Depth First Search

Author: tayllan

algorithms/graph/depth_first_search.js

@@ -0,0 +1,73 @@
+/**
+ * Copyright (C) 2014 Tayllan Búrigo
+ *
+ * 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.
+ */
+'use strict';
+
+var time = 0,
+    visitedNodes = {},
+    finishingTimes = {};
+    
+/**
+ * Depth First Search for all the vertices in the graph
+ * Worst Case Complexity: O(V * E)
+ * 
+ * @param {Object}
+ * @return {Object} representing the order in which the
+ *    vertices are visited
+ */
+var dfsAdjacencyListStart = function (graph) {
+  graph.vertices.forEach(function (v) {
+    if (visitedNodes[v] !== true) {
+      dfsAdjacencyList(graph, v);
+    }
+  });
+
+  return finishingTimes;
+};
+
+/**
+ * Depth First Search for the vertices reachable from 'startNode'
+ * Worst Case Complexity: O(V * E)
+ * 
+ * @param {Object}
+ * @param {Object}
+ * @return {Object}
+ */
+var dfsAdjacencyList = function (graph, startNode) {
+  visitedNodes[startNode] = true;
+
+  graph.neighbors(startNode).forEach(function (v) {
+    if (visitedNodes[v] !== true) {
+      dfsAdjacencyList(graph, v);
+    }
+  });
+
+  finishingTimes[startNode] = time++;
+
+  return finishingTimes;
+};
+
+var depthFirstSearch = {
+  dfsAdjacencyList: dfsAdjacencyList,
+  dfsAdjacencyListStart: dfsAdjacencyListStart
+};
+
+module.exports = depthFirstSearch;

main.js

@@ -28,6 +28,7 @@ var lib = {
     SPFA: require('./algorithms/graph/SPFA'),
     bellmanFord: require('./algorithms/graph/bellman_ford'),
     eulerPath: require('./algorithms/graph/euler_path'),
+    depthFirstSearch: require('./algorithms/graph/depth_first_search')
   },
   Math: {
     fibonacci: require('./algorithms/math/fibonacci'),

test/algorithms/graph/depth_first_search.js

@@ -0,0 +1,64 @@
+/**
+ * Copyright (C) 2014 Tayllan Búrigo
+ *
+ * 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.
+ */
+'use strict';
+
+var depthFirstSearch = require('../../../algorithms/graph/depth_first_search'),
+    Graph = require('../../../data_structures/graph'),
+    assert = require('assert'),
+    graph = new Graph(true);
+
+graph.addEdge('one', 'three');
+graph.addEdge('one', 'four');
+graph.addEdge('four', 'two');
+graph.addEdge('two', 'one');
+graph.addEdge('three', 'one');
+graph.addEdge('five', 'six');
+
+describe('Depth First Search Algorithm', function () {
+  it('should visit only the nodes reachable from the node {one} (inclusive)',
+    function () {
+      var finishingTimes = depthFirstSearch.dfsAdjacencyList(graph, 'one');
+
+      assert.equal(finishingTimes.five, undefined);
+      assert.equal(finishingTimes.six, undefined);
+
+      assert.equal(finishingTimes.one, 3);
+      assert.equal(finishingTimes.two, 1);
+      assert.equal(finishingTimes.three, 0);
+      assert.equal(finishingTimes.four, 2);
+    }
+  );
+
+  it('should visit all the nodes in the graph',
+    function () {
+      var finishingTimes = depthFirstSearch.dfsAdjacencyListStart(graph);
+
+      assert.equal(finishingTimes.one, 3);
+      assert.equal(finishingTimes.two, 1);
+      assert.equal(finishingTimes.three, 0);
+      assert.equal(finishingTimes.four, 2);
+      assert.equal(finishingTimes.five, 5);
+      assert.equal(finishingTimes.six, 4);
+    }
+  );
+});
+