Algorithm goal

Given a of dependencies (eg 'Task A depends on Task B', 'Task B depends on Task C'), establish the order in which the Tasks should be executed, eg in this case 'Task C' has to happen before 'Task B', and 'Task B' has to happen before 'Task A' can happen.

There are no cycles, ie A depends on B depends on A.

This is also known as a Topological sorting which allows you, from a complex set of dependencies to find out what needs to happen first. This sort of an algorithm has many applications, especially in project management and rendering Gantt charts.

Test cases in Scala

assert(dependencyOrder('a' -> 'b') == List('b', 'a'))
assert(dependencyOrder('a' -> 'b', 'b' -> 'c') == List('c', 'b', 'a'))
assert(
  dependencyOrder('a' -> 'b', 'a' -> 'c', 'c' -> 'd', 'b' -> 'd') ==
    List('d', 'c', 'b', 'a')
)

Algorithm in Scala

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

Explanation

There are a couple of ways to implement this (such as depth-first search), however the simplest is 'Kahn's algorithm', which is what we implement here.

The key principle is that we find nodes that have nothing pointing to them, which makes them the first set of nodes to be executed. Then, we can exclude these nodes from the graph to find a new set of nodes that are not being pointed to. This is repeated until no nodes remain in the graph. (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")
   

   ▶ Run code in the IDE

2. Def Inside Def

   A great aspect of Scala is being able to declare functions inside functions, making it possible to reduce repetition.

   def exampleDef(input: String): String = {
     def surroundInputWith(char: Char): String = s"$char$input$char"
     surroundInputWith('-')
   }
   
   assert(exampleDef("test") == "-test-")
   

   ▶ Run code in the IDE

   It is also frequently used in combination with Tail Recursion.

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")
   

   ▶ Run code in the IDE

4. 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)
   

   ▶ Run code in the IDE

5. Tail Recursion

   In Scala, tail recursion enables you to rewrite a mutable structure such as a while-loop, into an immutable algorithm.

   def fibonacci(n: Int): Int = {
     @scala.annotation.tailrec
     def go(i: Int, previous: Int, beforePrevious: Int): Int =
       if (i >= n) previous else go(i + 1, previous + beforePrevious, previous)
   
     go(i = 1, previous = 1, beforePrevious = 0)
   }
   
   assert(fibonacci(8) == 21)
   

   ▶ Run code in the IDE