Add detect cycle.

Author: trekhleb

README.md

@@ -68,7 +68,7 @@
   * [Breadth-First Search](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/graph/breadth-first-search) (BFS)
   * [Dijkstra Algorithm](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/graph/dijkstra) - finding shortest path to all graph vertices
   * [Bellman-Ford Algorithm](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/graph/bellman-ford) - finding shortest path to all graph vertices
-  * [Detect Cycle](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/graph/detect-cycle)
+  * [Detect Cycle](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/graph/detect-cycle) - for both: directed and undirected graphs
   * Topological Sorting
   * Eulerian path, Eulerian circuit
   * Strongly Connected Component algorithm

src/algorithms/graph/detect-cycle/__test__/detectDirectedCycle.test.js

@@ -0,0 +1,42 @@
+import GraphVertex from '../../../../data-structures/graph/GraphVertex';
+import GraphEdge from '../../../../data-structures/graph/GraphEdge';
+import Graph from '../../../../data-structures/graph/Graph';
+import detectDirectedCycle from '../detectDirectedCycle';
+
+describe('detectDirectedCycle', () => {
+  it('should detect directed cycle', () => {
+    const vertexA = new GraphVertex('A');
+    const vertexB = new GraphVertex('B');
+    const vertexC = new GraphVertex('C');
+    const vertexD = new GraphVertex('D');
+    const vertexE = new GraphVertex('E');
+    const vertexF = new GraphVertex('F');
+
+    const edgeAB = new GraphEdge(vertexA, vertexB);
+    const edgeBC = new GraphEdge(vertexB, vertexC);
+    const edgeAC = new GraphEdge(vertexA, vertexC);
+    const edgeDA = new GraphEdge(vertexD, vertexA);
+    const edgeDE = new GraphEdge(vertexD, vertexE);
+    const edgeEF = new GraphEdge(vertexE, vertexF);
+    const edgeFD = new GraphEdge(vertexF, vertexD);
+
+    const graph = new Graph(true);
+    graph
+      .addEdge(edgeAB)
+      .addEdge(edgeBC)
+      .addEdge(edgeAC)
+      .addEdge(edgeDA)
+      .addEdge(edgeDE)
+      .addEdge(edgeEF);
+
+    expect(detectDirectedCycle(graph)).toBeNull();
+
+    graph.addEdge(edgeFD);
+
+    expect(detectDirectedCycle(graph)).toEqual({
+      D: vertexF,
+      F: vertexE,
+      E: vertexD,
+    });
+  });
+});

src/algorithms/graph/detect-cycle/detectDirectedCycle.js

@@ -0,0 +1,93 @@
+import depthFirstSearch from '../depth-first-search/depthFirstSearch';
+
+/**
+ * Detect cycle in directed graph using Depth First Search.
+ *
+ * @param {Graph} graph
+ */
+export default function detectDirectedCycle(graph) {
+  let cycle = null;
+
+  // Will store parents (previous vertices) for all visited nodes.
+  // This will be needed in order to specify what path exactly is a cycle.
+  const dfsParentMap = {};
+
+  // White set (UNVISITED) contains all the vertices that haven't been visited at all.
+  const whiteSet = {};
+
+  // Gray set (VISITING) contains all the vertices that are being visited right now
+  // (in current path).
+  const graySet = {};
+
+  // Black set (VISITED) contains all the vertices that has been fully visited.
+  // Meaning that all children of the vertex has been visited.
+  const blackSet = {};
+
+  // If we encounter vertex in gray set it means that we've found a cycle.
+  // Because when vertex in gray set it means that its neighbors or its neighbors
+  // neighbors are still being explored.
+
+  // Init white set and add all vertices to it.
+  /** @param {GraphVertex} vertex */
+  graph.getAllVertices().forEach((vertex) => {
+    whiteSet[vertex.getKey()] = vertex;
+  });
+
+  // Describe BFS callbacks.
+  const callbacks = {
+    enterVertex: ({ currentVertex, previousVertex }) => {
+      if (graySet[currentVertex.getKey()]) {
+        // If current vertex already in grey set it means that cycle is detected.
+        // Let's detect cycle path.
+        cycle = {};
+
+        let currentCycleVertex = currentVertex;
+        let previousCycleVertex = previousVertex;
+
+        while (previousCycleVertex.getKey() !== currentVertex.getKey()) {
+          cycle[currentCycleVertex.getKey()] = previousCycleVertex;
+          currentCycleVertex = previousCycleVertex;
+          previousCycleVertex = dfsParentMap[previousCycleVertex.getKey()];
+        }
+
+        cycle[currentCycleVertex.getKey()] = previousCycleVertex;
+      } else {
+        // Otherwise let's add current vertex to gray set and remove it from white set.
+        graySet[currentVertex.getKey()] = currentVertex;
+        delete whiteSet[currentVertex.getKey()];
+
+        // Update DFS parents list.
+        dfsParentMap[currentVertex.getKey()] = previousVertex;
+      }
+    },
+    leaveVertex: ({ currentVertex }) => {
+      // If all node's children has been visited let's remove it from gray set
+      // and move it to the black set meaning that all its neighbors are visited.
+      blackSet[currentVertex.getKey()] = currentVertex;
+      delete graySet[currentVertex.getKey()];
+    },
+    allowTraversal: ({ nextVertex }) => {
+      // If cycle was detected we must forbid all further traversing since it will
+      // cause infinite traversal loop.
+      if (cycle) {
+        return false;
+      }
+
+      // Allow traversal only for the vertices that are not in black set
+      // since all black set vertices have been already visited.
+      return !blackSet[nextVertex.getKey()];
+    },
+  };
+
+  // Start exploring vertices.
+  while (Object.keys(whiteSet).length) {
+    // Pick fist vertex to start BFS from.
+    const firstWhiteKey = Object.keys(whiteSet)[0];
+    const startVertex = whiteSet[firstWhiteKey];
+
+    // Do Depth First Search.
+    depthFirstSearch(graph, startVertex, callbacks);
+  }
+
+  return cycle;
+}