(patch) general code improvements and more documentation (#8)

Reviewed-on: #8

.pre-commit-config.yaml

@@ -1,7 +1,7 @@
 ---
 repos:
   - repo: https://github.com/pre-commit/pre-commit-hooks
-    rev: v4.5.0
+    rev: v6.0.0
     hooks:
       - id: end-of-file-fixer
       - id: trailing-whitespace
@@ -12,6 +12,6 @@ repos:
       - id: trailing-whitespace
       - id: check-yaml
   - repo: https://git.garrity.co/garrity-software/gs-pre-commit-scala
-    rev: v1.0.1
+    rev: v1.0.2
     hooks:
       - id: scalafmt

.scalafmt.conf

@@ -1,5 +1,5 @@
 // See: https://github.com/scalameta/scalafmt/tags for the latest tags.
-version = 3.10.2
+version = 3.10.4
 runner.dialect = scala3
 maxColumn = 80
 

build.sbt

@@ -1,4 +1,4 @@
-val scala3: String = "3.7.4"
+val scala3: String = "3.8.2"
 
 ThisBuild / scalaVersion  := scala3
 ThisBuild / versionScheme := Some("semver-spec")
@@ -31,14 +31,14 @@ val Deps = new {
   }
 
   val Fs2 = new {
-    val Core: ModuleID = "co.fs2" %% "fs2-core" % "3.12.2"
+    val Core: ModuleID = "co.fs2" %% "fs2-core" % "3.13.0"
   }
 
   val Gs = new {
-    val Datagen: ModuleID = "gs" %% "gs-datagen-core-v0" % "0.3.3"
+    val Datagen: ModuleID = "gs" %% "gs-datagen-core-v0" % "0.4.1"
   }
 
-  val MUnit: ModuleID = "org.scalameta" %% "munit" % "1.1.1"
+  val MUnit: ModuleID = "org.scalameta" %% "munit" % "1.2.4"
 }
 
 lazy val testSettings = Seq(
@@ -51,6 +51,7 @@ lazy val testSettings = Seq(
 lazy val `gs-graph` = project
   .in(file("."))
   .aggregate(core, cats, fs2)
+  .settings(noPublishSettings)
   .settings(sharedSettings)
   .settings(testSettings)
   .settings(name := s"${gsProjectName.value}-v${semVerMajor.value}")

modules/core/src/main/scala/gs/graph/v0/Adjacency.scala

@@ -20,6 +20,26 @@ final class Adjacency(val neighbors: Vector[Vector[Vertex]]):
     */
   def at(vertex: Vertex): Vector[Vertex] = neighbors(vertex.ordinal)
 
+  /** Get the vector of _incoming_ [[Vertex]] that point _to_ some input
+    * [[Vertex]].
+    *
+    * @param vertex
+    *   The [[Vertex]] for which to retrieve the incoming vertices.
+    * @return
+    *   The list of [[Vertex]] that have an edge _to_ the input [[Vertex]].
+    */
+  def incoming(vertex: Vertex): Vector[Vertex] =
+    if vertex.ordinal >= neighbors.length then Vector.empty
+    else
+      neighbors.zipWithIndex
+        .filter {
+          // ignore the neighbors of the input vertex
+          case (_, index) => index != vertex.ordinal
+        }
+        .filter(_._1.contains(vertex))
+        .map(_._2)
+        .map(Vertex(_))
+
   /** Express this [[Adjacency]] as a vector of [[Edge]].
     *
     * @return
@@ -31,10 +51,9 @@ final class Adjacency(val neighbors: Vector[Vector[Vertex]]):
       tos.map(to => Edge(from, to)).distinct
     }
 
-  /** @return
+  /** The number of vertices represented by this adjacency list.
-    *   The number of vertices represented by this adjacency list.
     */
-  def numberOfVertices: Size = Size.fromVector(neighbors)
+  lazy val numberOfVertices: Size = Size.fromVector(neighbors)
 
   /** Perform a linear traversal for each [[gs.graph.v0.Vertex]] to calculate
     * the total number of edges in this adjacency list.
@@ -42,9 +61,11 @@ final class Adjacency(val neighbors: Vector[Vector[Vertex]]):
     * @return
     *   The number of edges in this adjacency list.
     */
-  def numberOfEdges: Size = Size(neighbors.map(_.length).reduce(_ + _))
+  lazy val numberOfEdges: Size = Size(neighbors.map(_.length).reduce(_ + _))
 
-  def findRoots(): Vector[Vertex] =
+  /** All vertices that do not have inbound connections.
+    */
+  lazy val roots: Vector[Vertex] =
     val counts = Array.fill(neighbors.length)(0)
     neighbors.foreach { ns =>
       // Each vertex listed here is receiving an inbound connection, if we
@@ -74,6 +95,17 @@ object Adjacency:
     */
   def apply(adj: Vector[Vector[Vertex]]): Adjacency = new Adjacency(adj)
 
+  /** Create an empty adjacency list for some number of vertices. No vertex has
+    * any connections to another vertex.
+    *
+    * @param numberOfVertices
+    *   The number of vertices in this disconnected graph.
+    * @return
+    *   Some new empty adjacency.
+    */
+  def empty(numberOfVertices: Size): Adjacency =
+    new Adjacency(Vector.fill(numberOfVertices.value)(Vector.empty))
+
   given CanEqual[Adjacency, Adjacency] = CanEqual.derived
 
   /** @return
@@ -86,7 +118,8 @@ object Adjacency:
     */
   final val Single: Adjacency = new Adjacency(Vector(Vector.empty))
 
-  /** Calculate an [[Adjacency]] from some collection of [[Edge]].
+  /** Calculate an [[Adjacency]] from some collection of [[Edge]], where those
+    * edges are assumed to be directed.
     *
     * @param numberOfVertices
     *   The number of [[Vertex]] (`N`) in this graph.

modules/core/src/main/scala/gs/graph/v0/Edge.scala

@@ -1,5 +1,7 @@
 package gs.graph.v0
 
+import java.util.Objects
+
 /** Represents a relationship between two [[Vertex]].
   *
   * When used is a directed context, the edge goes _from_ `v1` _to_ `v2`.
@@ -41,6 +43,11 @@ final class Edge(
       case other: Edge => v1 == other.v1 && v2 == other.v2
       case _           => false
 
+  /** @inheritDocs
+    */
+  override def hashCode(): Int =
+    Objects.hash(v1, v2)
+
 end Edge
 
 object Edge:

modules/core/src/main/scala/gs/graph/v0/GraphDisposition.scala

@@ -1,5 +1,10 @@
 package gs.graph.v0
 
+/** Describes the fundamental disposition of some graph.
+  *
+  * @param name
+  *   The string value of this disposition.
+  */
 sealed abstract class GraphDisposition(val name: String):
 
   override def equals(that: Any): Boolean =
@@ -15,7 +20,12 @@ object GraphDisposition:
 
   given CanEqual[GraphDisposition, GraphDisposition] = CanEqual.derived
 
+  /** The graph has directed relationships between vertices.
+    */
   case object Directed extends GraphDisposition("directed")
+
+  /** The graph has relationships between vertices with no logical direction.
+    */
   case object Undirected extends GraphDisposition("undirected")
 
 end GraphDisposition

modules/core/src/main/scala/gs/graph/v0/GraphTraversal.scala

@@ -2,6 +2,7 @@ package gs.graph.v0
 
 import gs.graph.v0.data.AnyGraphWithData
 import scala.collection.mutable.ListBuffer
+import scala.collection.mutable.Queue
 import scala.collection.mutable.Stack
 
 /** Graph traversal algorithms including DFS and BFS.
@@ -26,9 +27,8 @@ object GraphTraversal:
     val s          = Stack.empty[Vertex]
     val discovered = Array.fill(graph.numberOfVertices.value)(false)
 
-    val root = Vertex.Zero
+    graph.selectRoots().foreach { root =>
-    s.push(root)
+      val _ = s.push(root)
-
       while !s.isEmpty
       do
         val v = s.pop()
@@ -38,6 +38,7 @@ object GraphTraversal:
           graph.neighbors(v).foreach(w => s.push(w))
         else ()
       ()
+    }
 
   /** Depth-first search that executes a function on each [[Vertex]] to produce
     * some output. This function will operate on _any_ [[Graph]].
@@ -60,9 +61,8 @@ object GraphTraversal:
     val s          = Stack.empty[Vertex]
     val discovered = Array.fill(graph.numberOfVertices.value)(false)
 
-    val root = Vertex.Zero
+    graph.selectRoots().foreach { root =>
-    s.push(root)
+      val _ = s.push(root)
-
       while !s.isEmpty
       do
         val v = s.pop()
@@ -71,6 +71,7 @@ object GraphTraversal:
           discovered(v.ordinal) = true
           graph.neighbors(v).foreach(w => s.push(w))
         else ()
+    }
 
     output.toList
 
@@ -84,8 +85,7 @@ object GraphTraversal:
     val discovered = Array.fill(graph.numberOfVertices.value)(false)
 
     graph.selectRoots().foreach { root =>
-      s.push(root)
+      val _ = s.push(root)
-
       while !s.isEmpty
       do
         val v = s.pop()
@@ -117,8 +117,7 @@ object GraphTraversal:
     val discovered = Array.fill(graph.numberOfVertices.value)(false)
 
     graph.selectRoots().foreach { root =>
-      s.push(root)
+      val _ = s.push(root)
-
       while !s.isEmpty
       do
         val v = s.pop()
@@ -153,8 +152,7 @@ object GraphTraversal:
     val discovered = Array.fill(graph.numberOfVertices.value)(false)
 
     graph.selectRoots().foreach { root =>
-      s.push(root)
+      val _ = s.push(root)
-
       while !s.isEmpty
       do
         val v = s.pop()
@@ -177,8 +175,7 @@ object GraphTraversal:
     val discovered = Array.fill(graph.numberOfVertices.value)(false)
 
     graph.selectRoots().foreach { root =>
-      s.push(root)
+      val _ = s.push(root)
-
       while !s.isEmpty
       do
         val v = s.pop()
@@ -191,4 +188,139 @@ object GraphTraversal:
 
     acc
 
+  def bfs(
+    graph: Graph,
+    visit: Vertex => Unit
+  ): Unit =
+    val q       = Queue.empty[Vertex]
+    val visited = Array.fill(graph.numberOfVertices.value)(false)
+    val _       = graph.selectRoots().foreach(q.enqueue)
+
+    while !q.isEmpty
+    do
+      val v = q.dequeue()
+      if !visited(v.ordinal) then
+        val _ = visit(v)
+        visited(v.ordinal) = true
+        graph.neighbors(v).foreach { neighbor =>
+          if !visited(neighbor.ordinal) then q.enqueue(neighbor)
+          else ()
+        }
+      else ()
+
+  def bfs[Out](
+    graph: Graph,
+    visit: Vertex => Out
+  ): List[Out] =
+    val output  = ListBuffer.empty[Out]
+    val q       = Queue.empty[Vertex]
+    val visited = Array.fill(graph.numberOfVertices.value)(false)
+    val _       = graph.selectRoots().foreach(q.enqueue)
+
+    while !q.isEmpty
+    do
+      val v = q.dequeue()
+      if !visited(v.ordinal) then
+        val _ = output.addOne(visit(v))
+        visited(v.ordinal) = true
+        graph.neighbors(v).foreach { neighbor =>
+          if !visited(neighbor.ordinal) then q.enqueue(neighbor)
+          else ()
+        }
+      else ()
+
+    output.toList
+
+  def bfsFold[Acc](
+    graph: Graph,
+    initial: Acc,
+    f: (Acc, Vertex) => Acc
+  ): Acc =
+    var acc     = initial
+    val q       = Queue.empty[Vertex]
+    val visited = Array.fill(graph.numberOfVertices.value)(false)
+    val _       = graph.selectRoots().foreach(q.enqueue)
+
+    while !q.isEmpty
+    do
+      val v = q.dequeue()
+      if !visited(v.ordinal) then
+        acc = f(acc, v)
+        visited(v.ordinal) = true
+        graph.neighbors(v).foreach { neighbor =>
+          if !visited(neighbor.ordinal) then q.enqueue(neighbor)
+          else ()
+        }
+      else ()
+
+    acc
+
+  def bfs[A](
+    graph: AnyGraphWithData[A],
+    visit: (Vertex, A) => Unit
+  ): Unit =
+    val q       = Queue.empty[Vertex]
+    val visited = Array.fill(graph.numberOfVertices.value)(false)
+    val _       = graph.selectRoots().foreach(q.enqueue)
+
+    while !q.isEmpty
+    do
+      val v = q.dequeue()
+      if !visited(v.ordinal) then
+        val _ = visit(v, graph.data(v.ordinal))
+        visited(v.ordinal) = true
+        graph.neighbors(v).foreach { neighbor =>
+          if !visited(neighbor.ordinal) then q.enqueue(neighbor)
+          else ()
+        }
+      else ()
+    ()
+
+  def bfs[A, Out](
+    graph: AnyGraphWithData[A],
+    visit: (Vertex, A) => Out
+  ): List[Out] =
+    val output  = ListBuffer.empty[Out]
+    val q       = Queue.empty[Vertex]
+    val visited = Array.fill(graph.numberOfVertices.value)(false)
+    val _       = graph.selectRoots().foreach(q.enqueue)
+
+    while !q.isEmpty
+    do
+      val v = q.dequeue()
+      if !visited(v.ordinal) then
+        val _ = output.addOne(visit(v, graph.data(v.ordinal)))
+        visited(v.ordinal) = true
+        graph.neighbors(v).foreach { neighbor =>
+          if !visited(neighbor.ordinal) then q.enqueue(neighbor)
+          else ()
+        }
+      else ()
+
+    output.toList
+
+  def bfsFold[A, Acc](
+    graph: AnyGraphWithData[A],
+    initial: Acc,
+    f: (Acc, A) => Acc
+  ): Acc =
+    var acc     = initial
+    val q       = Queue.empty[Vertex]
+    val visited = Array.fill(graph.numberOfVertices.value)(false)
+    val _       = graph.selectRoots().foreach(q.enqueue)
+
+    while !q.isEmpty
+    do
+      val v = q.dequeue()
+      if !visited(v.ordinal) then
+        acc = f(acc, graph.data(v.ordinal))
+        visited(v.ordinal) = true
+        graph.neighbors(v).foreach { neighbor =>
+          if !visited(neighbor.ordinal) then q.enqueue(neighbor)
+          else ()
+        }
+      else ()
+
+    acc
+
 end GraphTraversal

modules/core/src/main/scala/gs/graph/v0/directed/Digraph.scala

@@ -29,6 +29,8 @@ class Digraph(
     */
   override def selectRoots(): Vector[Vertex] = roots
 
+  /** @inheritDocs
+    */
   override def equals(that: Any): Boolean =
     that match
       case other: Digraph =>
@@ -78,7 +80,7 @@ object Digraph:
     new Digraph(
       numberOfVertices = adjacency.numberOfVertices,
       adjacency = adjacency,
-      roots = adjacency.findRoots()
+      roots = adjacency.roots
     )
 
   /** Find all roots for the given collection of [[Edge]].
@@ -102,7 +104,11 @@ object Digraph:
 
     // If there are any vertices with no incoming connections, those are roots.
     // Note that these may be completely disconnected.
-    counts.filter(_ == 0).map(Vertex(_)).toVector
+    counts.zipWithIndex
+      .filter(_._1 == 0)
+      .map { case (_, index) => Vertex(index) }
+      .toVector
+      .distinct
 
   /** Determine whether the given [[Digraph]] has any cycles.
     *

modules/core/src/main/scala/gs/graph/v0/directed/SingleRootDigraph.scala

@@ -6,14 +6,30 @@ import gs.graph.v0.GraphException
 import gs.graph.v0.Size
 import gs.graph.v0.Vertex
 
+/** Specialization of [[Digraph]] that always has a single root vertex.
+  *
+  * @param n
+  *   The number of [[Vertex]] present in this graph.
+  * @param a
+  *   The [[Adjacency]] that describes this graph.
+  * @param r
+  *   The singular root [[Vertex]].
+  */
 class SingleRootDigraph(
   n: Size,
   a: Adjacency,
-  r: Vertex
+  root: Vertex
-) extends Digraph(n, a, Vector(r))
+) extends Digraph(n, a, Vector(root))
 
 object SingleRootDigraph:
 
+  /** Attempt to show that the given [[Digraph]] has a single root.
+    *
+    * @param dg
+    *   The input [[Digraph]].
+    * @return
+    *   [[SingleRootDigraph]] or `None` if the number of roots is not 1.
+    */
   def fromDirectedGraph(dg: Digraph): Option[SingleRootDigraph] =
     if dg.roots.size == 1 then
       Some(
@@ -25,6 +41,18 @@ object SingleRootDigraph:
       )
     else None
 
+  /** Given some edges, build a [[SingleRootDigraph]]. Throw an exception if
+    * this operation fails.
+    *
+    * @param numberOfVertices
+    *   The number of [[Vertex]] in the graph.
+    * @param edges
+    *   The collection of [[Edge]] that describe the graph.
+    * @param root
+    *   The root [[Vertex]].
+    * @return
+    *   The new [[SingleRootDigraph]].
+    */
   def fromEdgesUnsafe(
     numberOfVertices: Size,
     edges: Iterable[Edge],
@@ -38,6 +66,17 @@ object SingleRootDigraph:
       )
     else throw GraphException.RootOutOfBounds(root, numberOfVertices)
 
+  /** Given some edges, build a [[SingleRootDigraph]] if that collection
+    * represents a graph with a single root.
+    *
+    * @param numberOfVertices
+    *   The number of [[Vertex]] in the graph.
+    * @param edges
+    *   The collection of [[Edge]] that describe the graph.
+    * @return
+    *   The new [[SingleRootDigraph]], or `None` if the edges do not describe a
+    *   digraph with a single root.
+    */
   def fromEdges(
     numberOfVertices: Size,
     edges: Iterable[Edge]
@@ -53,6 +92,19 @@ object SingleRootDigraph:
       )
     else None
 
+  /** Given some [[Adjacency]] and a given root [[Vertex]], instantiate a new
+    * [[SingleRootDigraph]].
+    *
+    * Throws an exception if the given root is not contained within the
+    * [[Adjacency]].
+    *
+    * @param adjacency
+    *   The [[Adjacency]] which describes the graph.
+    * @param root
+    *   The root [[Vertex]].
+    * @return
+    *   New [[SingleRootDigraph]]
+    */
   def fromAdjacencyUnsafe(
     adjacency: Adjacency,
     root: Vertex
@@ -65,10 +117,20 @@ object SingleRootDigraph:
       )
     else throw GraphException.RootOutOfBounds(root, adjacency.numberOfVertices)
 
+  /** Given some [[Adjacency]] and a given root [[Vertex]], instantiate a new
+    * [[SingleRootDigraph]] if the [[Vertex]] is within the graph..
+    *
+    * @param adjacency
+    *   The [[Adjacency]] which describes the graph.
+    * @param root
+    *   The root [[Vertex]].
+    * @return
+    *   New [[SingleRootDigraph]], or `None` if the given root is not valid.
+    */
   def fromAdjacency(
     adjacency: Adjacency
   ): Option[SingleRootDigraph] =
-    val roots = adjacency.findRoots()
+    val roots = adjacency.roots
     if roots.size == 1 then
       Some(
         new SingleRootDigraph(

modules/core/src/test/scala/gs/graph/v0/AdjacencyTests.scala

@@ -0,0 +1,27 @@
+package gs.graph.v0
+
+class AdjacencyTests extends munit.FunSuite:
+
+  test("should provide incoming connections") {
+    val N  = Size(7)
+    val vs = (0 until N.value).map(Vertex(_)).toArray
+    val E  = List(
+      Edge(vs(0), vs(1)),
+      Edge(vs(0), vs(2)),
+      Edge(vs(0), vs(3)),
+      Edge(vs(1), vs(4)),
+      Edge(vs(2), vs(4)),
+      Edge(vs(3), vs(4)),
+      Edge(vs(3), vs(5)),
+      Edge(vs(4), vs(6))
+    )
+    val A = Adjacency.fromDirectedEdges(N, E)
+
+    assertEquals(A.incoming(vs(0)), Vector.empty)
+    assertEquals(A.incoming(vs(1)), Vector(vs(0)))
+    assertEquals(A.incoming(vs(2)), Vector(vs(0)))
+    assertEquals(A.incoming(vs(3)), Vector(vs(0)))
+    assertEquals(A.incoming(vs(4)), Vector(vs(1), vs(2), vs(3)))
+    assertEquals(A.incoming(vs(5)), Vector(vs(3)))
+    assertEquals(A.incoming(vs(6)), Vector(vs(4)))
+  }

modules/fs2/src/main/scala/gs/graph/v0/fs2/GraphTraversalFs2.scala

@@ -1,12 +1,15 @@
 package gs.graph.v0.fs2
 
+import cats.effect.Async
 import cats.effect.Sync
+import cats.effect.std.Queue
+import cats.syntax.all.*
 import fs2.Pull
 import fs2.Stream
 import gs.graph.v0.Graph
 import gs.graph.v0.Size
 import gs.graph.v0.Vertex
-import scala.collection.mutable.Stack
+import gs.graph.v0.data.AnyGraphWithData
 
 object GraphTraversalFs2:
 
@@ -19,19 +22,127 @@ object GraphTraversalFs2:
       val state = new DfsState(graph.numberOfVertices)
       graph
         .selectRoots()
-        .map(root => pull(graph, state, visit, root).stream.unNoneTerminate)
+        .map(root => pullDfs(graph, state, visit, root).stream.unNoneTerminate)
         .reduce(_ ++ _)
 
-  private def pull[F[_]: Sync, Out](
+  def dfs[F[_]: Sync, A, Out](
+    graph: AnyGraphWithData[A],
+    visit: A => F[Out]
+  ): Stream[F, Out] =
+    if graph.isEmpty then Stream.empty
+    else
+      val state = new DfsState(graph.numberOfVertices)
+      graph
+        .selectRoots()
+        .map(root => pullDfs(graph, state, visit, root).stream.unNoneTerminate)
+        .reduce(_ ++ _)
+
+  def bfs[F[_]: Async, Out](
     graph: Graph,
-    state: DfsState,
+    visit: Vertex => F[Out]
+  ): F[Stream[F, Out]] =
+    if graph.isEmpty then Async[F].pure(Stream.empty)
+    else
+      graph
+        .selectRoots()
+        .map { root =>
+          BfsState.initialize[F](graph.numberOfVertices).flatMap { state =>
+            doBfs(graph, visit, state, root)
+          }
+        }
+        .sequence
+        .map(_.reduce(_ ++ _))
+        .map(_.unNone)
+
+  def bfs[F[_]: Async, A, Out](
+    graph: AnyGraphWithData[A],
+    visit: A => F[Out]
+  ): F[Stream[F, Out]] =
+    if graph.isEmpty then Async[F].pure(Stream.empty)
+    else
+      graph
+        .selectRoots()
+        .map { root =>
+          BfsState.initialize[F](graph.numberOfVertices).flatMap { state =>
+            doBfs(graph, visit, state, root)
+          }
+        }
+        .sequence
+        .map(_.reduce(_ ++ _))
+        .map(_.unNone)
+
+  private def doBfs[F[_]: Async, Out](
+    graph: Graph,
+    visit: Vertex => F[Out],
+    state: BfsState[F],
+    root: Vertex
+  ): F[Stream[F, Option[Out]]] =
+    state.enqueue(root).map { _ =>
+      Stream
+        .repeatEval(state.dequeue())
+        .unNoneTerminate
+        .evalMap { vertex =>
+          state.isVisited(vertex).flatMap {
+            case true  => Async[F].delay(None)
+            case false =>
+              for
+                _   <- state.visit(vertex)
+                out <- visit(vertex)
+                _   <- enqueueAllNeighbors(vertex, graph, state)
+              yield Some(out)
+          }
+        }
+    }
+
+  private def doBfs[F[_]: Async, A, Out](
+    graph: AnyGraphWithData[A],
+    visit: A => F[Out],
+    state: BfsState[F],
+    root: Vertex
+  ): F[Stream[F, Option[Out]]] =
+    state.enqueue(root).map { _ =>
+      Stream
+        .repeatEval(state.dequeue())
+        .unNoneTerminate
+        .evalMap { vertex =>
+          state.isVisited(vertex).flatMap {
+            case true  => Async[F].delay(None)
+            case false =>
+              for
+                _   <- state.visit(vertex)
+                out <- visit(graph.data(vertex.ordinal))
+                _   <- enqueueAllNeighbors(vertex, graph, state)
+              yield Some(out)
+          }
+        }
+    }
+
+  private def enqueueAllNeighbors[F[_]: Async](
+    vertex: Vertex,
+    graph: Graph,
+    state: BfsState[F]
+  ): F[Unit] =
+    graph
+      .neighbors(vertex)
+      .map { vertex =>
+        state.isVisited(vertex).flatMap {
+          case true  => Async[F].unit
+          case false => state.enqueue(vertex)
+        }
+      }
+      .sequence
+      .as(())
+
+  private def pullDfs[F[_]: Sync, Out](
+    graph: Graph,
+    state: DfsState[F],
     visit: Vertex => F[Out],
     current: Vertex
   ): Pull[F, Option[Out], Unit] =
-    Pull.eval(Sync[F].delay(state.isDiscovered(current))).flatMap { discovered =>
+    Pull.eval(state.isVisited(current)).flatMap { visited =>
-      if discovered then Pull.output1(None) >> Pull.done
+      if visited then Pull.output1(None) >> Pull.done
       else
-        Pull.eval(Sync[F].delay(state.discover(current)))
+        Pull.eval(state.visit(current))
           >> Pull.eval(visit(current)).flatMap(out => Pull.output1(Some(out)))
           >> graph
             .neighbors(current)
@@ -39,25 +150,62 @@ object GraphTraversalFs2:
               (
                 acc,
                 neighbor
-              ) => acc >> pull(graph, state, visit, neighbor)
+              ) => acc >> pullDfs(graph, state, visit, neighbor)
             }
     }
 
-  final private class DfsState(n: Size):
+  private def pullDfs[F[_]: Sync, A, Out](
+    graph: AnyGraphWithData[A],
+    state: DfsState[F],
+    visit: A => F[Out],
+    current: Vertex
+  ): Pull[F, Option[Out], Unit] =
+    Pull.eval(state.isVisited(current)).flatMap { visited =>
+      if visited then Pull.output1(None) >> Pull.done
+      else
+        Pull.eval(state.visit(current))
+          >> Pull
+            .eval(visit(graph.data(current.ordinal)))
+            .flatMap(out => Pull.output1(Some(out)))
+          >> graph
+            .neighbors(current)
+            .foldLeft(Pull.done: Pull[F, Option[Out], Unit]) {
+              (
+                acc,
+                neighbor
+              ) => acc >> pullDfs(graph, state, visit, neighbor)
+            }
+    }
 
-    val stack: Stack[Vertex]       = Stack.empty
+  abstract private class TraverseState[F[_]: Sync](n: Size):
-    val discovered: Array[Boolean] = Array.fill(n.value)(false)
+    val visited: Array[Boolean] = Array.fill(n.value)(false)
 
-    def push(vertex: Vertex): Unit = stack.push(vertex)
+    def isVisited(vertex: Vertex): F[Boolean] =
+      Sync[F].delay(visited(vertex.ordinal))
 
-    def pop(): Vertex = stack.pop()
+    def visit(vertex: Vertex): F[Unit] =
+      Sync[F].delay(visited(vertex.ordinal) = true)
 
-    def isDiscovered(vertex: Vertex): Boolean =
+  final private class DfsState[F[_]: Sync](n: Size) extends TraverseState[F](n)
-      discovered(vertex.ordinal)
-
-    def discover(vertex: Vertex): Unit =
-      discovered(vertex.ordinal) = true
 
   end DfsState
 
+  final private class BfsState[F[_]: Async](
+    n: Size,
+    queue: Queue[F, Vertex]
+  ) extends TraverseState[F](n):
+
+    def enqueue(vertex: Vertex): F[Unit] = queue.offer(vertex)
+
+    def dequeue(): F[Option[Vertex]] = queue.tryTake
+
+  end BfsState
+
+  private object BfsState:
+
+    def initialize[F[_]: Async](n: Size): F[BfsState[F]] =
+      Queue.bounded[F, Vertex](n.value).map(new BfsState(n, _))
+
+  end BfsState
+
 end GraphTraversalFs2

modules/fs2/src/test/scala/gs/graph/v0/fs2/Fs2BfsTests.scala

@@ -0,0 +1,93 @@
+package gs.graph.v0.fs2
+
+import cats.effect.IO
+import cats.effect.unsafe.IORuntime
+import gs.graph.v0.Edge
+import gs.graph.v0.Size
+import gs.graph.v0.UndirectedGraph
+import gs.graph.v0.Vertex
+import gs.graph.v0.directed.Digraph
+import munit.*
+
+class Fs2BfsTests extends FunSuite:
+  given IORuntime = IORuntime.global
+
+  private def iotest(
+    name: String
+  )(
+    body: => IO[Unit]
+  )(
+    using
+    Location
+  ): Unit =
+    test(name)(body.unsafeRunSync())
+
+  iotest("(BFS) should return an empty stream for an empty graph") {
+    val s = GraphTraversalFs2.bfs(
+      UndirectedGraph.Empty,
+      _ => IO.raiseError(IllegalStateException("Should not reach this point."))
+    )
+
+    s.flatMap(_.compile.last.map(result => assertEquals(result, None)))
+  }
+
+  iotest(
+    "(BFS) should return a stream of one for a graph with a single vertex"
+  ) {
+    val s1 = GraphTraversalFs2.bfs(UndirectedGraph.Single, v => IO(v))
+    val s2 = GraphTraversalFs2.bfs(Digraph.Single, v => IO(v))
+
+    for
+      r1 <- s1.flatMap(_.compile.toList)
+      r2 <- s2.flatMap(_.compile.toList)
+    yield
+      assertEquals(r1, List(Vertex.Zero))
+      assertEquals(r2, List(Vertex.Zero))
+  }
+
+  iotest(
+    "(BFS) should visit a graph of three nodes"
+  ) {
+    val vs    = Array(Vertex(0), Vertex(1), Vertex(2))
+    val edges = List(
+      Edge(vs(0), vs(1)),
+      Edge(vs(0), vs(2))
+    )
+    val expected = vs.toList
+    val graph    = Digraph.fromEdges(Size(vs.length), edges)
+    val s        = GraphTraversalFs2.bfs(graph, v => IO(v))
+    s.flatMap(_.compile.toList).map(assertEquals(_, expected))
+  }
+
+  iotest(
+    "(BFS) should visit a graph of five nodes"
+  ) {
+    val vs    = Array(Vertex(0), Vertex(1), Vertex(2), Vertex(3), Vertex(4))
+    val edges = List(
+      Edge(vs(0), vs(1)),
+      Edge(vs(0), vs(2)),
+      Edge(vs(1), vs(2)),
+      Edge(vs(2), vs(3)),
+      Edge(vs(2), vs(4))
+    )
+    val expected = vs.toList
+    val graph    = Digraph.fromEdges(Size(vs.length), edges)
+    val s        = GraphTraversalFs2.bfs(graph, v => IO(v))
+    s.flatMap(_.compile.toList).map(assertEquals(_, expected))
+  }
+
+  iotest(
+    "(BFS) should visit a multi-root graph with disconnected components"
+  ) {
+    val vs    = (0 until 6).map(Vertex(_)).toArray
+    val edges = List(
+      Edge(vs(0), vs(2)),
+      Edge(vs(0), vs(3)),
+      Edge(vs(2), vs(1)),
+      Edge(vs(4), vs(5))
+    )
+    val expected = List(vs(0), vs(2), vs(3), vs(1), vs(4), vs(5))
+    val graph    = Digraph.fromEdges(Size(vs.length), edges)
+    val s        = GraphTraversalFs2.bfs(graph, v => IO(v))
+    s.flatMap(_.compile.toList).map(assertEquals(_, expected))
+  }

project/build.properties

@@ -1 +1 @@
-sbt.version=1.11.7
+sbt.version=1.12.8

project/plugins.sbt

@@ -28,6 +28,6 @@ externalResolvers := Seq(
   "Garrity Software Releases" at "https://maven.garrity.co/gs"
 )
 
-addSbtPlugin("org.scoverage" % "sbt-scoverage"        % "2.3.1")
+addSbtPlugin("org.scoverage" % "sbt-scoverage"        % "2.4.4")
-addSbtPlugin("gs"            % "sbt-garrity-software" % "0.6.0")
+addSbtPlugin("gs"            % "sbt-garrity-software" % "0.7.0")
 addSbtPlugin("gs"            % "sbt-gs-semver"        % "0.3.0")