Add least common ancestors algorithm

README.md

@@ -210,6 +210,15 @@ Arguments:
  * *sourceNodes* (optional) - An array of node identifier strings. This specifies the subset of nodes to use as the sources of the depth-first search. If *sourceNodes* is not specified, all **[nodes](#nodes)** in the graph are used as source nodes.
  * *includeSourceNodes* (optional) - A boolean specifying whether or not to include the source nodes in the returned array. If *includeSourceNodes* is not specified, it is treated as `true` (all source nodes are included in the returned array).
 
+<a name="lca" href="#lca">#</a> <i>graph</i>.<b>lowestCommonAncestors</b>([<i>node1</i>][, <i>node2</i>])
+
+Performs search of [Lowest common ancestors](https://en.wikipedia.org/wiki/Lowest_common_ancestor). Returns an array of node identifier strings.
+
+Arguments:
+
+ * *node1* (required) - First node.
+ * *node2* (required) - Second node.
+
 <a name="topological-sort" href="#topological-sort">#</a> <i>graph</i>.<b>topologicalSort</b>([<i>sourceNodes</i>][, <i>includeSourceNodes</i>])
 
 Performs [Topological Sort](https://en.wikipedia.org/wiki/Topological_sorting). Returns an array of node identifier strings. The returned array includes nodes in topologically sorted order. This means that for each visited edge (**u** -> **v**), **u** comes before **v** in the topologically sorted order. Amazingly, this comes from simply reversing the result from depth first search. Inspired by by Cormen et al. "Introduction to Algorithms" 3rd Ed. p. 613.

index.js

@@ -14,6 +14,7 @@ module.exports = function Graph(serialized){
     indegree: indegree,
     outdegree: outdegree,
     depthFirstSearch: depthFirstSearch,
+    lowestCommonAncestors: lowestCommonAncestors,
     topologicalSort: topologicalSort,
     shortestPath: shortestPath,
     serialize: serialize,
@@ -46,7 +47,7 @@ module.exports = function Graph(serialized){
   // Removes a node from the graph.
   // Also removes incoming and outgoing edges.
   function removeNode(node){
-    
+
     // Remove incoming edges.
     Object.keys(edges).forEach(function (u){
       edges[u].forEach(function (v){
@@ -147,7 +148,7 @@ module.exports = function Graph(serialized){
 
   // Depth First Search algorithm, inspired by
   // Cormen et al. "Introduction to Algorithms" 3rd Ed. p. 604
-  // This variant includes an additional option 
+  // This variant includes an additional option
   // `includeSourceNodes` to specify whether to include or
   // exclude the source nodes from the result (true by default).
   // If `sourceNodes` is not specified, all nodes in the graph
@@ -187,6 +188,50 @@ module.exports = function Graph(serialized){
     return nodeList;
   }
 
+  // Least Common Ancestors
+  // Inspired by https://github.com/relaxedws/lca/blob/master/src/LowestCommonAncestor.php code
+  // but uses depth search instead of breadth. Also uses some optimizations
+  function lowestCommonAncestors(node1, node2){
+
+    var node1Ancestors = [];
+    var lcas = [];
+
+    function CA1Visit(visited, node){
+      if(!visited[node]){
+        visited[node] = true;
+        node1Ancestors.push(node);
+        if (node == node2) {
+          lcas.push(node);
+          return false; // found - shortcut
+        }
+        return adjacent(node).every(node => {
+          return CA1Visit(visited, node);
+        });
+      } else {
+        return true;
+      }
+    }
+
+    function CA2Visit(visited, node){
+      if(!visited[node]){
+        visited[node] = true;
+        if (node1Ancestors.indexOf(node) >= 0) {
+          lcas.push(node);
+        } else if (lcas.length == 0) {
+          adjacent(node).forEach(node => {
+            CA2Visit(visited, node);
+          });
+        }
+      }
+    }
+
+    if (CA1Visit({}, node1)) { // No shortcut worked
+      CA2Visit({}, node2);
+    }
+
+    return lcas;
+  }
+
   // The topological sort algorithm yields a list of visited nodes
   // such that for each visited edge (u, v), u comes before v in the list.
   // Amazingly, this comes from just reversing the result from depth first search.
@@ -326,6 +371,6 @@ module.exports = function Graph(serialized){
     serialized.links.forEach(function (link){ addEdge(link.source, link.target, link.weight); });
     return graph;
   }
-  
+
   return graph;
 }

test.js

@@ -198,8 +198,8 @@ describe("Graph", function() {
       graph.addEdge("a", "d"); //    |   d
       graph.addEdge("b", "c"); //    c   |
       graph.addEdge("d", "e"); //     \ /
-      graph.addEdge("c", "e"); //      e   
-      
+      graph.addEdge("c", "e"); //      e
+
       var sorted = graph.topologicalSort(["a"], false);
       assert.equal(sorted.length, 4);
       assert(contains(sorted, "b"));
@@ -245,6 +245,24 @@ describe("Graph", function() {
 
       output(graph, "cycles");
     });
+
+    it("Should compute lowest common ancestors.", function (){
+      var graph = Graph()
+
+        .addEdge("a", "b")
+        .addEdge("b", "d")
+        .addEdge("c", "d")
+        .addEdge("b", "e")
+        .addEdge("c", "e")
+        .addEdge("d", "g")
+        .addEdge("e", "g")
+        .addNode("f");
+
+      assert.deepStrictEqual(graph.lowestCommonAncestors("a", "a"), ["a"]);
+      assert.deepStrictEqual(graph.lowestCommonAncestors("a", "b"), ["b"]);
+      assert.deepStrictEqual(graph.lowestCommonAncestors("a", "c"), ["d", "e"]);
+      assert.deepStrictEqual(graph.lowestCommonAncestors("a", "f"), []);
+    });
   });
 
   describe("Edge cases and error handling", function() {