toposort.js

/*
Copyright (c) 2012 by Marcel Klehr <mklehr@gmx.net>

Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in
all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
THE SOFTWARE.
 */

class CyclicalDependencyError extends Error {
  constructor(message, node) {
    super(message);
    this.node = node;
  }
}

class Toposort {
  constructor(edges) {
    this.nodes = Toposort.makeUniqueNodes(edges);
    this.edges = edges;
    this.cursor = this.nodes.length;
    this.sorted = new Array(this.cursor);
    this.visited = {};
    // Better data structures make algorithm much faster.
    this.outgoingEdges = Toposort.makeOutgoingEdges(this.edges);
    this.nodesHash = Toposort.makeNodesHash(this.nodes);
  }

  sort() {
    for (let i = this.cursor - 1; i >= 0; i--) {
      if (!this.visited[i]) {
        this.visit(this.nodes[i], i, new Set());
      }
    }
    return this.sorted;
  }

  visit(node, i, predecessors) {
    if (predecessors.has(node)) {
      throw new CyclicalDependencyError('Cyclical dependency', node);
    }

    if (this.visited[i]) return;
    this.visited[i] = true;

    let outgoing = this.outgoingEdges.get(node) || new Set();
    outgoing = Array.from(outgoing);
    outgoing.sort();

    if (outgoing.length) {
      predecessors.add(node);
      for (let j = outgoing.length - 1; j >= 0; j--) {
        const child = outgoing[j];
        this.visit(child, this.nodesHash.get(outgoing[j]), predecessors);
      }
      predecessors.delete(node);
    }

    this.cursor -= 1;
    this.sorted[this.cursor] = node;
  }

  static makeOutgoingEdges(edges) {
    const outgoingEdges = new Map();
    for (const edge of edges) {
      if (!outgoingEdges.has(edge[0])) outgoingEdges.set(edge[0], new Set());
      if (!outgoingEdges.has(edge[1])) outgoingEdges.set(edge[1], new Set());
      outgoingEdges.get(edge[0]).add(edge[1]);
    }
    return outgoingEdges;
  }

  static makeNodesHash(nodes) {
    const nodesHash = new Map();
    for (let i = 0, length = nodes.length; i < length; i++) {
      nodesHash.set(nodes[i], i);
    }
    return nodesHash;
  }

  static makeUniqueNodes(edges) {
    const uniqueNodes = new Set();
    for (const edge of edges) {
      uniqueNodes.add(edge[0]);
      uniqueNodes.add(edge[1]);
    }
    return Array.from(uniqueNodes);
  }
}

const toposort = (edges) => new Toposort(edges).sort();

module.exports = {
  toposort,
  CyclicalDependencyError,
};

toposort.test.js

const assert = require('chai').assert;

const { toposort, CyclicalDependencyError } = require('./toposort.js');

describe('toposort', () => {
  it('should be sorted correctly', () => {
    assert.deepEqual(
      toposort([
        ['3', '2'],
        ['2', '1'],
        ['6', '5'],
        ['5', '2'],
        ['5', '4'],
      ]),
      ['3', '6', '5', '2', '1', '4']
    );
  });

  it('error on simple cyclic graphs', () => {
    assert.throws(() => {
      toposort([
        ['foo', 'bar'],
        ['bar', 'foo'], // cyclic dependency
      ]);
    }, CyclicalDependencyError);
  });

  it('error on complex cyclic graphs', () => {
    assert.throws(() => {
      toposort([
        ['foo', 'bar'],
        ['bar', 'ron'],
        ['john', 'bar'],
        ['tom', 'john'],
        ['ron', 'tom'], // cyclic dependency
      ]);
    }, CyclicalDependencyError);
  });

  it('should sort triangular dependency', () => {
    assert.deepEqual(
      toposort([
        ['a', 'b'],
        ['a', 'c'],
        ['b', 'c'],
      ]),
      ['a', 'b', 'c']
    );
  });

  it('should sort giant graphs quickly', () => {
    const graph = [];
    for (let i = 0; i < 100000; i++) {
      graph.push([i, i + 1]);
    }

    const start = Date.now();
    toposort(graph);
    const end = Date.now();

    assert.isBelow(end - start, 1000);
  });

  it('should handle objects', () => {
    const o1 = { k1: 'v1', nested: { k2: 'v2' } };
    const o2 = { k2: 'v2' };
    const o3 = { k3: 'v3' };
    assert.deepEqual(
      toposort([
        [o1, o2],
        [o2, o3],
      ]),
      [{ k1: 'v1', nested: { k2: 'v2' } }, { k2: 'v2' }, { k3: 'v3' }]
    );
  });
});