rectangle-into-squares

Rectangle into Squares

The drawing below gives an idea of how to cut a given "true" rectangle into squares ("true" rectangle meaning that the two dimensions are different).

Can you translate this drawing into an algorithm?

You will be given two dimensions

1. a positive integer length (parameter named lng)
2. a positive integer width (parameter named wdth)

You will return an array or a string (depending on the language; Shell bash, PowerShell and Fortran return a string) with the size of each of the squares.

  sqInRect(5, 3) should return [3, 2, 1, 1]
  sqInRect(3, 5) should return [3, 2, 1, 1]
  or (Haskell)
  squaresInRect  5  3 `shouldBe` Just [3,2,1,1]
  squaresInRect  3  5 `shouldBe` Just [3,2,1,1]
  or (Fsharp)
  squaresInRect  5  3 should return Some [3,2,1,1]
  squaresInRect  3  5 should return Some [3,2,1,1]
  or (Swift)
  squaresInRect  5  3 should return [3,2,1,1] as optional
  squaresInRect  3  5 should return [3,2,1,1] as optional
  or (Cpp)
  sqInRect(5, 3) should return {3, 2, 1, 1}
  sqInRect(3, 5) should return {3, 2, 1, 1}
  (C)
  C returns a structure, see the "Solution" and "Examples" tabs.
  Your result and the reference test solution are compared by strings.

Notes:

• • lng == wdth as a starting case would be an entirely different problem and the drawing is planned to be interpreted with lng != wdth.

• When the initial parameters are so that lng == wdth, the solution [lng] would be the most obvious but not in the spirit of this kata so, in that case, return None/nil/null/Nothing

• return {} with C++, Array() with Scala.

• In that case the returned structure of C will have its sz component equal to 0.

• Return the string "nil" with Bash, PowerShell and Fortran.