# Copyright (c) 2007-2008 Pedro Matiello <pmatiello@gmail.com>

#

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"""

Accessibility algorithms for python-graph.

@sort: accessibility, connected_components, cut_edges, cut_nodes, mutual_accessibility

"""

# Transitive-closure

def accessibility(graph):

	"""

	Accessibility matrix (transitive closure).

	@type  graph: graph

	@param graph: Graph.

	@rtype:  dictionary

	@return: Accessibility information for each node.

	"""

	accessibility = {}		# Accessibility matrix

	# For each node i, mark each node j if that exists a path from i to j.

	for each in graph:

		access = {}

		# Perform DFS to explore all reachable nodes

		_dfs(graph, access, 1, each)

		accessibility[each] = access.keys()

	return accessibility

# Strongly connected components

def mutual_accessibility(graph):

	"""

	Mutual-accessibility matrix (strongly connected components).

	@type  graph: graph

	@param graph: Graph.

	@rtype:  dictionary

	@return: Mutual-accessibility information for each node.

	"""

	mutual_access = {}

	access = graph.accessibility()

	for i in graph:

		mutual_access[i] = []

		for j in graph:

			if (i in access[j] and j in access[i]):

				mutual_access[i].append(j)

	return mutual_access

# Connected components

def connected_components(graph):

	"""

	Connected components.

	@attention: Indentification of connected components is meaningful only for non-directed graphs.

	@type  graph: graph

	@param graph: Graph.

	@rtype:  dictionary

	@return: Pairing that associates each node to its connected component.

	"""

	visited = {}

	count = 1

	# For 'each' node not found to belong to a connected component, find its connected component.

	for each in graph:

		if (each not in visited):

			_dfs(graph, visited, count, each)

			count = count + 1

	return visited

# Limited DFS implementations used by algorithms here

def _dfs(graph, visited, count, node):

	"""

	Depht-first search subfunction adapted for accessibility algorithms.

	@type  graph: graph

	@param graph: Graph.

	@type  visited: dictionary

	@param visited: List of nodes (visited nodes are marked non-zero).

	@type  count: number

	@param count: Counter of connected components.

	@type  node: number

	@param node: Node to be explored by DFS.

	"""

	visited[node] = count

	# Explore recursively the connected component

	for each in graph[node]:

		if (each not in visited):

			_dfs(graph, visited, count, each)

# Cut-Edge and Cut-Vertex identification

def cut_edges(graph):

	"""

	Return the cut-edges of the given graph.

	@rtype:  list

	@return: List of cut-edges.

	"""

	pre = {}

	low = {}

	spanning_tree = {}

	reply = []

	pre[None] = 0

	for each in graph:

		if (not pre.has_key(each)):

			spanning_tree[each] = None

			_cut_dfs(graph, spanning_tree, pre, low, reply, each)

	return reply

def cut_nodes(graph):

	"""

	Return the cut-nodes of the given graph.

	@rtype:  list

	@return: List of cut-nodes.

	"""

	pre = {}	# Pre-ordering

	low = {}	# Lowest pre[] reachable from this node going down the spanning tree + one backedge

	reply = {}

	spanning_tree = {}

	pre[None] = 0

	# Create spanning trees, calculate pre[], low[]

	for each in graph:

		if (not pre.has_key(each)):

			spanning_tree[each] = None

			_cut_dfs(graph, spanning_tree, pre, low, [], each)

	# Find cuts

	for each in graph:

		# If node is not a root

		if (spanning_tree[each] is not None):

			for other in graph[each]:

				# If there is no back-edge from descendent to a ancestral of each

				if (low[other] >= pre[each] and spanning_tree[other] == each):

					reply[each] = 1

		# If node is a root

		else:

			children = 0

			for other in graph:

				if (spanning_tree[other] == each):

					children = children + 1

			# root is cut-vertex iff it has two or more children

			if (children >= 2):

				reply[each] = 1

	return reply.keys()

def _cut_dfs(graph, spanning_tree, pre, low, reply, node):

	"""

	Depth first search adapted for identification of cut-edges and cut-nodes.

	@type  graph: graph

	@param graph: Graph

	@type  spanning_tree: dictionary

	@param spanning_tree: Spanning tree being built for the graph by DFS.

	@type  pre: dictionary

	@param pre: Graph's preordering.

	@type  low: dictionary

	@param low: Associates to each node, the preordering index of the node of lowest preordering

	accessible from the given node.

	@type  reply: list

	@param reply: List of cut-edges.

	@type  node: node

	@param node: Node to be explored by DFS.

	"""

	pre[node] = pre[None]

	low[node] = pre[None]

	pre[None] = pre[None] + 1

	for each in graph[node]:

		if (not pre.has_key(each)):

			spanning_tree[each] = node

			_cut_dfs(graph, spanning_tree, pre, low, reply, each)

			if (low[node] > low[each]):

				low[node] = low[each]

			if (low[each] == pre[each]):

				reply.append((node, each))

		elif (low[node] > pre[each] and spanning_tree[node] != each):

			low[node] = pre[each]