Scala algorithm: Read a matrix as a spiral

Published , last updated

Algorithm goal

For a matrix, read it in a clockwise spiral order. For example, if this is the matrix:

123
456
789

Would be read as:

123698745

Test cases in Scala

assert(
  getIndicesBased(
    Vector(
      Vector(1, 2, 3),
      Vector(4, 5, 6),
      Vector(7, 8, 9),
      Vector(10, 11, 12)
    )
  ).toVector == Vector(1, 2, 3, 6, 9, 12, 11, 10, 7, 4, 5, 8)
)
assert(
  getIndicesBased(
    Vector(
      Vector(1, 2, 3, 4),
      Vector(5, 6, 7, 8),
      Vector(9, 10, 11, 12),
      Vector(13, 14, 15, 16),
      Vector(17, 18, 19, 20)
    )
  ).toVector == Vector(
    1, 2, 3, 4, 8, 12, 16, 20, 19, 18, 17, 13, 9, 5, 6, 7, 11, 15, 14, 10
  )
)
assert(getIndicesBased(Vector(Vector(1, 2, 3))).toVector == Vector(1, 2, 3))
assert(
  getIndicesBased(Vector(Vector(1), Vector(2), Vector(3))).toVector ==
    Vector(1, 2, 3)
)

Algorithm in Scala

27 lines of Scala (version 2.13), showing how concise Scala can be!

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Explanation

There are different approaches to this problem, but this approach is the most interesting as it first of all does not mutate the matrix nor perform any heavy transformations of the inputs: by representing the matrix indices in the form of a pair of Ranges, we can simply get the indices and then after getting those indices, extract the respective elements.

The key concept here is that if we take the top part of the matrix, and then rotate it anti-clockwise, that is our next set of indices, and we just keep on going. To do that, in each iteration, the horizontal range becomes the vertical range (without the first line), and vertical range becomes the horizontal range, reversed. (this is © from www.scala-algorithms.com)

In essence, the example matrix would be treated like this (where the outline indicates what we are selecting in this iteration):

123
456
789

After the second transformation, it would look like this:

69
58
47

Full explanation is available for subscribers Scala algorithms logo, maze part, which looks quirky

Scala concepts & Hints

  1. Drop, Take, dropRight, takeRight

    Scala's `drop` and `take` methods typically remove or select `n` items from a collection.

    assert(List(1, 2, 3).drop(2) == List(3))
    
    assert(List(1, 2, 3).take(2) == List(1, 2))
    
    assert(List(1, 2, 3).dropRight(2) == List(1))
    
    assert(List(1, 2, 3).takeRight(2) == List(2, 3))
    
    assert((1 to 5).take(2) == (1 to 2))
    
  2. Lazy List

    The 'LazyList' type (previously known as 'Stream' in Scala) is used to describe a potentially infinite list that evaluates only when necessary ('lazily').

  3. Range

    The (1 to n) syntax produces a "Range" which is a representation of a sequence of numbers.

    assert((1 to 5).toString == "Range 1 to 5")
    
    assert((1 to 5).reverse.toString() == "Range 5 to 1 by -1")
    
    assert((1 to 5).toList == List(1, 2, 3, 4, 5))
    

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  6. Find combinations adding up to N (unique)
  7. Find k closest elements to a value in a sorted Array
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  10. Quick Sort sorting algorithm in pure immutable Scala
  11. Compute a Roman numeral for an Integer, and vice-versa
  12. Matching parentheses algorithm with foldLeft and a state machine
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  14. Read a matrix as a spiral
  15. Remove duplicates from a sorted list (state machine)
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  30. Counting inversions of a sequence (array) using a Merge Sort
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  58. Find combinations adding up to N (non-unique)
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Explore the 21 most useful Scala concepts

To save you going through various tutorials, we cherry-picked the most useful Scala concepts in a consistent form.

  1. Class Inside Class
  2. Class Inside Def
  3. Collect
  4. Def Inside Def
  5. Drop, Take, dropRight, takeRight
  6. foldLeft and foldRight
  7. For-comprehension
  8. Lazy List
  9. Option Type
  10. Ordering
  11. Partial Function
  12. Pattern Matching
  13. Range
  14. scanLeft and scanRight
  15. Sliding / Sliding Window
  16. Stack Safety
  17. State machine
  18. Tail Recursion
  19. Type Class
  20. View
  21. Zip

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