Merge pull request #9 from harry0000/scc

Add SccGraph

Author: harry0000

src/main/scala/io/github/acl4s/Dsu.scala

@@ -56,25 +56,23 @@ case class Dsu(n: Int) {
     -parentOrSize(leader(a))
   }
 
-  def groups(): Seq[Seq[Int]] = {
+  def groups(): collection.Seq[collection.Seq[Int]] = {
     val leader_buf = new Array[Int](n)
     val group_size = new Array[Int](n)
     (0 until n).foreach(i => {
       leader_buf(i) = leader(i)
       group_size(leader_buf(i)) += 1
     })
 
-    val result = new Array[mutable.ArrayBuffer[Int]](n)
+    val result = new mutable.ArrayBuffer[mutable.Buffer[Int]](n)
     (0 until n).foreach(i => {
-      result(i) = new mutable.ArrayBuffer(group_size(i))
+      result += new mutable.ArrayBuffer(group_size(i))
     })
     (0 until n).foreach(i => {
       result(leader_buf(i)) += i
     })
 
-    result.collect {
-      case buf if buf.nonEmpty => buf.toSeq
-    }.toSeq
+    result.filter(_.nonEmpty)
   }
 
 }

src/main/scala/io/github/acl4s/SccGraph.scala

@@ -0,0 +1,22 @@
+package io.github.acl4s
+
+case class SccGraph(private val internal: io.github.acl4s.internal.SccGraph) {
+
+  def addEdge(from: Int, to: Int): Unit = {
+    val n = internal.numVertices
+    assert(0 <= from && from < n)
+    assert(0 <= to && to < n)
+    internal.addEdge(from, to)
+  }
+
+  def scc(): collection.Seq[collection.Seq[Int]] = {
+    internal.scc()
+  }
+
+}
+
+object SccGraph {
+  def apply(n: Int): SccGraph = {
+    new SccGraph(internal.SccGraph(n))
+  }
+}

src/main/scala/io/github/acl4s/internal/SccGraph.scala

@@ -0,0 +1,105 @@
+package io.github.acl4s.internal
+
+import scala.collection.mutable
+import scala.reflect.ClassTag
+
+private[internal] case class Edge(to: Int)
+
+private[internal] case class Csr[E] private (start: Array[Int], eList: Array[E])
+private[internal] object Csr {
+  def apply[E: ClassTag](n: Int, edges: collection.Seq[(Int, E)]): Csr[E] = {
+    val csr = Csr(new Array[Int](n + 1), new Array[E](edges.size))
+    for ((from, _) <- edges) {
+      csr.start(from + 1) += 1
+    }
+    (1 to n).foreach(i => {
+      csr.start(i) += csr.start(i - 1)
+    })
+    val counter = csr.start.clone()
+    for ((from, edge) <- edges) {
+      csr.eList(counter(from)) = edge
+      counter(from) += 1
+    }
+    csr
+  }
+}
+
+/**
+ * Reference:
+ * R. Tarjan,
+ * Depth-First Search and Linear Graph Algorithms
+ */
+case class SccGraph(private val n: Int) {
+  private val edges: mutable.Buffer[(Int, Edge)] = mutable.ListBuffer.empty
+
+  def numVertices: Int = n
+
+  def addEdge(from: Int, to: Int): Unit = {
+    edges += ((from, Edge(to)))
+  }
+
+  /**
+   * @return pair of (# of scc, scc id)
+   */
+  def sccIds(): (Int, Array[Int]) = {
+    val g = Csr(n, edges)
+    var now_ord = 0
+    var group_num = 0
+    val visited = new mutable.Stack[Int](n)
+    val ord = Array.fill(n)(-1)
+    val low = new Array[Int](n)
+    val ids = new Array[Int](n)
+
+    def dfs(v: Int): Unit = {
+      low(v) = now_ord
+      ord(v) = now_ord
+      now_ord += 1
+      visited.push(v)
+      (g.start(v) until g.start(v + 1)).foreach(i => {
+        val to = g.eList(i).to
+        if (ord(to) == -1) {
+          dfs(to)
+          low(v) = low(v).min(low(to))
+        } else {
+          low(v) = low(v).min(ord(to))
+        }
+      })
+      if (low(v) == ord(v)) {
+        while {
+          // do
+          val u = visited.pop()
+          ord(u) = n
+          ids(u) = group_num
+
+          // while
+          u != v
+        } do {}
+        group_num += 1
+      }
+    }
+
+    (0 until n).foreach(i => {
+      if (ord(i) == -1) { dfs(i) }
+    })
+    (0 until n).foreach(i => {
+      ids(i) = group_num - 1 - ids(i)
+    })
+
+    (group_num, ids)
+  }
+
+  def scc(): collection.Seq[collection.Seq[Int]] = {
+    val (group_nums, ids) = sccIds()
+    val counts = new Array[Int](group_nums)
+    ids.foreach(x => { counts(x) += 1 })
+    val groups = new mutable.ArrayBuffer[mutable.Buffer[Int]](n)
+    (0 until group_nums).foreach(i => {
+      groups += new mutable.ArrayBuffer[Int](counts(i))
+    })
+    (0 until n).foreach(i => {
+      groups(ids(i)) += i
+    })
+
+    groups
+  }
+}

src/test/scala/io/github/acl4s/SccGraphSuite.scala

@@ -0,0 +1,45 @@
+package io.github.acl4s
+
+class SccGraphSuite extends munit.FunSuite {
+
+  /**
+   * @see https://atcoder.jp/contests/practice2/tasks/practice2_g
+   */
+  test("AtCoder Library Practice Contest G - SCC") {
+    val graph = SccGraph(6)
+    graph.addEdge(1, 4)
+    graph.addEdge(5, 2)
+    graph.addEdge(3, 0)
+    graph.addEdge(5, 5)
+    graph.addEdge(4, 1)
+    graph.addEdge(0, 3)
+    graph.addEdge(4, 2)
+
+    val scc = graph.scc()
+    assertEquals(scc.size, 4)
+    assertEquals(scc.map(_.toSet).toSet, Set(Set(5), Set(1, 4), Set(2), Set(0, 3)))
+  }
+
+  test("empty") {
+    assertEquals(SccGraph(0).scc(), Seq())
+  }
+
+  test("simple") {
+    val graph = SccGraph(2)
+    graph.addEdge(0, 1)
+    graph.addEdge(1, 0)
+
+    val scc = graph.scc()
+    assertEquals(scc.size, 1)
+  }
+
+  test("self loop") {
+    val graph = SccGraph(2)
+    graph.addEdge(0, 0)
+    graph.addEdge(0, 0)
+    graph.addEdge(1, 1)
+
+    val scc = graph.scc()
+    assertEquals(scc.size, 2)
+  }
+}