Add Eulerian Path.

trekhleb · trekhleb · commit e5a0b4ba0d43 · 2018-05-12T07:54:14.000+03:00
diff --git a/README.md b/README.md
@@ -74,7 +74,7 @@
   * [Topological Sorting](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/graph/topological-sorting) - DFS method
   * [Articulation Points](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/graph/articulation-points) - Tarjan's algorithm (DFS based)
   * [Bridges](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/graph/bridges) - DFS based algorithm
-  * [Eulerian Path and Eulerian Circuit](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/graph/eulerian-path)
+  * [Eulerian Path and Eulerian Circuit](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/graph/eulerian-path) - Fleury's algorithm
   * Strongly Connected Component algorithm
   * Shortest Path Faster Algorithm (SPFA)
 * **Uncategorized**  
diff --git a/src/algorithms/graph/articulation-points/__test__/articulationPoints.test.js b/src/algorithms/graph/articulation-points/__test__/articulationPoints.test.js
@@ -21,7 +21,7 @@ describe('articulationPoints', () => {
       .addEdge(edgeBC)
       .addEdge(edgeCD);
 
-    const articulationPointsSet = articulationPoints(graph);
+    const articulationPointsSet = Object.values(articulationPoints(graph));
 
     expect(articulationPointsSet.length).toBe(2);
     expect(articulationPointsSet[0].getKey()).toBe(vertexC.getKey());
@@ -47,7 +47,7 @@ describe('articulationPoints', () => {
       .addEdge(edgeBC)
       .addEdge(edgeCD);
 
-    const articulationPointsSet = articulationPoints(graph);
+    const articulationPointsSet = Object.values(articulationPoints(graph));
 
     expect(articulationPointsSet.length).toBe(1);
     expect(articulationPointsSet[0].getKey()).toBe(vertexC.getKey());
@@ -75,7 +75,7 @@ describe('articulationPoints', () => {
       .addEdge(edgeBC)
       .addEdge(edgeCD);
 
-    const articulationPointsSet = articulationPoints(graph);
+    const articulationPointsSet = Object.values(articulationPoints(graph));
 
     expect(articulationPointsSet.length).toBe(1);
     expect(articulationPointsSet[0].getKey()).toBe(vertexC.getKey());
@@ -114,7 +114,7 @@ describe('articulationPoints', () => {
       .addEdge(edgeGF)
       .addEdge(edgeFH);
 
-    const articulationPointsSet = articulationPoints(graph);
+    const articulationPointsSet = Object.values(articulationPoints(graph));
 
     expect(articulationPointsSet.length).toBe(4);
     expect(articulationPointsSet[0].getKey()).toBe(vertexF.getKey());
@@ -156,7 +156,7 @@ describe('articulationPoints', () => {
       .addEdge(edgeGF)
       .addEdge(edgeFH);
 
-    const articulationPointsSet = articulationPoints(graph);
+    const articulationPointsSet = Object.values(articulationPoints(graph));
 
     expect(articulationPointsSet.length).toBe(4);
     expect(articulationPointsSet[0].getKey()).toBe(vertexF.getKey());
@@ -187,7 +187,7 @@ describe('articulationPoints', () => {
       .addEdge(edgeCD)
       .addEdge(edgeDE);
 
-    const articulationPointsSet = articulationPoints(graph);
+    const articulationPointsSet = Object.values(articulationPoints(graph));
 
     expect(articulationPointsSet.length).toBe(2);
     expect(articulationPointsSet[0].getKey()).toBe(vertexD.getKey());
@@ -224,7 +224,7 @@ describe('articulationPoints', () => {
       .addEdge(edgeEG)
       .addEdge(edgeFG);
 
-    const articulationPointsSet = articulationPoints(graph);
+    const articulationPointsSet = Object.values(articulationPoints(graph));
 
     expect(articulationPointsSet.length).toBe(1);
     expect(articulationPointsSet[0].getKey()).toBe(vertexC.getKey());
diff --git a/src/algorithms/graph/articulation-points/articulationPoints.js b/src/algorithms/graph/articulation-points/articulationPoints.js
@@ -17,7 +17,7 @@ class VisitMetadata {
  * Tarjan's algorithm for finding articulation points in graph.
  *
  * @param {Graph} graph
- * @return {GraphVertex[]}
+ * @return {Object}
  */
 export default function articulationPoints(graph) {
   // Set of vertices we've already visited during DFS.
@@ -109,5 +109,5 @@ export default function articulationPoints(graph) {
   // Do Depth First Search traversal over submitted graph.
   depthFirstSearch(graph, startVertex, dfsCallbacks);
 
-  return Object.values(articulationPointsSet);
+  return articulationPointsSet;
 }
diff --git a/src/algorithms/graph/bridges/__test__/graphBridges.test.js b/src/algorithms/graph/bridges/__test__/graphBridges.test.js
@@ -21,7 +21,7 @@ describe('graphBridges', () => {
       .addEdge(edgeBC)
       .addEdge(edgeCD);
 
-    const bridges = graphBridges(graph);
+    const bridges = Object.values(graphBridges(graph));
 
     expect(bridges.length).toBe(3);
     expect(bridges[0].getKey()).toBe(edgeCD.getKey());
@@ -48,7 +48,7 @@ describe('graphBridges', () => {
       .addEdge(edgeBC)
       .addEdge(edgeCD);
 
-    const bridges = graphBridges(graph);
+    const bridges = Object.values(graphBridges(graph));
 
     expect(bridges.length).toBe(1);
     expect(bridges[0].getKey()).toBe(edgeCD.getKey());
@@ -87,7 +87,7 @@ describe('graphBridges', () => {
       .addEdge(edgeGF)
       .addEdge(edgeFH);
 
-    const bridges = graphBridges(graph);
+    const bridges = Object.values(graphBridges(graph));
 
     expect(bridges.length).toBe(3);
     expect(bridges[0].getKey()).toBe(edgeFH.getKey());
@@ -128,7 +128,7 @@ describe('graphBridges', () => {
       .addEdge(edgeGF)
       .addEdge(edgeFH);
 
-    const bridges = graphBridges(graph);
+    const bridges = Object.values(graphBridges(graph));
 
     expect(bridges.length).toBe(3);
     expect(bridges[0].getKey()).toBe(edgeFH.getKey());
@@ -158,7 +158,7 @@ describe('graphBridges', () => {
       .addEdge(edgeCD)
       .addEdge(edgeDE);
 
-    const bridges = graphBridges(graph);
+    const bridges = Object.values(graphBridges(graph));
 
     expect(bridges.length).toBe(2);
     expect(bridges[0].getKey()).toBe(edgeDE.getKey());
@@ -195,7 +195,7 @@ describe('graphBridges', () => {
       .addEdge(edgeEG)
       .addEdge(edgeFG);
 
-    const bridges = graphBridges(graph);
+    const bridges = Object.values(graphBridges(graph));
 
     expect(bridges.length).toBe(1);
     expect(bridges[0].getKey()).toBe(edgeCD.getKey());
diff --git a/src/algorithms/graph/bridges/graphBridges.js b/src/algorithms/graph/bridges/graphBridges.js
@@ -12,7 +12,7 @@ class VisitMetadata {
 
 /**
  * @param {Graph} graph
- * @return {GraphVertex[]}
+ * @return {Object}
  */
 export default function graphBridges(graph) {
   // Set of vertices we've already visited during DFS.
@@ -91,5 +91,5 @@ export default function graphBridges(graph) {
   // Do Depth First Search traversal over submitted graph.
   depthFirstSearch(graph, startVertex, dfsCallbacks);
 
-  return Object.values(bridges);
+  return bridges;
 }
diff --git a/src/algorithms/graph/eulerian-path/__test__/eulerianPath.test.js b/src/algorithms/graph/eulerian-path/__test__/eulerianPath.test.js
@@ -0,0 +1,139 @@
+import GraphVertex from '../../../../data-structures/graph/GraphVertex';
+import GraphEdge from '../../../../data-structures/graph/GraphEdge';
+import Graph from '../../../../data-structures/graph/Graph';
+import eulerianPath from '../eulerianPath';
+
+describe('eulerianPath', () => {
+  it('should throw an error when graph is not Eulerian', () => {
+    function findEulerianPathInNotEulerianGraph() {
+      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 edgeAB = new GraphEdge(vertexA, vertexB);
+      const edgeAC = new GraphEdge(vertexA, vertexC);
+      const edgeBC = new GraphEdge(vertexB, vertexC);
+      const edgeBD = new GraphEdge(vertexB, vertexD);
+      const edgeCE = new GraphEdge(vertexC, vertexE);
+
+      const graph = new Graph();
+
+      graph
+        .addEdge(edgeAB)
+        .addEdge(edgeAC)
+        .addEdge(edgeBC)
+        .addEdge(edgeBD)
+        .addEdge(edgeCE);
+
+      eulerianPath(graph);
+    }
+
+    expect(findEulerianPathInNotEulerianGraph).toThrowError();
+  });
+
+  it('should find Eulerian Circuit in graph', () => {
+    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 vertexG = new GraphVertex('G');
+
+    const edgeAB = new GraphEdge(vertexA, vertexB);
+    const edgeAE = new GraphEdge(vertexA, vertexE);
+    const edgeAF = new GraphEdge(vertexA, vertexF);
+    const edgeAG = new GraphEdge(vertexA, vertexG);
+    const edgeGF = new GraphEdge(vertexG, vertexF);
+    const edgeBE = new GraphEdge(vertexB, vertexE);
+    const edgeEB = new GraphEdge(vertexE, vertexB);
+    const edgeBC = new GraphEdge(vertexB, vertexC);
+    const edgeED = new GraphEdge(vertexE, vertexD);
+    const edgeCD = new GraphEdge(vertexC, vertexD);
+
+    const graph = new Graph();
+
+    graph
+      .addEdge(edgeAB)
+      .addEdge(edgeAE)
+      .addEdge(edgeAF)
+      .addEdge(edgeAG)
+      .addEdge(edgeGF)
+      .addEdge(edgeBE)
+      .addEdge(edgeEB)
+      .addEdge(edgeBC)
+      .addEdge(edgeED)
+      .addEdge(edgeCD);
+
+    const graphEdgesCount = graph.getAllEdges().length;
+
+    const eulerianPathSet = eulerianPath(graph);
+
+    expect(eulerianPathSet.length).toBe(graphEdgesCount + 1);
+
+    expect(eulerianPathSet[0].getKey()).toBe(vertexA.getKey());
+    expect(eulerianPathSet[1].getKey()).toBe(vertexB.getKey());
+    expect(eulerianPathSet[2].getKey()).toBe(vertexE.getKey());
+    expect(eulerianPathSet[3].getKey()).toBe(vertexB.getKey());
+    expect(eulerianPathSet[4].getKey()).toBe(vertexC.getKey());
+    expect(eulerianPathSet[5].getKey()).toBe(vertexD.getKey());
+    expect(eulerianPathSet[6].getKey()).toBe(vertexE.getKey());
+    expect(eulerianPathSet[7].getKey()).toBe(vertexA.getKey());
+    expect(eulerianPathSet[8].getKey()).toBe(vertexF.getKey());
+    expect(eulerianPathSet[9].getKey()).toBe(vertexG.getKey());
+    expect(eulerianPathSet[10].getKey()).toBe(vertexA.getKey());
+  });
+
+  it('should find Eulerian Path in graph', () => {
+    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 vertexG = new GraphVertex('G');
+    const vertexH = new GraphVertex('H');
+
+    const edgeAB = new GraphEdge(vertexA, vertexB);
+    const edgeAC = new GraphEdge(vertexA, vertexC);
+    const edgeBD = new GraphEdge(vertexB, vertexD);
+    const edgeDC = new GraphEdge(vertexD, vertexC);
+    const edgeCE = new GraphEdge(vertexC, vertexE);
+    const edgeEF = new GraphEdge(vertexE, vertexF);
+    const edgeFH = new GraphEdge(vertexF, vertexH);
+    const edgeFG = new GraphEdge(vertexF, vertexG);
+    const edgeHG = new GraphEdge(vertexH, vertexG);
+
+    const graph = new Graph();
+
+    graph
+      .addEdge(edgeAB)
+      .addEdge(edgeAC)
+      .addEdge(edgeBD)
+      .addEdge(edgeDC)
+      .addEdge(edgeCE)
+      .addEdge(edgeEF)
+      .addEdge(edgeFH)
+      .addEdge(edgeFG)
+      .addEdge(edgeHG);
+
+    const graphEdgesCount = graph.getAllEdges().length;
+
+    const eulerianPathSet = eulerianPath(graph);
+
+    expect(eulerianPathSet.length).toBe(graphEdgesCount + 1);
+
+    expect(eulerianPathSet[0].getKey()).toBe(vertexC.getKey());
+    expect(eulerianPathSet[1].getKey()).toBe(vertexA.getKey());
+    expect(eulerianPathSet[2].getKey()).toBe(vertexB.getKey());
+    expect(eulerianPathSet[3].getKey()).toBe(vertexD.getKey());
+    expect(eulerianPathSet[4].getKey()).toBe(vertexC.getKey());
+    expect(eulerianPathSet[5].getKey()).toBe(vertexE.getKey());
+    expect(eulerianPathSet[6].getKey()).toBe(vertexF.getKey());
+    expect(eulerianPathSet[7].getKey()).toBe(vertexH.getKey());
+    expect(eulerianPathSet[8].getKey()).toBe(vertexG.getKey());
+    expect(eulerianPathSet[9].getKey()).toBe(vertexF.getKey());
+  });
+});
diff --git a/src/algorithms/graph/eulerian-path/eulerianPath.js b/src/algorithms/graph/eulerian-path/eulerianPath.js
@@ -0,0 +1,101 @@
+import graphBridges from '../bridges/graphBridges';
+
+/**
+ * Fleury's algorithm of finding Eulerian Path (visit all graph edges exactly once).
+ *
+ * @param {Graph} graph
+ * @return {GraphVertex[]}
+ */
+export default function eulerianPath(graph) {
+  const eulerianPathVertices = [];
+
+  // Set that contains all vertices with even rank (number of neighbors).
+  const evenRankVertices = {};
+
+  // Set that contains all vertices with odd rank (number of neighbors).
+  const oddRankVertices = {};
+
+  // Set of all not visited edges.
+  const notVisitedEdges = {};
+  graph.getAllEdges().forEach((vertex) => {
+    notVisitedEdges[vertex.getKey()] = vertex;
+  });
+
+  // Detect whether graph contains Eulerian Circuit or Eulerian Path or none of them.
+  /** @params {GraphVertex} vertex */
+  graph.getAllVertices().forEach((vertex) => {
+    if (vertex.getDegree() % 2) {
+      oddRankVertices[vertex.getKey()] = vertex;
+    } else {
+      evenRankVertices[vertex.getKey()] = vertex;
+    }
+  });
+
+  // Check whether we're dealing with Eulerian Circuit or Eulerian Path only.
+  // Graph would be an Eulerian Circuit in case if all its vertices has even degree.
+  // If not all vertices have even degree then graph must contain only two odd-degree
+  // vertices in order to have Euler Path.
+  const isCircuit = !Object.values(oddRankVertices).length;
+
+  if (!isCircuit && Object.values(oddRankVertices).length !== 2) {
+    throw new Error('Eulerian path must contain two odd-ranked vertices');
+  }
+
+  // Pick start vertex for traversal.
+  let startVertex = null;
+
+  if (isCircuit) {
+    // For Eulerian Circuit it doesn't matter from what vertex to start thus we'll just
+    // peek a first node.
+    const evenVertexKey = Object.keys(evenRankVertices)[0];
+    startVertex = evenRankVertices[evenVertexKey];
+  } else {
+    // For Eulerian Path we need to start from one of two odd-degree vertices.
+    const oddVertexKey = Object.keys(oddRankVertices)[0];
+    startVertex = oddRankVertices[oddVertexKey];
+  }
+
+  // Start traversing the graph.
+  let currentVertex = startVertex;
+  while (Object.values(notVisitedEdges).length) {
+    // Add current vertex to Eulerian path.
+    eulerianPathVertices.push(currentVertex);
+
+    // Detect all bridges in graph.
+    // We need to do it in order to not delete bridges if there are other edges
+    // exists for deletion.
+    const bridges = graphBridges(graph);
+
+    // Peek the next edge to delete from graph.
+    const currentEdges = currentVertex.getEdges();
+    /** @var {GraphEdge} edgeToDelete */
+    let edgeToDelete = null;
+    if (currentEdges.length === 1) {
+      // If there is only one edge left we need to peek it.
+      [edgeToDelete] = currentEdges;
+    } else {
+      // If there are many edges left then we need to peek any of those except bridges.
+      [edgeToDelete] = currentEdges.filter(edge => !bridges[edge.getKey()]);
+    }
+
+    // Detect next current vertex.
+    if (currentVertex.getKey() === edgeToDelete.startVertex.getKey()) {
+      currentVertex = edgeToDelete.endVertex;
+    } else {
+      currentVertex = edgeToDelete.startVertex;
+    }
+
+    // Delete edge from not visited edges set.
+    delete notVisitedEdges[edgeToDelete.getKey()];
+
+    // If last edge were deleted then add finish vertex to Eulerian Path.
+    if (Object.values(notVisitedEdges).length === 0) {
+      eulerianPathVertices.push(currentVertex);
+    }
+
+    // Delete the edge from graph.
+    graph.deleteEdge(edgeToDelete);
+  }
+
+  return eulerianPathVertices;
+}

Original file line number	Diff line number	Diff line change
`@@ -17,7 +17,7 @@ class VisitMetadata {`
`17`	`17`	`* Tarjan's algorithm for finding articulation points in graph.`
`18`	`18`	`*`
`19`	`19`	`* @param {Graph} graph`
`20`		`- * @return {GraphVertex[]}`
	`20`	`+ * @return {Object}`
`21`	`21`	`*/`
`22`	`22`	`export default function articulationPoints(graph) {`
`23`	`23`	`// Set of vertices we've already visited during DFS.`
`@@ -109,5 +109,5 @@ export default function articulationPoints(graph) {`
`109`	`109`	`// Do Depth First Search traversal over submitted graph.`
`110`	`110`	`depthFirstSearch(graph, startVertex, dfsCallbacks);`
`111`	`111`
`112`		`- return Object.values(articulationPointsSet);`
	`112`	`+ return articulationPointsSet;`
`113`	`113`	`}`