[Feature] Added cycle detection to graphs.

Author: exterkamp

README.md

@@ -53,6 +53,8 @@ $ coverage report -m
 * [Linked List](structures/linked_list.py)
   * [Contains Cycles](structures/linked_list.py)
   * [Find Start of Cycle](structures/linked_list.py)
+* [Graph](structures/graph.py)
+  * [Detect Cycle](structures/graph.py)
 
 ### Algorithms
 

structures/graph.py

@@ -35,6 +35,45 @@ def add_edge(self, source, destination):
         """
         self.graph[source].append(destination)
 
+    def has_cycle(self):
+        """
+        Detect if a graph has a cycle.
+
+        Returns:
+            True if the graph has a cycle and
+            False if the graph is acyclic.
+
+        """
+
+        visited = [0] * self.verticies
+
+        def valid(node):
+            # print(visited, node)
+            if visited[node] == -1:
+                return False
+            elif visited[node] == 1:
+                return True
+            visited[node] = -1
+            for neighbor in self.graph[node]:
+                if not valid(neighbor):
+                    return False
+            return True
+
+        for node in range(self.verticies):
+            # dfs from each, mark as -1 when visited
+            # after dfs set all -1 -> 1
+            # cancel if find a 1, as its already been explored
+            if not visited[node]:
+                # print(visited)
+                if valid(node):
+                    # set all -1 to 1
+                    visited = list(map(lambda x: abs(x),visited))
+                else:
+                    # cycle!
+                    return True
+        # no cycle available
+        return False
+
     def topological_sort(self):
         """
         Sort the graph topologically.

tests/test_graph_cycles.py

@@ -0,0 +1,62 @@
+import unittest
+from structures.graph import Graph
+
+class TestCycle(unittest.TestCase):
+
+    def test_cycles_true(self):
+
+        graph = Graph(4)
+
+        graph.add_edge(0,1)
+        graph.add_edge(1,2)
+        graph.add_edge(2,3)
+        graph.add_edge(3,0)
+
+        self.assertEqual(True, graph.has_cycle())
+    
+    def test_cycles_true_complex_graph(self):
+
+        graph = Graph(7)
+
+        graph.add_edge(0,1)
+        graph.add_edge(1,2)
+        graph.add_edge(3,2)
+        graph.add_edge(4,3)
+        graph.add_edge(4,6)
+        graph.add_edge(5,3)
+        graph.add_edge(5,4)
+        graph.add_edge(6,5)
+
+        self.assertEqual(True, graph.has_cycle())
+
+    def test_cycles_true_2_node_graph(self):
+
+        graph = Graph(2)
+
+        graph.add_edge(0,1)
+        graph.add_edge(1,0)
+
+        self.assertEqual(True, graph.has_cycle())
+
+    def test_cycle_with_discrete_forest(self):
+
+        graph = Graph(6)
+
+        graph.add_edge(0,1)
+        graph.add_edge(1,2)
+        graph.add_edge(3,4)
+        graph.add_edge(4,5)
+        graph.add_edge(5,3)
+
+        self.assertEqual(True, graph.has_cycle())
+
+
+    def test_cycles_false(self):
+
+        graph = Graph(4)
+
+        graph.add_edge(0,1)
+        graph.add_edge(1,2)
+        graph.add_edge(2,3)
+
+        self.assertEqual(False, graph.has_cycle())