bidirectional dijkstra and A*

Author: JakubSchwenkbeck

src/main/scala/Main.scala

@@ -0,0 +1,2 @@
+@main
+def main(): Unit = println("Hello World")

src/main/scala/algorithms/dynamic/FileDiff.scala

@@ -0,0 +1,83 @@
+package algorithms.dynamic
+
+import algorithms.dynamic.LCS
+
+/// Prints a git-style diff to transform file A into file B using LCS.
+/// Shows context lines, added (`+`), and removed (`-`) lines.
+///
+/// @param a First file (original)
+/// @param b Second file (modified)
+def printGitDiff(a: Seq[String], b: Seq[String]): Unit = {
+  val (_, _, lcsStr) = LCS(a.mkString("\n").toArray, b.mkString("\n").toArray)
+  val lcsSet = lcsStr.split("\n").toSet
+
+  println("--- Original")
+  println("+++ Modified")
+
+  var i = 0
+  var j = 0
+
+  while (i < a.length || j < b.length) {
+    if (i < a.length && j < b.length && a(i) == b(j)) {
+      // Context line (unchanged)
+      println(s"  ${a(i)}")
+      i += 1
+      j += 1
+    } else if (i < a.length && !lcsSet.contains(a(i))) {
+      // Removed line
+      println(s"- ${a(i)}")
+      i += 1
+    } else if (j < b.length && !lcsSet.contains(b(j))) {
+      // Added line
+      println(s"+ ${b(j)}")
+      j += 1
+    } else {
+      // Move to next match in LCS
+      i += 1
+      j += 1
+    }
+  }
+}
+
+@main def main(): Unit = {
+  // Longer C++ programs as strings
+  val cppProgram1 =
+    """#include <iostream>
+      |using namespace std;
+      |
+      |void greet() {
+      |    cout << "Hello, World!" << endl;
+      |}
+      |
+      |int main() {
+      |    greet();
+      |    return 0;
+      |}""".stripMargin
+
+  val cppProgram2 =
+    """#include <iostream>
+      |#include <vector>  // Added new header
+      |using namespace std;
+      |
+      |void greet() {
+      |    cout << "Hello, Universe!" << endl;  // Modified output
+      |}
+      |
+      |int main() {
+      |    vector<int> nums = {1, 2, 3};  // Added new feature
+      |    for (int num : nums) {
+      |        cout << num << " ";
+      |    }
+      |    cout << endl;
+      |    
+      |    greet();
+      |    return 0;
+      |}""".stripMargin
+
+  // Convert C++ programs into line sequences
+  val fileA = cppProgram1.split("\n").toSeq
+  val fileB = cppProgram2.split("\n").toSeq
+
+  // Compute and print the git diff-style output
+  printGitDiff(fileA, fileB)
+}

src/main/scala/algorithms/graph/Dijkstra.scala

@@ -36,3 +36,39 @@ def dijkstra[T](graph: Graph[T], start: T): Map[T, Int] = {
   distances.toMap
 
 }
+
+/// Dijkstra's Algorithm (Targeted Version) - Now returning a Map instead of Option
+/// Finds the shortest path from a starting node to a specific target node in a weighted graph
+/// Uses a priority queue-based approach
+/// Runs in O((V + E) log V) in the worst case
+
+def dijkstra[T](graph: Graph[T], start: T, target: T): Map[T, Int] = {
+  val distances = mutable.Map[T, Int]().withDefaultValue(Int.MaxValue)
+  val visited = mutable.Set[T]()
+  val priorityQueue = PriorityQueue[(T, Int)]()(Ordering.by(-_._2))
+
+  distances(start) = 0
+  priorityQueue.enqueue((start, 0))
+  while (!priorityQueue.isEmpty) {
+    val (currentNode: T, currentDistance: Int) = priorityQueue.dequeue().get // unsafe getter for now
+    if (currentNode == target) {
+      return distances.toMap // Return the distances map if target is reached
+    }
+
+    if (!visited.contains(currentNode)) {
+      visited.add(currentNode)
+
+      for ((neighbor, weight) <- graph.getNeighbors(currentNode)) {
+        if (!visited.contains(neighbor)) {
+          val newDistance = currentDistance + weight
+          if (newDistance < distances(neighbor)) {
+            distances(neighbor) = newDistance.toInt
+            priorityQueue.enqueue((neighbor, newDistance.toInt))
+          }
+        }
+      }
+    }
+  }
+
+  distances.toMap // Return distances even if the target is unreachable
+}

src/main/scala/algorithms/graph/aStar.scala

@@ -0,0 +1,58 @@
+package algorithms.graph
+
+import datastructures.graph.Graph
+import datastructures.basic.PriorityQueue
+import scala.collection.mutable
+
+/// A* Algorithm
+/// Finds the shortest path from a starting node to a target node in a weighted graph.
+/// Uses a heuristic function to guide the search towards the target node more efficiently.
+/// Is proven to be the best algorithm
+/// https://github.com/bb4/bb4-A-star/blob/master/scala-source/com/barrybecker4/search/AStarSearch.scala
+/// Runs in O((V + E) log V) in the worst case, depending on the quality of the heuristic.
+
+def aStar[T](graph: Graph[T], start: T, target: T, heuristic: T => Int): Option[Int] = {
+  // Check if start and target are the same, return 0 if true
+  if (start == target) return Some(0)
+
+  // Map to store the shortest known distance from the start node to each node
+  val gScores = mutable.Map[T, Int]().withDefaultValue(Int.MaxValue)
+  gScores(start) = 0
+
+  // Map to store the estimated distance from each node to the target
+  val fScores = mutable.Map[T, Int]().withDefaultValue(Int.MaxValue)
+  fScores(start) = heuristic(start)
+
+  // Set to keep track of visited nodes
+  val visited = mutable.Set[T]()
+
+  // Priority queue (min-heap) to select the node with the lowest f-score
+  val priorityQueue = PriorityQueue[(T, Int)]()(Ordering.by(-_._2))
+  priorityQueue.enqueue((start, fScores(start)))
+
+  // Process the queue until it is empty or the target is reached
+  while (!priorityQueue.isEmpty) {
+    val (currentNode, currentFScore) = priorityQueue.dequeue().get
+
+    // If we reach the target, return the cost to get here
+    if (currentNode == target) return Some(gScores(currentNode))
+
+    // If node has been visited, skip it
+    if (!visited.contains(currentNode)) {
+      visited.add(currentNode)
+
+      // For each neighbor of the current node, calculate the potential new g-score and f-score
+      for ((neighbor, weight) <- graph.getNeighbors(currentNode)) {
+        val tentativeGScore: Int = gScores(currentNode) + weight.toInt
+        if (tentativeGScore < gScores(neighbor)) {
+          gScores(neighbor) = tentativeGScore
+          fScores(neighbor) = tentativeGScore + heuristic(neighbor)
+          priorityQueue.enqueue((neighbor, fScores(neighbor)))
+        }
+      }
+    }
+  }
+
+  // Return None if the target is unreachable
+  None
+}

src/main/scala/algorithms/graph/biDirectionalDijkstra.scala

@@ -0,0 +1,70 @@
+package algorithms.graph
+
+import datastructures.graph.Graph
+import datastructures.basic.PriorityQueue
+import scala.collection.mutable
+
+/// Bidirectional Dijkstra's Algorithm
+/// Finds the shortest path between two nodes by running Dijkstra's algorithm from both the source and target simultaneously
+/// This approach can be faster than standard Dijkstra when the target is known
+/// Runs in O((V + E) log V) in the worst case, but may terminate earlier
+
+def bidirectionalDijkstra[T](graph: Graph[T], start: T, target: T): Map[T, Int] = {
+  if (start == target) return Map(start -> 0)
+
+  val forwardDistances = mutable.Map[T, Int]().withDefaultValue(Int.MaxValue)
+  val backwardDistances = mutable.Map[T, Int]().withDefaultValue(Int.MaxValue)
+  val forwardVisited = mutable.Set[T]()
+  val backwardVisited = mutable.Set[T]()
+  val forwardQueue = PriorityQueue[(T, Int)]()(Ordering.by(-_._2))
+  val backwardQueue = PriorityQueue[(T, Int)]()(Ordering.by(-_._2))
+
+  forwardDistances(start) = 0
+  backwardDistances(target) = 0
+  forwardQueue.enqueue((start, 0))
+  backwardQueue.enqueue((target, 0))
+
+  def processQueue(
+    queue: PriorityQueue[(T, Int)],
+    distances: mutable.Map[T, Int],
+    visited: mutable.Set[T],
+    otherDistances: mutable.Map[T, Int]
+  ): Option[Int] = {
+    queue.dequeue() match {
+      case Some((currentNode: T, currentDistance: Int)) =>
+        if (otherDistances.contains(currentNode)) return Some(currentDistance + otherDistances(currentNode))
+
+        if (!visited.contains(currentNode)) {
+          visited.add(currentNode)
+
+          for ((neighbor, weight) <- graph.getNeighbors(currentNode)) {
+            if (!visited.contains(neighbor)) {
+              val newDistance = currentDistance + weight
+              if (newDistance < distances(neighbor)) {
+                distances(neighbor) = newDistance.toInt
+                queue.enqueue((neighbor, newDistance.toInt))
+              }
+            }
+          }
+        }
+      case None =>
+    }
+    None
+  }
+
+  // While both queues are non-empty, continue processing
+  while (!forwardQueue.isEmpty && !backwardQueue.isEmpty) {
+    processQueue(forwardQueue, forwardDistances, forwardVisited, backwardDistances) match {
+      case Some(_) => // Found the shortest path, continue
+      case None    =>
+    }
+    processQueue(backwardQueue, backwardDistances, backwardVisited, forwardDistances) match {
+      case Some(_) => // Found the shortest path, continue
+      case None    =>
+    }
+  }
+
+  // Return the merged distances from both directions
+  // The final result will be the combination of forward and backward distances
+  forwardDistances.toMap ++ backwardDistances.toMap
+}

src/test/scala/algorithms/graph/AStarTest.scala

@@ -0,0 +1,70 @@
+package algorithms.graph
+
+import munit.FunSuite
+import datastructures.graph.Graph
+
+class AStarTest extends FunSuite {
+
+  // Example heuristic function (Manhattan Distance for grid-based problems)
+  def heuristic(node: String): Int = node match {
+    case "A" => 6
+    case "B" => 5
+    case "C" => 2
+    case "D" => 0 // Target node
+    case _   => Int.MaxValue
+  }
+
+  test("A* should find the shortest path in a small graph") {
+    val graph = new Graph[String](isDirected = true)
+    graph.addEdge("A", "B", 1)
+    graph.addEdge("A", "C", 4)
+    graph.addEdge("B", "C", 2)
+    graph.addEdge("B", "D", 5)
+    graph.addEdge("C", "D", 1)
+
+    val result = aStar(graph, "A", "D", heuristic)
+
+    assertEquals(result, Some(4)) // The shortest path from A to D is via B and C: A -> B -> C -> D (1 + 2 + 1)
+  }
+
+  test("A* should handle the case where the start is the same as the target") {
+    val graph = new Graph[String](isDirected = true)
+    graph.addEdge("A", "B", 1)
+
+    val result = aStar(graph, "A", "A", heuristic)
+
+    assertEquals(result, Some(0)) // If start and target are the same, the cost is 0
+  }
+
+  test("A* should return None if the target is unreachable") {
+    val graph = new Graph[String](isDirected = true)
+    graph.addEdge("A", "B", 1)
+    graph.addEdge("B", "C", 1)
+
+    val result = aStar(graph, "A", "D", heuristic)
+
+    assertEquals(result, None) // "D" is unreachable from "A"
+  }
+
+  test("A* should work with different heuristics") {
+    // Using a different heuristic function for this case
+    def alternativeHeuristic(node: String): Int = node match {
+      case "A" => 7
+      case "B" => 4
+      case "C" => 3
+      case "D" => 0
+      case _   => Int.MaxValue
+    }
+
+    val graph = new Graph[String](isDirected = true)
+    graph.addEdge("A", "B", 3)
+    graph.addEdge("A", "C")
+    graph.addEdge("B", "C", 7)
+    graph.addEdge("B", "D", 5)
+    graph.addEdge("C", "D", 2)
+
+    val result = aStar(graph, "A", "D", alternativeHeuristic)
+
+    assertEquals(result, Some(3)) // The shortest path from A to D is via C: A -> C -> D (1 + 2)
+  }
+}