# Implement the section IV in Puzis 2012 paper
# straight_lineent the section IV in Puzis 2012 paper
# Heuristic Betweenness Centrality - Partitioning to Bi-connected Components

import os
import sys
import pprint
import networkx as nx
import betweenness_centrality as centrality
import utility
from pdb import set_trace as debugger

MAIN_CODE_DIR = os.environ.get('MAIN_CODE_DIR', '')


class HeuristicBetweennessCentrality():
    def __init__(self, subgraphs, bicomponents, cutpoints, num_vertices, link_weight, traffic_matrix):
        self.subgraphs = subgraphs
        self.bicomponents = bicomponents
        self.cutpoints = cutpoints
        self.num_vertices = num_vertices
        self.link_weight = link_weight
        self.traffic_matrix = traffic_matrix

        self.bc_components = list()
        self.calculate_bc_non_cutpoint()
        self.calculate_bc_cutpoint()

        self.bc = dict()
        self.finalize()

    def calculate_bc_non_cutpoint(self):
        """BC for non cutpoint
        """
        for i, subgraphs in enumerate(self.subgraphs):
            traffic_matrix = self.traffic_matrix[i]
            results = centrality.weight_betweenness_centrality(subgraphs, traffic_matrix)
            self.bc_components.append(results)

    def calculate_bc_cutpoint(self):
        self.bc_cutpoints = dict()

        bc_inter = dict()
        for v in self.cutpoints:
            inter = 0
            for i, comp in enumerate(self.bicomponents):
                if v in comp:
                    inter += self.link_weight.get_link_weight(i, v
                        ) * self.link_weight.get_reverse_link_weight(i, v)
            bc_inter[v] = inter

        print 'XXXX bc_components = %s' % self.bc_components
        print 'XXXX inter = %s' % bc_inter

        for v in self.cutpoints:
            bc_locally = 0
            for i, comp in enumerate(self.bicomponents):
                if v in comp:
                    bc_locally += self.bc_components[i][v]
            # self.bc_cutpoints[v] = bc_locally - bc_inter[v]
            # TODO: do not minus the bc_inter
            self.bc_cutpoints[v] = bc_locally

    def finalize(self):
        # Add the bc for non cutpoint vertices
        for bc_component in self.bc_components:
            for key, value in bc_component.iteritems():
                if key not in self.bc:
                    self.bc[key] = value

        # Add the bc for cutpoint vertices
        for key, value in self.bc_cutpoints.iteritems():
            self.bc[key] = value

        print '*** betweenness = %s' % self.bc
        # Rescale the bc according to the original graph
        factor = 1.0 / ((self.num_vertices - 1) * (self.num_vertices - 2))
        # TODO: check the scaling factor, how much should it be?
        # factor = 2.0 / (self.num_vertices*self.num_vertices - 3 * self.num_vertices + 2)
        for key, value in self.bc.iteritems():
            self.bc[key] = value * factor

    def write(self, file_suffix=''):
        filepath = '/output/heuristic_%s.csv'  % file_suffix
        with open(MAIN_CODE_DIR + filepath, 'w') as output:
            for node, centrality in self.bc.iteritems():
                output.write('%s, %s\n' % (node, centrality))

    def __str__(self):
        return str(self.bc)


class TrafficMatrix():
    def __init__(self, bicomponents, cutpoints, link_weight):
        self.bicomponents = bicomponents
        self.cutpoints = cutpoints
        self.num_components = len(bicomponents)
        self.link_weight = link_weight

        self.h = list()
        self.generate_empty_traffic_matrix()
        self.generate_traffic_matrix()

    def generate_empty_traffic_matrix(self):
        for i in range(self.num_components):
            l = len(self.bicomponents[i])
            matrix = [[1 for x in range(l)] for y in range(l)]
            # update the main diagonal
            for x in range(l):
                matrix[x][x] = 0

            self.h.append(matrix)

    def generate_traffic_matrix(self):
        # Update the value when one vertex is a cut-point, another vertex is not a cut-point
        for i, components in enumerate(self.bicomponents):
            normal_points = components.difference(self.cutpoints)
            cutpoints = self.cutpoints.intersection(components)

            for cutpoint in cutpoints:
                for normal_point in normal_points:
                    communication_intensity = self.link_weight.get_reverse_link_weight(i, cutpoint) + 1
                    self.update(i, cutpoint, normal_point, communication_intensity)

        # Update the value when both vertices are cut-points
        for i, components in enumerate(self.bicomponents):
            cutpoints = list(self.cutpoints.intersection(components))
            len_cutpoints = len(cutpoints)
            if len_cutpoints > 1:
                for k in range(len_cutpoints - 1):
                    for l in range(1, len_cutpoints):
                        if k == l:
                            continue
                        communication_intensity = (
                            self.link_weight.get_reverse_link_weight(i, cutpoints[k]) + 1) * (
                            self.link_weight.get_reverse_link_weight(i, cutpoints[l]) + 1
                        )
                        self.update(i, cutpoints[k], cutpoints[l], communication_intensity)

    def simple_update(self, comp_index, x_pos, y_pos, value):
        self.h[comp_index][x_pos][y_pos] = value
        # to keep the symmetric property of Traffic Matrix
        self.h[comp_index][y_pos][x_pos] = value

    def update(self, comp_index, x, y, value):
        comp = sorted(self.bicomponents[comp_index])
        try:
            x_pos = list(comp).index(x)
            y_pos = list(comp).index(y)
        except:
            debugger()
            a = 2

        self.simple_update(comp_index, x_pos, y_pos, value)

    def __str__(self):
        return str(self.h)

    def __getitem__(self, key):
        return self.h[key]


class LinkWeight():
    def __init__(self, graph, bicomponents, cutpoints):
        self.num_vertices = nx.number_of_nodes(graph)
        self.bicomponents = bicomponents
        self.num_components = len(bicomponents)
        self.cutpoints = cutpoints

        self.Dv_B = [dict() for i in range(self.num_components)] # link weight
        self.compute_component_tree_weight()

        self.reverse_Dv_B = [dict() for i in range(self.num_components)] # reverse link weight
        self.generate_reverse_link_weight()

    def _components_sharing_cutpoint(self, B_cutpoints, point):
        indices = list()
        for i, cp in enumerate(B_cutpoints):
            if point in cp:
                indices.append(i)

        return indices

    def get_link_weight(self, comp_index, point):
        Dv_B_comp = self.Dv_B[comp_index]

        if point in Dv_B_comp:
            return Dv_B_comp[point]
        else:
            return 0

    def set_link_weight(self, comp_index, point, value):
        self.Dv_B[comp_index][point] = value

    def get_reverse_link_weight(self, comp_index, point):
        reverse_Dv_B_comp = self.reverse_Dv_B[comp_index]

        if point in reverse_Dv_B_comp:
            return reverse_Dv_B_comp[point]
        else:
            return 0

    def generate_link_weight(self):
        # How many cutpoints does this component have
        B_plus_v = list()
        B_cutpoints = list() # number of cutpoints in component B
        for comp in self.bicomponents:
            points = comp.intersection(self.cutpoints)
            B_plus_v.append(comp.difference(points))
            B_cutpoints.append(points)

        len_B_plus_v = [len(x) for x in B_plus_v]
        len_B_cutpoints = [len(x) for x in B_cutpoints]

        # Calculate the Dv_B

        # For the leaf in the block-cut tree
        level = 1
        for (i, cp) in enumerate(B_cutpoints):
            if len_B_cutpoints[i] == level:
                point = list(cp)[0] # there is only 1 element
                self.Dv_B[i][point] = len_B_plus_v[i]

        # For other nodes in the block-cut tree
        level += 1
        while level <= max(len_B_cutpoints):
            if level == 3:
                debugger()
            for (i, cp) in enumerate(B_cutpoints):
                if len_B_cutpoints[i] == level:

                    for point in cp:
                        # 1st way
                        shared_comp_indices = self._components_sharing_cutpoint(B_cutpoints, point)
                        shared_comp_indices.remove(i)
                        weight_shared_comp = list()

                        for index in shared_comp_indices:
                            weight_shared_comp.append(self.get_link_weight(index, point))

                        weight = self.num_vertices - 1 - sum(weight_shared_comp)

                        self.Dv_B[i][point] = weight

            level += 1

    def generate_reverse_link_weight(self):
        for i, Dv_B_i in enumerate(self.Dv_B):
            for key, value in Dv_B_i.iteritems():
                self.reverse_Dv_B[i][key] = self.num_vertices - 1 - self.get_link_weight(i, key)

    def compute_component_tree_weight(self):
        """Follows exactly the Algorithm 1 [Puzis 2012]
        """
        B_cutpoints = list() # number of cutpoints in component B
        for comp in self.bicomponents:
            points = comp.intersection(self.cutpoints)
            B_cutpoints.append(points)

        Q = self._inititalize_component_tree_weight()
        while Q:
            pair = Q.pop(0)
            if pair['type'] == 'component_vertex_pair':
                B_index = pair['value'][0]
                v = pair['value'][1]
                size = len(self.bicomponents[B_index]) - 1;
                all_cutpoints = self.bicomponents[B_index].intersection(self.cutpoints)
                all_cutpoints.remove(v)

                for cp in all_cutpoints:
                    if self.get_link_weight(B_index, cp) != -1:
                        size += self.num_vertices - self.get_link_weight(B_index, cp) - 1

                link_weight = size
                self._verify_link_weight(B_index, v, link_weight)
                self.set_link_weight(B_index, v, link_weight)

                # update Q
                Q = self._find_unknown_weight_wrt_cutpoint(v, Q)

            if pair['type'] == 'vertex_component_pair':
                size = 0
                B_index = pair['value'][0]
                v = pair['value'][1]
                shared_comp_indices = self._components_sharing_cutpoint(B_cutpoints, v)
                shared_comp_indices.remove(B_index)


                for i in shared_comp_indices:
                    if self.get_link_weight(i, v) != - 1:
                        size += self.get_link_weight(i, v)

                link_weight = self.num_vertices - 1 - size
                self._verify_link_weight(B_index, v, link_weight)
                self.set_link_weight(B_index, v, link_weight)

                # update Q
                Q = self._find_unknown_weight_wrt_component(B_index, Q)

    def _verify_link_weight(self, B_index, v, value):
        """ If the old_value exist in self.Dv_B, then it must be equal to new value

        Otherwise, do nothing
        """
        old_value = self.get_link_weight(B_index, v)

        if old_value != -1: # -1 is unknown
            if old_value != value:
                print "BUGS FOUND in _verify_link_weight()"
                sys.exit()


    def _inititalize_component_tree_weight(self):
        Q = []
        for i, comp in enumerate(self.bicomponents):
            current_cutpoints = self.cutpoints.intersection(comp)
            if len(current_cutpoints) == 1:
                Q.append({
                    'type': 'component_vertex_pair',
                    'value': (i, list(current_cutpoints)[0]) # (B_i, cutpoint) = (i-th component, the cutpoint name)
                    })
            for cp in current_cutpoints:
                self.set_link_weight(i, cp, -1)
        return Q

    def _find_unknown_weight_wrt_cutpoint(self, cutpoint, Q):
        # Cut-point v such that the weights of all but one of its links in T are already computed.
        num_of_uncomputed_weight = 0
        uncomputed_component_index = []

        for i, Dv_B_comp in enumerate(self.Dv_B):
            if cutpoint in Dv_B_comp:
                if Dv_B_comp[cutpoint] == -1:
                    num_of_uncomputed_weight += 1
                    uncomputed_component_index.append(i)
        if num_of_uncomputed_weight == 1:
            pair = {
                'type': 'vertex_component_pair',
                'value': (uncomputed_component_index.pop(), cutpoint)
            }
            Q.append(pair)
        return Q

    def _find_unknown_weight_wrt_component(self, comp_index, Q):
        # Component B such that weights of all but one of its links in T are already computed.
        Dv_B_comp = self.Dv_B[comp_index]
        values = Dv_B_comp.values()

        # Check if -1 value appear only 1 time
        flag = False
        minus_one_value = [x for x in values if x == -1]
        if len(minus_one_value) == 1:
            for cp, value in Dv_B_comp.iteritems():
                if value == -1:
                    pair = {
                        'type': 'component_vertex_pair',
                        'value': (comp_index, cp)
                    }
                    Q.append(pair)
        return Q

    def __str__(self):
        return str(self.Dv_B)

def analyse_biconnected_component(graph):
    bicomponents = list(nx.biconnected_components(graph))
    print bicomponents
    print [len(x) for x in bicomponents]

def find_heuristic_bc(filepath):
    filename = os.path.splitext(os.path.basename(filepath))[0]

    pp = pprint.PrettyPrinter(indent=4)

    graph = nx.read_weighted_edgelist(filepath)

    if not nx.is_connected(graph):
        print "Graph is not connected"
        # sys.exit()
    else:
        print "Graph is connected"

    # Find biconnected components
    analyse_biconnected_component(graph)

    subgraphs = list(nx.biconnected_component_subgraphs(graph))
    bicomponents = list(nx.biconnected_components(graph))
    component_edges = list(nx.biconnected_component_edges(graph))
    cutpoints = set(nx.articulation_points(graph))

    num_vertices = nx.number_of_nodes(graph)

    lw = LinkWeight(graph, bicomponents, cutpoints)

    tm = TrafficMatrix(bicomponents, cutpoints, lw)

    bc = HeuristicBetweennessCentrality(subgraphs, bicomponents, cutpoints, num_vertices, lw, tm)
    bc.write(file_suffix)
    print bc

def test_isomorphic_graphs(filepath1, filepath2):
    graph1 = nx.read_weighted_edgelist(filepath1)
    graph2 = nx.read_weighted_edgelist(filepath2)
    print "Isomorphic = %s" % nx.is_isomorphic(graph1, graph2)


if __name__ == '__main__':
    utility.initialize()
    f1 = MAIN_CODE_DIR + '/input/9_vertices_green.edges'
    f2 = MAIN_CODE_DIR + '/input/9_vertices_blue.edges'
    test_isomorphic_graphs(f1, f2)

    # filepath = MAIN_CODE_DIR + '/input/simple_house.edges'
    # filepath = MAIN_CODE_DIR + '/input/simple2.edges'
    # filepath = MAIN_CODE_DIR + '/input/simple.edges'
    # filepath = MAIN_CODE_DIR + '/input/ninux_simplified.edges'
    # filepath = MAIN_CODE_DIR + '/input/ninux_simplified_connected.edges'
    # filepath = MAIN_CODE_DIR + '/input/ninux_simplified_connected2.edges'
    # filepath = MAIN_CODE_DIR + '/input/ninux_simplified_connected3.edges'
    # filepath = MAIN_CODE_DIR + '/input/9_vertices_green.edges'
    # filepath = MAIN_CODE_DIR + '/input/9_vertices_blue.edges'
    # filepath = MAIN_CODE_DIR + '/input/simple_loop.edges'
    # filepath = MAIN_CODE_DIR + '/input/straight_line.edges'
    # filepath = MAIN_CODE_DIR + '/input/ninux_connected.edges'
    # filepath = MAIN_CODE_DIR + '/input/ninux_unweighted.edges'
    # filepath = MAIN_CODE_DIR + '/input/ninux_unweighted_simplified.edges'
    # filepath = MAIN_CODE_DIR + '/input/ninux_unweighted_simplified_connected.edges'
    # filepath = MAIN_CODE_DIR + '/input/simple3.edges'
    # filepath = MAIN_CODE_DIR + '/input/simple4.edges'
    # filepath = MAIN_CODE_DIR + '/input/simple5.edges'

    filepath = MAIN_CODE_DIR + '/input/ninux.edges'
    file_suffix = 'edge_list'

    # Weight betweenness centrality
    utility.weight_betweenness_centrality(filepath, file_suffix)

    # Brandess betweenness centrality
    utility.brandes_betweenness_centrality(filepath, file_suffix)

    # Heuristic BC
    find_heuristic_bc(filepath)