# -*- coding: utf-8 -*-
"""Swap edges in a graph.
"""
#    Copyright (C) 2004-2016 by
#    Aric Hagberg <hagberg@lanl.gov>
#    Dan Schult <dschult@colgate.edu>
#    Pieter Swart <swart@lanl.gov>
#    All rights reserved.
#    BSD license.
from __future__ import division

import math
import random

import networkx as nx

__author__ = "\n".join(['Aric Hagberg (hagberg@lanl.gov)',
                        'Pieter Swart (swart@lanl.gov)',
                        'Dan Schult (dschult@colgate.edu)',
                        'Joel Miller (joel.c.miller.research@gmail.com)',
                        'Ben Edwards'])

__all__ = ['double_edge_swap',
           'connected_double_edge_swap']


def double_edge_swap(G, nswap=1, max_tries=100):
    """Swap two edges in the graph while keeping the node degrees fixed.

    A double-edge swap removes two randomly chosen edges u-v and x-y
    and creates the new edges u-x and v-y::

     u--v            u  v
            becomes  |  |
     x--y            x  y

    If either the edge u-x or v-y already exist no swap is performed
    and another attempt is made to find a suitable edge pair.

    Parameters
    ----------
    G : graph
       An undirected graph

    nswap : integer (optional, default=1)
       Number of double-edge swaps to perform

    max_tries : integer (optional)
       Maximum number of attempts to swap edges

    Returns
    -------
    G : graph
       The graph after double edge swaps.

    Notes
    -----
    Does not enforce any connectivity constraints.

    The graph G is modified in place.
    """
    if G.is_directed():
        raise nx.NetworkXError(\
            "double_edge_swap() not defined for directed graphs.")
    if nswap>max_tries:
        raise nx.NetworkXError("Number of swaps > number of tries allowed.")
    if len(G) < 4:
        raise nx.NetworkXError("Graph has less than four nodes.")
    # Instead of choosing uniformly at random from a generated edge list,
    # this algorithm chooses nonuniformly from the set of nodes with
    # probability weighted by degree.
    n=0
    swapcount=0
    keys,degrees = zip(*G.degree()) # keys, degree
    cdf=nx.utils.cumulative_distribution(degrees)  # cdf of degree
    while swapcount < nswap:
#        if random.random() < 0.5: continue # trick to avoid periodicities?
        # pick two random edges without creating edge list
        # choose source node indices from discrete distribution
        (ui,xi)=nx.utils.discrete_sequence(2,cdistribution=cdf)
        if ui==xi:
            continue # same source, skip
        u=keys[ui] # convert index to label
        x=keys[xi]
        # choose target uniformly from neighbors
        v=random.choice(list(G[u]))
        y=random.choice(list(G[x]))
        if v==y:
            continue # same target, skip
        if (x not in G[u]) and (y not in G[v]): # don't create parallel edges
            G.add_edge(u,x)
            G.add_edge(v,y)
            G.remove_edge(u,v)
            G.remove_edge(x,y)
            swapcount+=1
        if n >= max_tries:
            e=('Maximum number of swap attempts (%s) exceeded '%n +
            'before desired swaps achieved (%s).'%nswap)
            raise nx.NetworkXAlgorithmError(e)
        n+=1
    return G


def connected_double_edge_swap(G, nswap=1, _window_threshold=3):
    """Attempts the specified number of double-edge swaps in the graph `G`.

    A double-edge swap removes two randomly chosen edges `(u, v)` and `(x,
    y)` and creates the new edges `(u, x)` and `(v, y)`::

     u--v            u  v
            becomes  |  |
     x--y            x  y

    If either `(u, x)` or `(v, y)` already exist, then no swap is performed
    so the actual number of swapped edges is always *at most* `nswap`.

    Parameters
    ----------
    G : graph
       An undirected graph

    nswap : integer (optional, default=1)
       Number of double-edge swaps to perform

    _window_threshold : integer

       The window size below which connectedness of the graph will be checked
       after each swap.

       The "window" in this function is a dynamically updated integer that
       represents the number of swap attempts to make before checking if the
       graph remains connected. It is an optimization used to decrease the
       running time of the algorithm in exchange for increased complexity of
       implementation.

       If the window size is below this threshold, then the algorithm checks
       after each swap if the graph remains connected by checking if there is a
       path joining the two nodes whose edge was just removed. If the window
       size is above this threshold, then the algorithm performs do all the
       swaps in the window and only then check if the graph is still connected.

    Returns
    -------
    int
       The number of successful swaps

    Raises
    ------

    NetworkXError

       If the input graph is not connected, or if the graph has fewer than four
       nodes.

    Notes
    -----

    The initial graph `G` must be connected, and the resulting graph is
    connected. The graph `G` is modified in place.

    References
    ----------
    .. [1] C. Gkantsidis and M. Mihail and E. Zegura,
           The Markov chain simulation method for generating connected
           power law random graphs, 2003.
           http://citeseer.ist.psu.edu/gkantsidis03markov.html
    """
    if not nx.is_connected(G):
        raise nx.NetworkXError("Graph not connected")
    if len(G) < 4:
        raise nx.NetworkXError("Graph has less than four nodes.")
    n = 0
    swapcount = 0
    deg = G.degree()
    # Label key for nodes
    dk = list(n for n, d in G.degree())
    cdf = nx.utils.cumulative_distribution(list(d for n, d in G.degree()))
    window = 1
    while n < nswap:
        wcount = 0
        swapped = []
        # If the window is small, we just check each time whether the graph is
        # connected by checking if the nodes that were just separated are still
        # connected.
        if window < _window_threshold:
            # This Boolean keeps track of whether there was a failure or not.
            fail = False
            while wcount < window and n < nswap:
                # Pick two random edges without creating the edge list. Choose
                # source nodes from the discrete degree distribution.
                (ui, xi) = nx.utils.discrete_sequence(2, cdistribution=cdf)
                # If the source nodes are the same, skip this pair.
                if ui == xi:
                    continue
                # Convert an index to a node label.
                u = dk[ui]
                x = dk[xi]
                # Choose targets uniformly from neighbors.
                v = random.choice(list(G.neighbors(u)))
                y = random.choice(list(G.neighbors(x)))
                # If the target nodes are the same, skip this pair.
                if v == y:
                    continue
                if x not in G[u] and y not in G[v]:
                    G.remove_edge(u, v)
                    G.remove_edge(x, y)
                    G.add_edge(u, x)
                    G.add_edge(v, y)
                    swapped.append((u, v, x, y))
                    swapcount += 1
                n += 1
                # If G remains connected...
                if nx.has_path(G, u, v):
                    wcount += 1
                # Otherwise, undo the changes.
                else:
                    G.add_edge(u, v)
                    G.add_edge(x, y)
                    G.remove_edge(u, x)
                    G.remove_edge(v, y)
                    swapcount -= 1
                    fail = True
            # If one of the swaps failed, reduce the window size.
            if fail:
                window = int(math.ceil(window / 2))
            else:
                window += 1
        # If the window is large, then there is a good chance that a bunch of
        # swaps will work. It's quicker to do all those swaps first and then
        # check if the graph remains connected.
        else:
            while wcount < window and n < nswap:
                # Pick two random edges without creating the edge list. Choose
                # source nodes from the discrete degree distribution.
                (ui, xi) = nx.utils.discrete_sequence(2, cdistribution=cdf)
                # If the source nodes are the same, skip this pair.
                if ui == xi:
                    continue
                # Convert an index to a node label.
                u = dk[ui]
                x = dk[xi]
                # Choose targets uniformly from neighbors.
                v = random.choice(list(G.neighbors(u)))
                y = random.choice(list(G.neighbors(x)))
                # If the target nodes are the same, skip this pair.
                if v == y:
                    continue
                if x not in G[u] and y not in G[v]:
                    G.remove_edge(u, v)
                    G.remove_edge(x, y)
                    G.add_edge(u, x)
                    G.add_edge(v, y)
                    swapped.append((u, v, x, y))
                    swapcount += 1
                n += 1
                wcount += 1
            # If the graph remains connected, increase the window size.
            if nx.is_connected(G):
                window += 1
            # Otherwise, undo the changes from the previous window and decrease
            # the window size.
            else:
                while swapped:
                    (u, v, x, y) = swapped.pop()
                    G.add_edge(u, v)
                    G.add_edge(x, y)
                    G.remove_edge(u, x)
                    G.remove_edge(v, y)
                    swapcount -= 1
                window = int(math.ceil(window / 2))
    return swapcount
