Scala algorithm: Count dist intersections

Published

Algorithm goal

This problem is similar to NumberOfDiscIntersections from Codility.

The best illustration for this algorithm is on Stack Overflow: Counting Disk Intersections.

Given a list L, the item at index k is a disc on a 2D plane at position (0, i), and L[k] is the disc's radius. An intersection is if two discs at minimum touch each other.

For instance, a List of [1, 1] has just 1 intersection, whereas a list [1, 1, 1] has 2 because every disc touches every other disc.

Test cases in Scala

assert(brute(List(1)) == 0)
assert(brute(List(0, 0)) == 0)
assert(brute(List(0, 1)) == 1)
assert(brute(List(1, 1)) == 1)
assert(brute(List(1, 1, 1)) == 3)
assert(brute(List(1, 0, 0, 1)) == 2)
assert(brute(List(5, 0, 0, 1)) == 4)
assert(efficient(List(1)) == 0)
assert(efficient(List(0, 0)) == 0)
assert(efficient(List(0, 1)) == 1)
assert(efficient(List(1, 1)) == 1)
assert(efficient(List(1, 1, 1)) == 3)
assert(efficient(List(1, 0, 0, 1)) == 2)
assert(efficient(List(5, 0, 0, 1)) == 4)

Algorithm in Scala

69 lines of Scala (compatible versions 2.13 & 3.0).

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Explanation

We begin with a brute-force solution, so that we could compare it to an optimised solution. The brute solution is highly inefficient as it traverses the list twice. We can do better by traversing it once:

We begin by counting the total range using O(n) operations, and then for each item in that range, we check how many new openings there are compared against what has been opened. When 5 new openings are added, if there are 4 existing ones, that gives us 20 extra openings, as well as the number of openings that we get from the 5 intersecting each other (that is 5 * 4 / 2, ie Binomial '(n choose 2)'). (this is © from www.scala-algorithms.com)

Note that this solution is highly verbose for the purpose of comprehension and readability. Many online solutions use convoluted logic that is quite hard to comprehend. It means: this can be written much more concisely if needed.

Scala concepts & Hints

  1. foldLeft and foldRight

    A 'fold' allows you to perform the equivalent of a for-loop, but with a lot less code.

    def foldMutable[I, O](initialState: O)(items: List[I])(f: (O, I) => O): O =
  items.foldLeft(initialState)(f)

  2. For-comprehension

    The for-comprehension is highly important syntatic enhancement in functional programming languages.

    val Multiplier = 10

val result: List[Int] = for {
  num <- List(1, 2, 3)
  anotherNum <-
    List(num * Multiplier - 1, num * Multiplier, num * Multiplier + 1)
} yield anotherNum + 1

assert(result == List(10, 11, 12, 20, 21, 22, 30, 31, 32))

  3. Pattern Matching

    Pattern matching in Scala lets you quickly identify what you are looking for in a data, and also extract it.

    assert("Hello World".collect {
  case character if Character.isUpperCase(character) => character.toLower
} == "hw")

  4. 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))

  5. Stack Safety

    Stack safety is present where a function cannot crash due to overflowing the limit of number of recursive calls.

    This function will work for n = 5, but will not work for n = 2000 (crash with java.lang.StackOverflowError) - however there is a way to fix it :-)

    In Scala Algorithms, we try to write the algorithms in a stack-safe way, where possible, so that when you use the algorithms, they will not crash on large inputs. However, stack-safe implementations are often more complex, and in some cases, overly complex, for the task at hand.

    def sum(from: Int, until: Int): Int =
  if (from == until) until else from + sum(from + 1, until)

def thisWillSucceed: Int = sum(1, 5)

def thisWillFail: Int = sum(1, 300)

  6. State machine

    A state machine is the use of `sealed trait` to represent all the possible states (and transitions) of a 'machine' in a hierarchical form.

  7. View

    The .view syntax creates a structure that mirrors another structure, until "forced" by an eager operation like .toList, .foreach, .forall, .count.

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Explore the 22 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. Variance
  21. View
  22. Zip

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