Scala algorithm: Count passing cars

Published

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!

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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)

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

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")

  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))

  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. 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))

  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.

  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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  4. Links to Scala concepts used in this specific algorithm, also unit-tested.
  5. An implementation in pure-functional immutable Scala, with efficiency in mind (for most algorithms, this is for paid subscribers only).
  6. Unit tests, with a button to run them immediately in our in-browser IDE.
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Fully unit-tested, with explanations and relevant concepts; new algorithms published about once a week.

  1. Compute the length of longest valid parentheses
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  4. Remove duplicates from an unsorted List
  5. Make a queue using stacks (Lists in Scala)
  6. Find height of binary tree
  7. Single-elimination tournament tree
  8. Reverse Polish Notation calculator
  9. Quick Sort sorting algorithm in pure immutable Scala
  10. Check word in grid (depth-first search)
  11. Maximum wait at a fuel station
  12. Find minimum missing positive number in a sequence
  13. Least-recently used cache (LRU)
  14. Count pairs of a given expected sum
  15. Binary heap (min-heap)
  16. Compute a Roman numeral for an Integer, and vice-versa
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  18. Matching parentheses algorithm with foldLeft and a state machine
  19. Traverse a tree Breadth-First, immutably
  20. Read a matrix as a spiral
  21. Remove duplicates from a sorted list (state machine)
  22. Token Bucket Rate Limiter
  23. Check word in grid (stack-safe)
  24. Leaky Bucket Rate Limiter
  25. Merge Sort: stack-safe, tail-recursive, in pure immutable Scala, N-way
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  27. Longest increasing sub-sequence length
  28. Reverse first n elements of a queue
  29. Binary search a generic Array
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  31. Merge Sort: in pure immutable Scala
  32. Make a queue using Maps
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  34. Count number of contiguous countries by colors
  35. Add numbers without using addition (plus sign)
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  39. Find kth largest element in a List
  40. Balanced parentheses algorithm with tail-call recursion optimisation
  41. Reverse a String's words efficiently
  42. Count number of changes (manipulations) needed to make an anagram with an efficient foldLeft
  43. Count passing cars
  44. Count dist intersections
  45. Establish execution order from dependencies
  46. Counting inversions of a sequence (array) using a Merge Sort
  47. Longest common prefix of strings
  48. Check if an array is a palindrome
  49. Compute missing ranges
  50. Check a directed graph has a routing between two nodes (depth-first search)
  51. Compute nth row of Pascal's triangle
  52. Run-length encoding (RLE) Decoder
  53. Check if a number is a palindrome
  54. In a range of numbers, count the numbers divisible by a specific integer
  55. Merge intervals
  56. Compute minimum number of Fibonacci numbers to reach sum
  57. Find the longest palindrome within a string
  58. Find the index of a substring ('indexOf')
  59. Reshape a matrix
  60. Compute the steps to transform an anagram only using swaps
  61. Compute modulo of an exponent without exponentiation
  62. Closest pair of coordinates in a 2D plane
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  77. Monitor success rate of a process that may fail
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  84. Find triplets that sum to a target ('3Sum')
  85. Find combinations adding up to N (non-unique)
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  97. Find k closest elements to a value in a sorted Array
  98. Print a binary tree vertically
  99. QuickSelect Selection Algorithm (kth smallest item/order statistic)
  100. Rotate a matrix by 90 degrees clockwise

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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