javascript-algorithms/src/algorithms/graph/bridges/graphBridges.js

import depthFirstSearch from '../depth-first-search/depthFirstSearch';

/**
 * Helper class for visited vertex metadata.
 */
class VisitMetadata {
  constructor({ discoveryTime, lowDiscoveryTime }) {
    this.discoveryTime = discoveryTime;
    this.lowDiscoveryTime = lowDiscoveryTime;
  }
}

/**
 * @param {Graph} graph
 * @return {Object}
 */
export default function graphBridges(graph) {
  // Set of vertices we've already visited during DFS.
  const visitedSet = {};

  // Set of bridges.
  const bridges = {};

  // Time needed to discover to the current vertex.
  let discoveryTime = 0;

  // Peek the start vertex for DFS traversal.
  const startVertex = graph.getAllVertices()[0];

  const dfsCallbacks = {
    /**
     * @param {GraphVertex} currentVertex
     */
    enterVertex: ({ currentVertex }) => {
      // Tick discovery time.
      discoveryTime += 1;

      // Put current vertex to visited set.
      visitedSet[currentVertex.getKey()] = new VisitMetadata({
        discoveryTime,
        lowDiscoveryTime: discoveryTime,
      });
    },
    /**
     * @param {GraphVertex} currentVertex
     * @param {GraphVertex} previousVertex
     */
    leaveVertex: ({ currentVertex, previousVertex }) => {
      if (previousVertex === null) {
        // Don't do anything for the root vertex if it is already current (not previous one).
        return;
      }

      // Check if current node is connected to any early node other then previous one.
      visitedSet[currentVertex.getKey()].lowDiscoveryTime = currentVertex.getNeighbors()
        .filter(earlyNeighbor => earlyNeighbor.getKey() !== previousVertex.getKey())
        .reduce(
          /**
           * @param {number} lowestDiscoveryTime
           * @param {GraphVertex} neighbor
           */
          (lowestDiscoveryTime, neighbor) => {
            const neighborLowTime = visitedSet[neighbor.getKey()].lowDiscoveryTime;
            return neighborLowTime < lowestDiscoveryTime ? neighborLowTime : lowestDiscoveryTime;
          },
          visitedSet[currentVertex.getKey()].lowDiscoveryTime,
        );

      // Compare low discovery times. In case if current low discovery time is less than the one
      // in previous vertex then update previous vertex low time.
      const currentLowDiscoveryTime = visitedSet[currentVertex.getKey()].lowDiscoveryTime;
      const previousLowDiscoveryTime = visitedSet[previousVertex.getKey()].lowDiscoveryTime;
      if (currentLowDiscoveryTime < previousLowDiscoveryTime) {
        visitedSet[previousVertex.getKey()].lowDiscoveryTime = currentLowDiscoveryTime;
      }

      // Compare current vertex low discovery time with parent discovery time. Check if there
      // are any short path (back edge) exists. If we can't get to current vertex other then
      // via parent then the parent vertex is articulation point for current one.
      const parentDiscoveryTime = visitedSet[previousVertex.getKey()].discoveryTime;
      if (parentDiscoveryTime < currentLowDiscoveryTime) {
        const bridge = graph.findEdge(previousVertex, currentVertex);
        bridges[bridge.getKey()] = bridge;
      }
    },
    allowTraversal: ({ nextVertex }) => {
      return !visitedSet[nextVertex.getKey()];
    },
  };

  // Do Depth First Search traversal over submitted graph.
  depthFirstSearch(graph, startVertex, dfsCallbacks);

  return bridges;
}