add check_cycle.py (#5475)

* add check_cycle.py

* Update graphs/check_cycle.py
Co-authored-by: NJohn Law <johnlaw.po@gmail.com>

* Update check_cycle.py

* Apply suggestions from code review
Co-authored-by: NJohn Law <johnlaw.po@gmail.com>
Co-authored-by: NChristian Clauss <cclauss@me.com>

graphs/check_cycle.py

+"""
+Program to check if a cycle is present in a given graph
+"""
+
+
+def check_cycle(graph: dict) -> bool:
+    """
+    Returns True if graph is cyclic else False
+
+    >>> check_cycle(graph={0:[], 1:[0, 3], 2:[0, 4], 3:[5], 4:[5], 5:[]})
+    False
+    >>> check_cycle(graph={0:[1, 2], 1:[2], 2:[0, 3], 3:[3]})
+    True
+    """
+    # Keep track of visited nodes
+    visited = set()
+    # To detect a back edge, keep track of vertices currently in the recursion stack
+    rec_stk = set()
+    for node in graph:
+        if node not in visited:
+            if depth_first_search(graph, node, visited, rec_stk):
+                return True
+    return False
+
+
+def depth_first_search(graph: dict, vertex: int, visited: set, rec_stk: set) -> bool:
+    """
+    Recur for all neighbours.
+    If any neighbour is visited and in rec_stk then graph is cyclic.
+
+    >>> graph = {0:[], 1:[0, 3], 2:[0, 4], 3:[5], 4:[5], 5:[]}
+    >>> vertex, visited, rec_stk = 0, set(), set()
+    >>> depth_first_search(graph, vertex, visited, rec_stk)
+    False
+    """
+    # Mark current node as visited and add to recursion stack
+    visited.add(vertex)
+    rec_stk.add(vertex)
+
+    for node in graph[vertex]:
+        if node not in visited:
+            if depth_first_search(graph, node, visited, rec_stk):
+                return True
+        elif node in rec_stk:
+            return True
+
+    # The node needs to be removed from recursion stack before function ends
+    rec_stk.remove(vertex)
+    return False
+
+
+if __name__ == "__main__":
+    from doctest import testmod
+
+    testmod()