Algorithm goal

An Array represents a sequence of cars in a sequence, either going East or West.

Count the pairs of cars that pass each other eventually.

For example, if we represent the cars as a string EEWEW, then the number of passes would be 5: First 2 EEs pass both WWs, so 4 passes, and then the last E passes the last W, so in total 5 passes.

Test cases in Scala

assert(countPassingCars(List.empty) == 0)
assert(countPassingCars(List(CarDirection.East)) == 0)
assert(countPassingCars(List(CarDirection.West)) == 0)
assert(countPassingCars(List(CarDirection.East, CarDirection.East)) == 0)
assert(countPassingCars(List(CarDirection.West, CarDirection.West)) == 0)
assert(countPassingCars(List(CarDirection.East, CarDirection.West)) == 1)
assert(
  countPassingCars(
    List(CarDirection.East, CarDirection.East, CarDirection.West)
  ) == 2
)
assert(
  countPassingCars(
    List(
      CarDirection.East,
      CarDirection.East,
      CarDirection.West,
      CarDirection.West
    )
  ) == 4
)
assert(
  countPassingCars(
    List(
      CarDirection.East,
      CarDirection.East,
      CarDirection.West,
      CarDirection.East,
      CarDirection.West
    )
  ) == 5
)

Algorithm in Scala

27 lines of Scala (compatible versions 2.13 & 3.0), showing how concise Scala can be!

Explanation

For every car going West, we need to know how many cars going East it will cross, and then combine that count to get the total number of passes.

Let's say if we have EEWEW representing 5 cars in total, then we can represent them as prefix sums: Number of cars going East from position 0 is 1, from position 1 is 2, from position 2 is 2, and so forth; so 12233. (this is © from www.scala-algorithms.com)

Scala concepts & Hints

1. Collect

   'collect' allows you to use Pattern Matching, to filter and map items.

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

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2. 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))
   

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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")
   

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4. scanLeft and scanRight

   Scala's `scan` functions enable you to do folds like foldLeft and foldRight, while collecting the intermediate results

   assert(List(1, 2, 3, 4, 5).scanLeft(0)(_ + _) == List(0, 1, 3, 6, 10, 15))
   

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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)
   

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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.

8. Zip

   'zip' allows you to combine two lists pair-wise (meaning turn a pair of lists, into a list of pairs)

   It can be used over Arrays, Lists, Views, Iterators and other collections.

   assert(List(1, 2, 3).zip(List(5, 6, 7)) == List(1 -> 5, 2 -> 6, 3 -> 7))
   
   assert(List(1, 2).zip(List(5, 6, 7)) == List(1 -> 5, 2 -> 6))
   
   assert(List(5, 6).zipWithIndex == List(5 -> 0, 6 -> 1))
   
   assert(List(5, 6).zipAll(List('A'), 9, 'Z') == List(5 -> 'A', 6 -> 'Z'))
   
   assert(List(5).zipAll(List('A', 'B'), 1, 'Z') == List(5 -> 'A', 1 -> 'B'))
   

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