Add detect cycle.

This commit is contained in:
Oleksii Trekhleb 2018-05-05 10:05:09 +03:00
parent 97f8bd3a9f
commit 20bc442dcf
3 changed files with 136 additions and 1 deletions

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* [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

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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,
});
});
});

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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;
}