations The Cool Way

I recently had to calculate all possible combinations of a set. I needed to calculate combinations of 1..N size, where N is the size of the original set of things. Order inside of the resulting combinations did not matter to me, as I am treating the combinations as true sets.

For example, given the set [A,B,C], I needed to calculate the following combinations:


  • []

  • [A]

  • [B]

  • [C]

  • [AB]

  • [AC]

  • [BC]

  • [ABC]



It dawned on me that a cool way to generate the combinations was to treat the sets (the original set and the resulting combination sets) as bit strings. If the bit corresponding to the member is on, I include the member in the combination.

To explain, I start with the set [A,B,C]. I create a number that has three bits, all on, one for each member of the set. I therefore have the binary number 111 matching [A,B,C]. 111 happens to be 7 in decimal, which is one less than the total number of combinations I require.

Starting with zero, I loop up and including seven (for a total of eight iterations, once for each combo that I want). I convert each iteration count to a binary string, which will give me which bits are on for this combination.

For example, here's the ruby code:



original_set = [:A, :B, :C]
combinations = []

def create_combo(bit_string, original_set)
  combo = []
  bit_string.split(//).each_with_index do |bit, i|
    combo << original_set[i] if bit == "1"
  end
  combo
end

(2**original_set.size).times do |i|
  bit_string = sprintf("%03b", i)
  combinations << create_combo(bit_string, original_set)
end

require 'pp'
pp combinations



This will print out:

[[], [:C], [:B], [:B, :C], [:A], [:A, :C], [:A, :B], [:A, :B, :C]]

Neat, huh?

I'm sure you can speed this up by checking each bit in the iteration count instead of first converting to a bit string.

Popular posts from this blog

Lists and arrays in Dart

(This is Part 3 in a series about Dart. Check out Part 2, Function in Dart .) Warning : We expect the Dart libraries to undergo potentially sweeping changes before Dart goes to alpha. This document is relevant as of 2011-12-22. Intro Dart is a "batteries included" effort to help app developers build modern web apps. An important "battery" is the bundled core Dart libraries, providing common and rich functionality. Dart is building a solution for large, complex web apps, and providing well tested, integrated, and common libraries is key to helping a web app developer be more productive out of the box. The Collection libraries are a crucial set of APIs that Dart developers get for free. Much more than simple arrays and maps, the Collection library includes standard ways to filter, iterate, inspect, compose, and sort your data. This post specifically looks at List<E> , Dart's ordered, indexable collection of objects. Aside: The Dart project is lucky
Read more

Converting Array to List in Scala

Now, this has to have a built-in somewhere in Scala , because it just seems too common. So, how to convert an Array to a List in Scala? Why do I need this? I needed to drop to Java for some functionality, which in this case returns an Array. I wanted to get that Array into a List to practice my functional programming skillz. **Update**: I figured out how to convert Arrays to Lists the Scala way. Turns out it's a piece of cake. val myList = List.fromArray(Array("one", "two", "three")) or val myList = Array("one","two","three").elements.toList The call to elements returns an Iterator , and from there you can convert to a List via toList . Nice. Because my first version wasn't actually tail recursive, what follows is a true tail recursive solution, if I were to implement this by hand. The above, built in mechanism is much better, though. object ArrayUtil { def toList[a](array: Array[a]): List[a] = { d
Read more

Null-aware operators in Dart

Image
Three new language features just landed in the latest dev channel build of the Dart ! Collectively known as null-aware operators , these new features will help you reduce the code required to work with potentially null objects. I'm excited for these new abilities, because typing less is always a good thing. Read on to learn more, and be sure to try these new features on Dart Pad . ?? Use ?? when you want to evaluate and return an expression IFF another expression resolves to null. exp ?? otherExp is similar to ((x) => x == null ? otherExp : x)(exp) ??= Use ??= when you want to assign a value to an object IFF that object is null. Otherwise, return the object. obj ??= value is similar to ((x) => x == null ? obj = value : x)(obj) ?. Use ?. when you want to call a method/getter on an object IFF that object is not null (otherwise, return null). obj?.method() is similar to ((x) => x == null ? null : x.method())(obj) Yo
Read more