Merge pull request keon#86 from karpinski/cycle-detection

Adding a cycle detection algorithm for graphs.

Author: ankit167

README.md

@@ -68,6 +68,7 @@ Minimal and clean example implementations of data structures and algorithms in P
     - [word_break](dp/word_break.py)
 - [graph](graph)
     - [clone_graph](graph/clone_graph.py)
+    - [cycle_detection](graph/cycle_detection.py)
     - [find_path](graph/find_path.py)
     - [graph](graph/graph.py)
     - [traversal](graph/traversal.py)

graph/cycle_detection.py

@@ -0,0 +1,52 @@
+"""
+Given a directed graph, check whether it contains a cycle.
+
+Real-life scenario: deadlock detection in a system. Processes may be
+represented by vertices, then and an edge A -> B could mean that process A is
+waiting for B to release its lock on a resource.
+"""
+from enum import Enum
+
+
+class TraversalState(Enum):
+    WHITE = 0
+    GRAY = 1
+    BLACK = 2
+
+
+example_graph_with_cycle = {'A': ['B', 'C'],
+                            'B': ['D'],
+                            'C': ['F'],
+                            'D': ['E', 'F'],
+                            'E': ['B'],
+                            'F': []}
+
+example_graph_without_cycle = {'A': ['B', 'C'],
+                               'B': ['D', 'E'],
+                               'C': ['F'],
+                               'D': ['E'],
+                               'E': [],
+                               'F': []}
+                               
+
+def is_in_cycle(graph, traversal_states, vertex):
+    if traversal_states[vertex] == TraversalState.GRAY:
+        return True
+    traversal_states[vertex] = TraversalState.GRAY
+    for neighbor in graph[vertex]:
+        if is_in_cycle(graph, traversal_states, neighbor):
+            return True
+    traversal_states[vertex] = TraversalState.BLACK
+    return False
+
+
+def contains_cycle(graph):
+    traversal_states = {vertex: TraversalState.WHITE for vertex in graph}
+    for vertex, state in traversal_states.items():
+        if (state == TraversalState.WHITE and
+           is_in_cycle(graph, traversal_states, vertex)):
+            return True
+    return False
+
+print(contains_cycle(example_graph_with_cycle))
+print(contains_cycle(example_graph_without_cycle))