dagre-d3-es/src/graphlib/alg/tarjan.js

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/**
 * @import { Graph, NodeID } from '../graph.js';
 */

export { tarjan };

/**
 * This function is an implementation of [Tarjan's algorithm][] which finds
 * all [strongly connected components][] in the directed graph `g`. Each
 * strongly connected component is composed of nodes that can reach all other
 * nodes in the component via directed edges. A strongly connected component
 * can consist of a single node if that node cannot both reach and be reached
 * by any other specific node in the graph. Components of more than one node
 * are guaranteed to have at least one cycle.
 *
 * [Tarjan's algorithm]: http://en.wikipedia.org/wiki/Tarjan's_strongly_connected_components_algorithm
 * [strongly connected components]: http://en.wikipedia.org/wiki/Strongly_connected_component
 *
 * @example
 *
 * ![](https://github.com/dagrejs/graphlib/wiki/images/tarjan.png)
 * <!-- SOURCE:
 * digraph {
 * node [shape=circle, style="fill:white;stroke:#333;stroke-width:1.5px"]
 * edge [lineInterpolate=bundle]
 * rankdir=lr
 *
 * A -> B -> C -> D -> H -> G -> F
 * F -> G
 * D -> C
 * H -> D
 * B -> E -> G
 * E -> A
 * }
 * -->
 *
 * ```js
 * graphlib.alg.tarjan(g);
 * // => [ [ 'F', 'G' ],
 * //      [ 'H', 'D', 'C' ],
 * //      [ 'E', 'B', 'A' ] ]
 * ```
 *
 * @param {Graph} g - The directed graph to analyze.
 * @returns {NodeID[][]} an array of components. Each component is itself an
 * array that contains the ids of all nodes in the component.
 */
function tarjan(g) {
  var index = 0;
  /** @type {NodeID[]} */
  var stack = [];
  /**
   * @type {Record<NodeID, { onStack: boolean, lowlink: number, index: number }>}
   */
  var visited = {};
  /** @type {NodeID[][]} */
  var results = [];

  /**
   * @param {NodeID} v - Node to recursively visit
   */
  function dfs(v) {
    var entry = (visited[v] = {
      onStack: true,
      lowlink: index,
      index: index++,
    });
    stack.push(v);

    g.successors(v).forEach(function (w) {
      if (!Object.prototype.hasOwnProperty.call(visited, w)) {
        dfs(w);
        entry.lowlink = Math.min(entry.lowlink, visited[w].lowlink);
      } else if (visited[w].onStack) {
        entry.lowlink = Math.min(entry.lowlink, visited[w].index);
      }
    });

    if (entry.lowlink === entry.index) {
      /** @type {NodeID[]} */
      var cmpt = [];
      /** @type {NodeID} */
      var w;
      do {
        w = stack.pop();
        visited[w].onStack = false;
        cmpt.push(w);
      } while (v !== w);
      results.push(cmpt);
    }
  }

  g.nodes().forEach(function (v) {
    if (!Object.prototype.hasOwnProperty.call(visited, v)) {
      dfs(v);
    }
  });

  return results;
}