################################################################################
#
#       This file is part of Gato (Graph Animation Toolbox) 
#
#	file:   Graph.py
#	author: Alexander Schliep (alexander@schliep.org)
#
#       Copyright (C) 1998-2011, Alexander Schliep, Winfried Hochstaettler and 
#       Copyright 1998-2001 ZAIK/ZPR, Universitaet zu Koeln
#                                   
#       Contact: alexander@schliep.org, winfried.hochstaettler@fernuni-hagen.de             
#
#       Information: http://gato.sf.net
#
#       This library is free software; you can redistribute it and/or
#       modify it under the terms of the GNU Library General Public
#       License as published by the Free Software Foundation; either
#       version 2 of the License, or (at your option) any later version.
#
#       This library is distributed in the hope that it will be useful,
#       but WITHOUT ANY WARRANTY; without even the implied warranty of
#       MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
#       Library General Public License for more details.
#
#       You should have received a copy of the GNU Library General Public
#       License along with this library; if not, write to the Free
#       Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
#
#
#
#       This file is version $Revision: 435 $ 
#                       from $Date: 2011-05-05 12:36:29 -0400 (Thu, 05 May 2011) $
#             last change by $Author: schliep $.
#
################################################################################
 
from GatoGlobals import *
from DataStructures import Point2D, VertexLabeling, EdgeLabeling, EdgeWeight
import GraphUtil #import ConnectedComponents, FindBipartitePartitions 
 
 
from math import sqrt
import logging
import string
log = logging.getLogger("Graph.py")
 
################################################################################
#
# Graph
#
################################################################################
class Graph:
    """ Provides a mathematical graph object consisting of vertices 
        and (directed) edges connecting those vertices. Graphs have
 
        - a labeling for vertices allowing to specify names
 
        - an embedding of vertices into 2D-space
 
        - one or more sets of edge weights  
 
        Vertices are specified via id (integer number) and edges via
        (tail,head)-tuples 
 
        NOTE: ids are supposed to be consecutive and ranging from 0
        to G.Order() - 1 !!! Use the labeling to *display* other numbers
        for vertices.
 
        At least one set of edge weights is assumed to exist and accessible
        as self.edgeWeights[0]; self.euclidian and Euclidify refer to this
        self.edgeWeights[0]
 
    """
 
    def __init__(self):
        self.simple           = 1
        self.euclidian        = 1
        self.directed         = 0
        self.vertices         = [] 
        self.adjLists         = {}
        self.invAdjLists      = {}   # Inverse Adjazenzlisten
        self.highVertexID     = 0    # INTERNAL
        self.embedding        = VertexLabeling() # 2D-Positions
        self.labeling         = VertexLabeling() # Names of vertices
        self.edgeWeights      = {}   # Dictionary of edge labellings
        self.edgeWeights[0]   = EdgeWeight(self)
        self.vertexWeights    = {}   # None by default
        self.size             = 0
        self.edgeWidth        = None
        self.vertexAnnotation = None
        self.edgeAnnotation   = None
        self.properties       = {}
 
    def AddVertex(self):
        """ Add an isolated vertex. Returns the id of the new vertex """
        id = self.GetNextVertexID()	
        self.vertices.append(id)
        self.adjLists[id]    = []
        self.invAdjLists[id] = []
        return id
 
    def DeleteVertex(self, v):
        """ Delete the vertex v and its incident edges """
        outVertices = self.OutNeighbors(v)[:] # Need a copy here
        inVertices = self.InNeighbors(v)[:]
        for w in outVertices:
            self.DeleteEdge(v,w)
        for w in inVertices:
            if w != v: # We have already deleted loops
                self.DeleteEdge(w,v)
        self.vertices.remove(v)
        #self.adjLists[v] = None
        #self.invAdjLists[v] = None 
        # XXX Should clean up all other stuff too ...
 
 
    def QVertex(self, v):
        """ Check whether v is a vertex """
        return v in self.vertices
 
    def AddEdge(self, tail, head, initialize_weight=True):
        """ Add an edge (tail,head). Returns tail, head. See SubGraph.AddEdge
            for an explanation.
            Raises GraphNotSimpleError if
            - trying to add a loop
            - trying to add an edge multiply 
 
            In case of directed graphs (tail,head) and (head,tail)
            are distinct edges """
        if self.simple == 1 and tail == head: # Loop
            raise GraphNotSimpleError('(%d,%d) is a loop' % (tail,head))
        if self.directed == 0 and tail in self.adjLists[head]: 
            raise GraphNotSimpleError('(%d,%d) is already an undirected edge' % (head,tail))
        if head in self.adjLists[tail]: # Multiple edge
            raise GraphNotSimpleError('(%d,%d) is already an directed edge' % (tail,head))
 
        self.adjLists[tail].append(head)
        self.invAdjLists[head].append(tail)
        self.size = self.size + 1
 
        if not initialize_weight:
            return tail, head
 
        if self.QEuclidian():
            t = self.GetEmbedding(tail)
            h = self.GetEmbedding(head)
            self.SetEdgeWeight(0,tail,head,sqrt((h.x - t.x)**2 + (h.y - t.y)**2))
        else:
            self.SetEdgeWeight(0,tail,head,0)
        for i in xrange(1,self.NrOfEdgeWeights()):
            self.SetEdgeWeight(i,tail,head,0)
        return tail, head
 
 
    def DeleteEdge(self,tail,head):
        """ Deletes edge (tail,head). Does *not* handle undirected graphs
            implicitely. Raises NoSuchEdgeError upon error. """
 
        try:
            self.adjLists[tail].remove(head)
            self.invAdjLists[head].remove(tail)
            self.size = self.size - 1
        except KeyError:
            raise NoSuchEdgeError("(%d,%d) is not an edge." % (tail,head))
 
 
    def Edge(self,tail,head):
        """  Handles undirected graphs by return correct ordered
             vertices as (tail,head). Raises NoSuchEdgeError upon error. """
 
        if tail not in self.vertices or head not in self.vertices:
            raise NoSuchEdgeError("(%d,%d) is not an edge." % (tail,head))
 
        if head in self.adjLists[tail]:
            return (tail,head)
        elif self.directed == 0 and tail in self.adjLists[head]:
            return (head,tail)
        else:
            raise NoSuchEdgeError("(%d,%d) is not an edge." % (tail,head))
 
 
    def QEdge(self,tail,head):
        """ Returns 1 if (tail,head) is an edge in G. If G is undirected
            order of vertices does not matter """
        if self.directed == 1:	
            return head in self.adjLists[tail]
        else: 
            return (head in self.adjLists[tail]) or (tail in self.adjLists[head])
 
 
    def QEdgeWidth(self):
        """ Returns 1 if individual edge widths are defined, 0 else """
        return self.edgeWidth != None
 
 
    def EdgeWidth(self, tail, head):
        return self.edgeWidth[(tail,head)]
 
 
    def Neighborhood(self,v):
        """ Returns the vertices which are connected to v. Does handle
            undirected graphs (i.e., returns vertices w s.t. either 
            (v,w) or (w,v) is an edge) """
 
        if self.directed:
            return self.OutNeighbors(v)
        else:
            return self.InOutNeighbors(v)
 
 
    def InNeighbors(self,v):
        """ Returns vertices w for which (w,v) is an edge """
        return self.invAdjLists[v]
 
 
    def OutNeighbors(self,v):
        """ Returns vertices w for which (v,w) is an edge """
        return self.adjLists[v]
 
 
    def InOutNeighbors(self,v):
        """ Returns vertices w for which (v,w) or (w,v) is an edge """	
        return self.InNeighbors(v) + self.OutNeighbors(v)
 
 
    def InEdges(self,v):
        """ Returns edges (*,v) """	
        f = lambda x, vertex = v : (x,vertex)
        return map(f, self.invAdjLists[v])
 
 
    def OutEdges(self,v):
        """ Returns edges (v,*) """	
        f = lambda x, vertex = v : (vertex,x)
        return map(f ,self.adjLists[v])
 
 
    def IncidentEdges(self,v):
        """ Returns edges (v,*) and (*,v) """	
        return self.InEdges(v) + self.OutEdges(v)
 
 
    def Edges(self):
        """ Returns all edges """		
        tmp = []
        for v in self.vertices:
            tmp = tmp + self.OutEdges(v)
        return tmp
 
    def Vertices(self):
        """ Returns all edges """		
        return self.vertices
 
    def printMy(self):
        """ Debugging only """
        for v in self.vertices:
            print v, " -- ", self.adjLists[v]
 
 
    def GetNextVertexID(self):
        """ *Internal* returns next free vertex id """
        self.highVertexID = self.highVertexID + 1
        return self.highVertexID
 
 
    def Order(self):
        """ Returns order i.e., the number of vertices """
        return len(self.vertices)
 
 
    def Size(self):
        """ Returns size i.e., the number of edge """
        return self.size 
 
 
    def Degree(self, v):
        """ Returns the degree of the vertex v, which is
            - the number of incident edges in the undirect case
            - the number of outgoing edges in the directed case """
 
        if self.directed:
            return len(self.adjLists[v])
        else:
            return len(self.adjLists[v]) + len(self.invAdjLists[v])
 
    def InDegree(self, v):
        """ Returns the number of incoming edges for direct graphs """
        if self.directed:
            return len(self.invAdjLists[v])
        else:
            return None # Proper error to raise?
 
 
    def OutDegree(self, v):
        """ Returns the number of incoming edges for direct graphs """
        if self.directed:
            return len(self.adjLists[v])
        else:
            return None # Proper error to raise?
 
 
    def QEuclidian(self):
        """ Returns 1 if the graph is euclidian, 0 else """
        return self.euclidian
 
 
    def QDirected(self):
        """ Returns 1 if the graph is directed, 0 else """
        return self.directed
 
 
    def QIsolated(self, v):
        """ Returns 1 if the vertex v is isolated"""
        return (len(self.adjLists[v]) == 0) and (len(self.invAdjLists[v]) == 0)
 
 
    def CalculateWidthFromWeight(self, scale, weightID = 0):
        """ Calculate width of edges (self.edgeWidth will be used by 
            GraphDisplay if not none) from the specified set of edge
            weights. 
 
            Default: weightID = 0 is used """
 
        self.edgeWidth = EdgeLabeling()
        edges = self.Edges()
        if len(edges) > 0:
            maxWeight = max(self.edgeWeights[weightID].label.values())
            for e in edges:
                self.edgeWidth[e] = max(
                    scale * (1 + 35 * self.edgeWeights[weightID][e] / maxWeight),
                    0.001)
 
    def NrOfEdgeWeights(self):
        return len(self.edgeWeights.keys())
 
    def SetEdgeWeight(self,i,v,w,value):
        self.edgeWeights[i][(v,w)] = value
 
    def GetEdgeWeight(self,i,v,w):
        return self.edgeWeights[i][(v,w)]
 
    def NrOfVertexWeights(self):
        return len(self.vertexWeights.keys())
 
    def SetVertexWeight(self,i,v,value):
        self.vertexWeights[i][v] = value
 
    def GetVertexWeight(self,i,v):
        return self.vertexWeights[i][v]
 
    def GetLabeling(self,v):
        return self.labeling[v]
 
    def SetLabeling(self,v, value):
        self.labeling[v] = value
 
    def GetEmbedding(self,v):
        return self.embedding[v]
 
    def SetEmbedding(self,v, x, y):
        self.embedding[v] = Point2D(x,y)
 
    def Euclidify(self):
        """ Replace edge weights with weightID = 0 with Euclidean distance 
            between incident vertices """
 
        for v in self.vertices:
            for w in self.adjLists[v]:
                d = ((self.embedding[v].x - self.embedding[w].x)**2 + 
                     (self.embedding[v].y - self.embedding[w].y)**2)**(.5)
 
                if self.edgeWeights[0].QInteger():
                    self.edgeWeights[0][(v,w)] = int(round(d))
                else:
                    self.edgeWeights[0][(v,w)] = d
 
        self.euclidian = 1
 
 
    def Integerize(self, weightID = 0):
        """ Integerize: Make all edge weights integers """
 
        if weightID == 'all':
            for w in self.edgeWeights.keys():
                self.edgeWeights[w].Integerize()
        else:
            self.edgeWeights[weightID].Integerize()
 
 
    def Undirect(self):
        """ If (u,v) and (v,u) are edges in the directed graph, remove one of them.
            to make graph undirected (no multiple edges allowed). Which one gets
            deleted depends on ordering in adjacency lists. """
        if not self.directed:
            return
 
        for v in self.vertices:
            for w in self.adjLists[v]:
                if v in self.adjLists[w]:
                    self.DeleteEdge(w,v)
 
        self.directed = 0
 
    def SetProperty(self, name, val):
        """ Set the value of property 'name' to 'val' """
        self.properties[name] = val
 
    def Property(self,name):
        """ Return the value of property 'name'. If the property
           'name' has not been set 'Unknown' is returned
 
            XXX the catbox format does not support storing properties
        """
        if name == "Directed":
            return self.directed
        elif name == "Undirected":
            return not self.directed
        elif name == "EdgeWeights":
            return self.NrOfEdgeWeights()
        elif name == "Euclidean":
            return self.euclidian       
        elif name == "Simple":
            return self.simple
        elif name == "VertexWeights":
            return self.NrOfVertexWeights()
        elif name == "Connected":
            # NOTE: Connected only for Undirected graphs
            if self.directed:
                return 0
            else:
                return self.QConnected()
        elif name == "Bipartite":
            # NOTE: Bipartite only for Undirected graphs
            if self.directed:
                return 0
            else:
                return self.QBipartite()
        elif name == "EvenOrder":
            return (self.Order() % 2) == 0
        elif name == 'NonNegativeEdgeWeights':
            # There is a bug in gred which allows editing edge weights of
            # Euclidean graphs.
            #if self.euclidian:
            #    return True
            #else:
            return self.QNonNegativeEdgeWeights()     
        else:
            try:
                return self.properties[name]
            except KeyError:
                return 'Unknown'
 
    def QConnected(self):
        """ Check if I am connected (assuming I am undirected)"""
        components = GraphUtil.ConnectedComponents(self)
        return len(components) == 1
 
    def QBipartite(self):
        """ Check if I am bipartite (assuming I am undirected)"""
        partitions = GraphUtil.FindBipartitePartitions(self)
        return len(partitions[0]) > 0 and len(partitions[1]) > 0 
 
 
    def QNonNegativeEdgeWeights(self):
        """ Check that all edge-weights of edgeWeights[0] are non-negative """
        if self.NrOfEdgeWeights() > 0:
            for e in self.Edges():
                if self.edgeWeights[0][e] < 0:
                    return False
        return True
 
    def About(self, graphName=""):
        """ Return string containing HTML code providing information
            about the graph
 
        """
        unknownProps = []
        knownProps = ""
        for name in  gProperty.keys():
            value = self.Property(name)
            if value == 'Unknown':
                unknownProps.append(gProperty[name][2])
            else:
                if gProperty[name][0] == 0:
                    if value == 1:
                        knownProps += "<li> The graph is %s.\n" % gProperty[name][2]
                    else:
                        knownProps += "<li> The graph is not %s.\n" % gProperty[name][2]
                else:
                        knownProps += "<li> The graph has %s %s.\n" % (str(value), gProperty[name][2])
 
        result = """<HTML><BODY>
        <H3>Graph information</H3>
 
        <p>The graph <tt>%s</tt> has order %d and size %d and has the following
        properties:
        <ul>
        %s
        </ul>
        </p>
 
        <p>The properties %s are unknown or undetermined.</p>
        </BODY></HTML>
        """ % (graphName, self.Order(), self.Size(), knownProps, string.join(unknownProps,', '))
        return result
 
 
 
 
 
        ################################################################################
        #
        # Induced Subgraph
        #
        ################################################################################
 
class SubGraph(Graph):
    """ Provides a subgraph, i.e., a subset of the vertices and edges 
        of a specified graph
 
        Vertices are specified via ids from its supergraph and edges via
        (tail,head)-tuples 
 
        It also keeps track of the subgraphs total weight (= sum of edge 
        weights) for weights with weightID == 0
    """
 
 
    def __init__(self,G):
        Graph.__init__(self)
        self.superGraph    = G
 
        self.embedding     = self.superGraph.embedding
        self.labeling      = self.superGraph.labeling
        self.edgeWeights   = self.superGraph.edgeWeights
 
        self.directed = self.superGraph.directed
 
        self.totalWeight   = 0
 
 
    def AddVertex(self,v):
        """ Add a vertex from the supergraph to the subgraph.
            Returns NoSuchVertexError if v does not exist in
            supergraph """
        try:
            if not v in self.vertices:
                self.vertices.append(v)
                #f = lambda x, vertexList=self.vertices: x in vertexList
                #self.adjLists[v]    = filter(f, self.superGraph.adjLists[v])
                #self.invAdjLists[v] = filter(f, self.superGraph.invAdjLists[v])
                self.adjLists[v] = []
                self.invAdjLists[v] = []
        except:
            raise NoSuchVertexError("%d is not a vertex in the supergraph" % v)
 
    def AddEdge(self,tail,head):
        """ Add an edge from the supergraph to the subgraph. Note: For undirected
            graphs the edge (tail, head) might actually be (head, tail), so we
            return the correct tail, head to caller.
 
            Will also add tail and/or head if there are not already in subgraph """
        try:
            if not self.directed:
                tail, head = self.superGraph.Edge(tail,head) 
            if not tail in self.vertices:
                self.AddVertex(tail)
            if not head in self.vertices:
                self.AddVertex(head)
            self.adjLists[tail].append(head)
            self.invAdjLists[head].append(tail)
            self.size = self.size + 1
            try:
                w = self.superGraph.edgeWeights[0][(tail,head)]
            except KeyError:
                w = 0.0 # XXX we dont have w weight for the edge. Make totalWeight configurable/subclass
            self.totalWeight += w
            return tail, head
 
        except (KeyError, NoSuchVertexError, NoSuchEdgeError):
            raise NoSuchEdgeError("(%d,%d) is not an edge in the supergraph." % (tail,head))
 
    def AddSubGraph(self,G):
        """ Add subgraph G to self. Will do nothing if self and G 
            have distinct supergraphs """
        if self.superGraph != G.superGraph:
            log.error("AddSubGraph: distinct superGraphs")
            return
        for e in G.Edges():
            self.AddEdge(e[0],e[1])
        for v in G.vertices:
            self.AddVertex(v)
 
 
    def DeleteEdge(self,tail,head):
        """ Delete edge from subgraph. Raises NoSuchEdgeError
            upon error """
        if tail in self.vertices and head in self.vertices:
            superEdge = self.superGraph.Edge(tail,head)
            self.totalWeight =  self.totalWeight - self.superGraph.edgeWeights[0][superEdge]
            self.adjLists[tail].remove(head)
            self.invAdjLists[head].remove(tail)
            self.size = self.size - 1
        else:
            raise NoSuchEdgeError("(%d,%d) is not an edge." % (tail,head))
 
    def Clear(self):
        """ Delete all vertices and edges from the subgraph. """
        self.vertices         = [] 
        self.adjLists         = {}
        self.invAdjLists      = {}   # Inverse Adjazenzlisten
        self.size = 0
        self.totalWeight   = 0
 
 
    def GetNextVertexID(self):
        """ *Internal* safeguard """
        log.error("Induced Subgraph -> GetNextVertexID should never have been called")
 
    def Weight(self):
        """ Returns the total weight (= sum of edge weights) of subgraph """
        return self.totalWeight
 
 
    def QEuclidian(self):
        """ Returns 1 if the super graph is euclidian, 0 else """
        return self.superGraph.euclidian
 
 
    def QDirected(self):
        """ Returns 1 if the super graph is directed, 0 else"""
        return self.superGraph.directed
 
    def QEdge(self,tail,head):
        """ Returns 1 if (tail,head) is an edge in G """
        if not tail in self.vertices or not head in self.vertices:
            return 0
        if self.directed == 1:	
            return head in self.adjLists[tail]
        else: 
            return head in self.adjLists[tail] or tail in self.adjLists[head]