feat(algs): add articulation point finding alg (brute force)

Author: jessicayung

algorithms/articulation_points.py

@@ -0,0 +1,41 @@
+"""
+Articulation Points
+- vertices of graphs which, when removed, will increase the number of 'islands' in the graph.
+- i.e. vulnerable points of a network
+
+Based on tutorial on HackerEarth: https://www.hackerearth.com/practice/algorithms/graphs/articulation-points-and-bridges/tutorial/
+
+Jessica Yung
+Jan 2018
+"""
+import numpy as np
+from graph import Graph
+
+class find_articulation_points(Graph):
+
+    def __init__(self, adjacency_matrix, num_vertices):
+        Graph.__init__(self, adjacency_matrix, num_vertices)
+        self.saved_adj_mat = self.adj_mat
+
+    def brute_force(self):
+        """Alternative brute force approach: find islands using a DFS for each vertex."""
+        self.articulation_points = []
+        original_islands = self.find_num_islands()
+        print("Original number of islands: ", original_islands)
+        for vertex in range(self.v):
+            self.remove_vertex(vertex)
+            if self.find_num_islands() > original_islands:
+                print(self.num_islands, "islands with vertex", vertex, "removed.")
+                self.articulation_points.append(vertex)
+            # Restore vertex
+            self.v += 1
+            self.adj_mat = self.saved_adj_mat
+        return self.articulation_points
+
+adjmat = np.zeros((6,6))
+edges = [[0,1],[0,5],[1,2],[1,3],[2,3],[2,4],[3,4]]
+test1 = find_articulation_points(adjmat, 6)
+test1.add_edges(edges)
+test1.brute_force()
+print(test1.articulation_points)
+