# Scala algorithm: Check a directed graph has a routing between two nodes (depth-first search)

Published

## Algorithm goal

A directed graph is a set of edges from `T` to a set of nodes (`Set[T]`(edges). It can be represented with a `Map[T, Set[T]]`.

Find if there is a direct routing between two nodes. For example, for a mapping `1 -> {2}, 3 -> {4}`, there is no routing from `1 --> 4`, but for `1 -> {2}, 2 -> {3}, 3 -> {4}` has a direct routing.

## Test cases in Scala

``````assert(hasRouting(Map(1 -> Set(1)), 1, 1))
assert(hasRouting(Map(1 -> Set(2)), 1, 2))
assert(!hasRouting(Map(1 -> Set(2)), 2, 1))
assert(!hasRouting(Map(1 -> Set(2), 3 -> Set(4)), 1, 4))
assert(!hasRouting(Map(1 -> Set(2), 3 -> Set(4)), 4, 1))
assert(hasRouting(Map(1 -> Set(2, 3), 2 -> Set(3), 3 -> Set(4)), 1, 4))
``````

## Algorithm in Scala

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

## Explanation

We use depth-first search (TraverseTreeDepthFirst): we begin from the start node, and if we reach the end node straight away, we have found a routing. Otherwise, we mark this node as visited in a visited-set, and append the next unvisited nodes to the List of 'remaining' nodes, Then, we iterate the process, until we either run out of remaining nodes, or reach the end. (this is © from www.scala-algorithms.com)

## Scala concepts & Hints

1. ### 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-")
``````

It is also frequently used in combination with Tail Recursion.

2. ### 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")
``````
3. ### 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)
``````
4. ### 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)
``````

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