feat(graphs): add Tarjan's algorithm for SCC

Fix mgechev#98

Author: mgechev

package.json

@@ -16,7 +16,7 @@
     "jshint-stylish": "^1.0.0"
   },
   "scripts": {
-    "test": "echo \"Error: no test specified\" && exit 1"
+    "test": "gulp test"
   },
   "repository": {
     "type": "git",

src/graphs/others/tarjan-connected-components.js

@@ -0,0 +1,70 @@
+(function (exports) {
+
+ /**
+   * Tarjan's algorithm for finding the connected components in a graph.<br><br>
+   * Time complexity: O(|E| + |V|) where E is a number of edges and |V|
+   * is the number of nodes.
+   *
+   * @public
+   * @module graphs/others/tarjan-connected-components
+   * @param {Array} graph Adjacency list, which represents the graph.
+   * @returns {Array} Connected components.
+   *
+   * @example
+   * var tarjanConnectedComponents =
+   *  require('path-to-algorithms/src/graphs/' +
+   * 'others/tarjan-connected-components').tarjanConnectedComponents;
+   * var graph = {
+   *     v1: ['v2', 'v5'],
+   *     v2: [],
+   *     v3: ['v1', 'v2', 'v4', 'v5'],
+   *     v4: [],
+   *     v5: []
+   * };
+   * var vertices = topsort(graph); // ['v3', 'v4', 'v1', 'v5', 'v2']
+   */
+  function tarjanConnectedComponents(graph) {
+    graph = graph || {};
+    const indexes = {};
+    const lowIndexes = {};
+    const onStack = {};
+    const result = [];
+    const stack = [];
+    let index = 1;
+
+    const connectedComponent = node => {
+      stack.push(node);
+      onStack[node] = true;
+      indexes[node] = index;
+      lowIndexes[node] = index;
+      index += 1;
+      graph[node].forEach(n => {
+        if (indexes[n] === undefined) {
+          connectedComponent(n);
+          lowIndexes[node] = Math.min(lowIndexes[n], lowIndexes[node]);
+        } else if (onStack[n]) {
+          lowIndexes[node] = Math.min(lowIndexes[node], indexes[n]);
+        }
+      });
+      // This is a "root" node
+      const cc = [];
+      if (indexes[node] === lowIndexes[node]) {
+        let current;
+        do {
+          current = stack.pop();
+          onStack[current] = false;
+          cc.push(current);
+        } while (stack.length > 0 && node !== current);
+        result.push(cc);
+      }
+    };
+
+    Object.keys(graph)
+      .forEach(n => !indexes[n] && connectedComponent(n));
+
+    return result;
+  }
+
+  exports.tarjanConnectedComponents = tarjanConnectedComponents;
+
+}(typeof exports === 'undefined' ? window : exports));

src/graphs/others/topological-sort.js

@@ -22,7 +22,8 @@
 
     /**
      * Topological sort algorithm of a directed acyclic graph.<br><br>
-     * Time complexity: O(|E|) where E is a number of edges.
+     * Time complexity: O(|E| + |V|) where E is a number of edges
+     * and |V| is the number of nodes.
      *
      * @public
      * @module graphs/others/topological-sort

test/graphs/others/tarjan-connected-components.spec.js

@@ -0,0 +1,38 @@
+var tj = require('../../../src/graphs/others/tarjan-connected-components').tarjanConnectedComponents;
+
+var nonConnected = {
+  v1: [],
+  v2: [],
+  v3: [],
+  v4: [],
+  v5: []
+};
+
+var cyclicGraph = {
+  v1: ['v2'],
+  v2: ['v3'],
+  v3: ['v4'],
+  v4: ['v5'],
+  v5: ['v1']
+};
+
+
+describe('Tarjan\'s algorithm for finding connected components', function () {
+  'use strict';
+  it('should be defined', function () {
+    expect(typeof tj).toBe('function');
+  });
+
+  it('should return an array', function () {
+    expect(tj() instanceof Array).toBeTruthy();
+  });
+
+  it('should work with non-connected graphs', function () {
+    expect(tj(nonConnected)).toEqual([['v1'], ['v2'], ['v3'], ['v4'], ['v5']]);
+  });
+
+  it('should workw ith cycles', () => {
+    expect(tj(cyclicGraph)).toEqual([['v5', 'v4', 'v3', 'v2', 'v1']]);
+  });
+
+});