Algorithm goal

Representing a graph with edges as a Set[(T, T)], identify whether there are any cycles.Such an algorithm could be used for cycle detection eg in a compiler or a dependency tracker, or lock detection, to identify situations where one thing is waiting for another which is waiting for the original thing.

Test cases in Scala

assert(
  !FunctionalGraph(edges = Set(1 -> 2, 2 -> 3)).hasCycles,
  "A simple graph does not have cycles"
)
assert(
  FunctionalGraph(edges = Set(1 -> 2, 2 -> 3, 3 -> 4, 4 -> 2)).hasCycles,
  "A graph with a cycle registers as such"
)
assert(
  !FunctionalGraph(edges = Set(1 -> 2, 1 -> 3, 2 -> 3, 3 -> 4)).hasCycles,
  "A graph that branches out and joins back has no cycles"
)

Algorithm in Scala

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

Explanation

The algorithm can be done using standard breadth/depth searches, but it is simpler to explain when done using the topological sorting approach.

The Kahn's algorithm which is mutable can be implemented using plain sets, where we perform what the algorithm is describing: to find whether there are cycles, keep on eliminating nodes that have no edges towards them. when there are no nodes without incoming edges, but there are edges then we have detected a cycle. (this is © from www.scala-algorithms.com)

Scala concepts & Hints

1. 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

2. 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

3. 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