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) - for both directed and undirected graphs
+  * [Detect Cycle](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/graph/detect-cycle) - for both directed and undirected graphs (DFS and Disjoint Set based versions)
   * Topological Sorting
   * Eulerian path, Eulerian circuit
   * Strongly Connected Component algorithm

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

@@ -27,10 +27,15 @@ describe('detectUndirectedCycle', () => {
       .addEdge(edgeBC)
       .addEdge(edgeCD);
 
-    expect(detectUndirectedCycle(graph)).toBeFalsy();
+    expect(detectUndirectedCycle(graph)).toBeNull();
 
     graph.addEdge(edgeDE);
 
-    expect(detectUndirectedCycle(graph)).toBeTruthy();
+    expect(detectUndirectedCycle(graph)).toEqual({
+      B: vertexC,
+      C: vertexD,
+      D: vertexE,
+      E: vertexB,
+    });
   });
 });

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

@@ -0,0 +1,36 @@
+import GraphVertex from '../../../../data-structures/graph/GraphVertex';
+import GraphEdge from '../../../../data-structures/graph/GraphEdge';
+import Graph from '../../../../data-structures/graph/Graph';
+import detectUndirectedCycleUsingDisjointSet from '../detectUndirectedCycleUsingDisjointSet';
+
+describe('detectUndirectedCycleUsingDisjointSet', () => {
+  it('should detect undirected 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 edgeAF = new GraphEdge(vertexA, vertexF);
+    const edgeAB = new GraphEdge(vertexA, vertexB);
+    const edgeBE = new GraphEdge(vertexB, vertexE);
+    const edgeBC = new GraphEdge(vertexB, vertexC);
+    const edgeCD = new GraphEdge(vertexC, vertexD);
+    const edgeDE = new GraphEdge(vertexD, vertexE);
+
+    const graph = new Graph();
+    graph
+      .addEdge(edgeAF)
+      .addEdge(edgeAB)
+      .addEdge(edgeBE)
+      .addEdge(edgeBC)
+      .addEdge(edgeCD);
+
+    expect(detectUndirectedCycleUsingDisjointSet(graph)).toBeFalsy();
+
+    graph.addEdge(edgeDE);
+
+    expect(detectUndirectedCycleUsingDisjointSet(graph)).toBeTruthy();
+  });
+});

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

@@ -1,32 +1,59 @@
-import DisjointSet from '../../../data-structures/disjoint-set/DisjointSet';
+import depthFirstSearch from '../depth-first-search/depthFirstSearch';
 
 /**
- * Detect cycle in undirected graph using disjoint sets.
+ * Detect cycle in undirected graph using Depth First Search.
  *
  * @param {Graph} graph
  */
-
 export default function detectUndirectedCycle(graph) {
-  // Create initial singleton disjoint sets for each graph vertex.
-  /** @param {GraphVertex} graphVertex */
-  const keyExtractor = graphVertex => graphVertex.getKey();
-  const disjointSet = new DisjointSet(keyExtractor);
-  graph.getAllVertices().forEach(graphVertex => disjointSet.makeSet(graphVertex));
-
-  // Go trough all graph edges one by one and check if edge vertices are from the
-  // different sets. In this case joint those sets together. Do this until you find
-  // an edge where to edge vertices are already in one set. This means that current
-  // edge will create a cycle.
-  let cycleFound = false;
-  /** @param {GraphEdge} graphEdge */
-  graph.getAllEdges().forEach((graphEdge) => {
-    if (disjointSet.inSameSet(graphEdge.startVertex, graphEdge.endVertex)) {
-      // Cycle found.
-      cycleFound = true;
-    } else {
-      disjointSet.union(graphEdge.startVertex, graphEdge.endVertex);
-    }
-  });
-
-  return cycleFound;
+  let cycle = null;
+
+  // List of vertices that we have visited.
+  const visitedVertices = {};
+
+  // List of parents vertices for every visited vertex.
+  const parents = {};
+
+  // Callbacks for DFS traversing.
+  const callbacks = {
+    allowTraversal: ({ currentVertex, nextVertex }) => {
+      // Don't allow further traversal in case if cycle has been detected.
+      if (cycle) {
+        return false;
+      }
+
+      // Don't allow traversal from child back to its parent.
+      const currentVertexParent = parents[currentVertex.getKey()];
+      const currentVertexParentKey = currentVertexParent ? currentVertexParent.getKey() : null;
+
+      return currentVertexParentKey !== nextVertex.getKey();
+    },
+    enterVertex: ({ currentVertex, previousVertex }) => {
+      if (visitedVertices[currentVertex.getKey()]) {
+        // Compile cycle path based on parents of previous vertices.
+        cycle = {};
+
+        let currentCycleVertex = currentVertex;
+        let previousCycleVertex = previousVertex;
+
+        while (previousCycleVertex.getKey() !== currentVertex.getKey()) {
+          cycle[currentCycleVertex.getKey()] = previousCycleVertex;
+          currentCycleVertex = previousCycleVertex;
+          previousCycleVertex = parents[previousCycleVertex.getKey()];
+        }
+
+        cycle[currentCycleVertex.getKey()] = previousCycleVertex;
+      } else {
+        // Add next vertex to visited set.
+        visitedVertices[currentVertex.getKey()] = currentVertex;
+        parents[currentVertex.getKey()] = previousVertex;
+      }
+    },
+  };
+
+  // Start DFS traversing.
+  const startVertex = graph.getAllVertices()[0];
+  depthFirstSearch(graph, startVertex, callbacks);
+
+  return cycle;
 }

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

@@ -0,0 +1,31 @@
+import DisjointSet from '../../../data-structures/disjoint-set/DisjointSet';
+
+/**
+ * Detect cycle in undirected graph using disjoint sets.
+ *
+ * @param {Graph} graph
+ */
+export default function detectUndirectedCycleUsingDisjointSet(graph) {
+  // Create initial singleton disjoint sets for each graph vertex.
+  /** @param {GraphVertex} graphVertex */
+  const keyExtractor = graphVertex => graphVertex.getKey();
+  const disjointSet = new DisjointSet(keyExtractor);
+  graph.getAllVertices().forEach(graphVertex => disjointSet.makeSet(graphVertex));
+
+  // Go trough all graph edges one by one and check if edge vertices are from the
+  // different sets. In this case joint those sets together. Do this until you find
+  // an edge where to edge vertices are already in one set. This means that current
+  // edge will create a cycle.
+  let cycleFound = false;
+  /** @param {GraphEdge} graphEdge */
+  graph.getAllEdges().forEach((graphEdge) => {
+    if (disjointSet.inSameSet(graphEdge.startVertex, graphEdge.endVertex)) {
+      // Cycle found.
+      cycleFound = true;
+    } else {
+      disjointSet.union(graphEdge.startVertex, graphEdge.endVertex);
+    }
+  });
+
+  return cycleFound;
+}