Added ICPC-Referat

presentations/ICPC-Referat/Material/tarjans-algorithm.py

@@ -0,0 +1,93 @@
+def strongly_connected_components(graph):
+	"""
+	Tarjan's Algorithm (named for its discoverer, Robert Tarjan) is a 
+	graph theory algorithm for finding the strongly connected 
+	components of a graph.
+	
+	Based on: http://en.wikipedia.org/wiki/Tarjan%27s_strongly_connected_components_algorithm
+	@author: Dries Verdegem, some minor edits by Martin Thoma
+	@source: http://www.logarithmic.net/pfh/blog/01208083168
+	"""
+
+	index_counter = 0
+	stack = []
+	lowlinks = {}
+	index = {}
+	result = []
+	
+	def strongconnect(node, index_counter):
+		print("Start with node: %s###########################" % node)
+		# set the depth index for this node to the smallest unused index
+		print("lowlinks:\t%s" % lowlinks)
+		print("index:\t%s" % index)
+		print("stack:\t%s" % stack)
+
+		index[node] = index_counter
+		lowlinks[node] = index_counter
+		index_counter += 1
+		stack.append(node)
+	
+		# Consider successors of `node`
+		try:
+			successors = graph[node]
+		except:
+			successors = []
+
+		# Depth first search
+		for successor in successors:
+			# Does the current node point to a node that was already
+			# visited?
+			if successor not in lowlinks:
+				print("successor not in lowlinks: %s -> %s (node, successor)" % (node, successor))
+				# Successor has not yet been visited; recurse on it
+				strongconnect(successor, index_counter)
+				lowlinks[node] = min(lowlinks[node],lowlinks[successor])
+			elif successor in stack:
+			#else:
+				print("successor in stack: %s -> %s" % (node, successor));
+				# the successor is in the stack and hence in the 
+				# current strongly connected component (SCC)
+				lowlinks[node] = min(lowlinks[node],index[successor])
+			else:
+				print("This happens sometimes. node: %s, successor: %s" % (node, successor))
+				print("Lowlinks: %s" %lowlinks)
+				print("stack: %s" % stack)
+		
+		# If `node` is a root node, pop the stack and generate an SCC
+		if lowlinks[node] == index[node]:
+			print("Got root node: %s (index/lowlink: %i)" % (node, lowlinks[node]))
+			connected_component = []
+			
+			while True:
+				successor = stack.pop()
+				print("pop: %s" % successor)
+				connected_component.append(successor)
+				if successor == node: break
+
+			component = tuple(connected_component)
+
+			# storing the result
+			result.append(component)
+		else:
+			print("Node: %s, lowlink: %i, index: %i" % (node, lowlinks[node], index[node]))
+	
+	for node in graph:
+		if node not in lowlinks:
+			strongconnect(node, index_counter)
+	
+	return result
+
+graph = {'a': ['b'],
+		'b': ['c'],
+		'c': ['d', 'e'],
+		'd': ['a', 'e', 'h'],
+		'e': ['c', 'f'],
+		'f': ['g', 'i'],
+		'g': ['h', 'f'],
+		'h': ['j'],
+		'i': ['g', 'f'],
+		'j': ['i'],
+		'k': [],
+		'h': []}
+
+print strongly_connected_components(graph)