# Source code for deap.tools.support

    from bisect import bisect_right
    from collections import defaultdict
    from copy import deepcopy
    from functools import partial
    from itertools import chain
    from operator import eq

    def identity(obj):
        """Returns directly the argument *obj*.
        """
        return obj

    class History(object):
        """The :class:`History` class helps to build a genealogy of all the
        individuals produced in the evolution. It contains two attributes,
        the :attr:`genealogy_tree` that is a dictionary of lists indexed by
        individual, the list contain the indices of the parents. The second
        attribute :attr:`genealogy_history` contains every individual indexed
        by their individual number as in the genealogy tree.

        The produced genealogy tree is compatible with `NetworkX
        <http://networkx.lanl.gov/index.html>`_, here is how to plot the genealogy
        tree ::

            history = History()

            # Decorate the variation operators
            toolbox.decorate("mate", history.decorator)
            toolbox.decorate("mutate", history.decorator)

            # Create the population and populate the history
            population = toolbox.population(n=POPSIZE)
            history.update(population)

            # Do the evolution, the decorators will take care of updating the
            # history
            # [...]

            import matplotlib.pyplot as plt
            import networkx

            graph = networkx.DiGraph(history.genealogy_tree)
            graph = graph.reverse()     # Make the graph top-down
            colors = [toolbox.evaluate(history.genealogy_history[i])[0] for i in graph]
            networkx.draw(graph, node_color=colors)
            plt.show()

        Using NetworkX in combination with `pygraphviz
        <http://networkx.lanl.gov/pygraphviz/>`_ (dot layout) this amazing
        genealogy tree can be obtained from the OneMax example with a population
        size of 20 and 5 generations, where the color of the nodes indicate their
        fitness, blue is low and red is high.

        .. image:: /_images/genealogy.png
           :width: 67%

        .. note::
           The genealogy tree might get very big if your population and/or the
           number of generation is large.

        """
        def __init__(self):
            self.genealogy_index = 0
            self.genealogy_history = dict()
            self.genealogy_tree = dict()

        def update(self, individuals):
            """Update the history with the new *individuals*. The index present in
            their :attr:`history_index` attribute will be used to locate their
            parents, it is then modified to a unique one to keep track of those
            new individuals. This method should be called on the individuals after
            each variation.

            :param individuals: The list of modified individuals that shall be
                                inserted in the history.

            If the *individuals* do not have a :attr:`history_index` attribute,
            the attribute is added and this individual is considered as having no
            parent. This method should be called with the initial population to
            initialize the history.

            Modifying the internal :attr:`genealogy_index` of the history or the
            :attr:`history_index` of an individual may lead to unpredictable
            results and corruption of the history.
            """
            try:
                parent_indices = tuple(ind.history_index for ind in individuals)
            except AttributeError:
                parent_indices = tuple()

            for ind in individuals:
                self.genealogy_index += 1
                ind.history_index = self.genealogy_index
                self.genealogy_history[self.genealogy_index] = deepcopy(ind)
                self.genealogy_tree[self.genealogy_index] = parent_indices

        @property
        def decorator(self):
            """Property that returns an appropriate decorator to enhance the
            operators of the toolbox. The returned decorator assumes that the
            individuals are returned by the operator. First the decorator calls
            the underlying operation and then calls the :func:`update` function
            with what has been returned by the operator. Finally, it returns the
            individuals with their history parameters modified according to the
            update function.
            """
            def decFunc(func):
                def wrapFunc(*args, **kargs):
                    individuals = func(*args, **kargs)
                    self.update(individuals)
                    return individuals
                return wrapFunc
            return decFunc

        def getGenealogy(self, individual, max_depth=float("inf")):
            """Provide the genealogy tree of an *individual*. The individual must
            have an attribute :attr:`history_index` as defined by
            :func:`~deap.tools.History.update` in order to retrieve its associated
            genealogy tree. The returned graph contains the parents up to
            *max_depth* variations before this individual. If not provided
            the maximum depth is up to the beginning of the evolution.

            :param individual: The individual at the root of the genealogy tree.
            :param max_depth: The approximate maximum distance between the root
                              (individual) and the leaves (parents), optional.
            :returns: A dictionary where each key is an individual index and the
                      values are a tuple corresponding to the index of the parents.
            """
            gtree = {}
            visited = set()     # Adds memory to the breadth first search

            def genealogy(index, depth):
                if index not in self.genealogy_tree:
                    return
                depth += 1
                if depth > max_depth:
                    return
                parent_indices = self.genealogy_tree[index]
                gtree[index] = parent_indices
                for ind in parent_indices:
                    if ind not in visited:
                        genealogy(ind, depth)
                    visited.add(ind)
            genealogy(individual.history_index, 0)
            return gtree

    class Statistics(object):
        """Object that compiles statistics on a list of arbitrary objects.
        When created the statistics object receives a *key* argument that
        is used to get the values on which the function will be computed.
        If not provided the *key* argument defaults to the identity function.

        The value returned by the key may be a multi-dimensional object, i.e.:
        a tuple or a list, as long as the statistical function registered
        support it. So for example, statistics can be computed directly on
        multi-objective fitnesses when using numpy statistical function.

        :param key: A function to access the values on which to compute the
                    statistics, optional.

        ::

            >>> import numpy
            >>> s = Statistics()
            >>> s.register("mean", numpy.mean)
            >>> s.register("max", max)
            >>> s.compile([1, 2, 3, 4])     # doctest: +SKIP
            {'max': 4, 'mean': 2.5}
            >>> s.compile([5, 6, 7, 8])     # doctest: +SKIP
            {'mean': 6.5, 'max': 8}
        """
        def __init__(self, key=identity):
            self.key = key
            self.functions = dict()
            self.fields = []

        def register(self, name, function, *args, **kargs):
            """Register a *function* that will be applied on the sequence each
            time :meth:`record` is called.

            :param name: The name of the statistics function as it would appear
                         in the dictionary of the statistics object.
            :param function: A function that will compute the desired statistics
                             on the data as preprocessed by the key.
            :param argument: One or more argument (and keyword argument) to pass
                             automatically to the registered function when called,
                             optional.
            """
            self.functions[name] = partial(function, *args, **kargs)
            self.fields.append(name)

        def compile(self, data):
            """Apply to the input sequence *data* each registered function
            and return the results as a dictionary.

            :param data: Sequence of objects on which the statistics are computed.
            """
            values = tuple(self.key(elem) for elem in data)

            entry = dict()
            for key, func in self.functions.items():
                entry[key] = func(values)
            return entry

    class MultiStatistics(dict):
        """Dictionary of :class:`Statistics` object allowing to compute
        statistics on multiple keys using a single call to :meth:`compile`. It
        takes a set of key-value pairs associating a statistics object to a
        unique name. This name can then be used to retrieve the statistics object.

        The following code computes statistics simultaneously on the length and
        the first value of the provided objects.
        ::

            >>> from operator import itemgetter
            >>> import numpy
            >>> len_stats = Statistics(key=len)
            >>> itm0_stats = Statistics(key=itemgetter(0))
            >>> mstats = MultiStatistics(length=len_stats, item=itm0_stats)
            >>> mstats.register("mean", numpy.mean, axis=0)
            >>> mstats.register("max", numpy.max, axis=0)
            >>> mstats.compile([[0.0, 1.0, 1.0, 5.0], [2.0, 5.0]])  # doctest: +SKIP
            {'length': {'mean': 3.0, 'max': 4}, 'item': {'mean': 1.0, 'max': 2.0}}
        """

        def compile(self, data):
            """Calls :meth:`Statistics.compile` with *data* of each
            :class:`Statistics` object.

            :param data: Sequence of objects on which the statistics are computed.
            """
            record = {}
            for name, stats in self.items():
                record[name] = stats.compile(data)
            return record

        @property
        def fields(self):
            return sorted(self.keys())

        def register(self, name, function, *args, **kargs):
            """Register a *function* in each :class:`Statistics` object.

            :param name: The name of the statistics function as it would appear
                         in the dictionary of the statistics object.
            :param function: A function that will compute the desired statistics
                             on the data as preprocessed by the key.
            :param argument: One or more argument (and keyword argument) to pass
                             automatically to the registered function when called,
                             optional.
            """
            for stats in self.values():
                stats.register(name, function, *args, **kargs)

    class Logbook(list):
        """Evolution records as a chronological list of dictionaries.

        Data can be retrieved via the :meth:`select` method given the appropriate
        names.

        The :class:`Logbook` class may also contain other logbooks referred to
        as chapters. Chapters are used to store information associated to a
        specific part of the evolution. For example when computing statistics
        on different components of individuals (namely :class:`MultiStatistics`),
        chapters can be used to distinguish the average fitness and the average
        size.
        """

        def __init__(self):
            self.buffindex = 0
            self.chapters = defaultdict(Logbook)
            """Dictionary containing the sub-sections of the logbook which are also
            :class:`Logbook`. Chapters are automatically created when the right hand
            side of a keyworded argument, provided to the *record* function, is a
            dictionary. The keyword determines the chapter's name. For example, the
            following line adds a new chapter "size" that will contain the fields
            "max" and "mean". ::

                logbook.record(gen=0, size={'max' : 10.0, 'mean' : 7.5})

            To access a specific chapter, use the name of the chapter as a
            dictionary key. For example, to access the size chapter and select
            the mean use ::

                logbook.chapters["size"].select("mean")

            Compiling a :class:`MultiStatistics` object returns a dictionary
            containing dictionaries, therefore when recording such an object in a
            logbook using the keyword argument unpacking operator (**), chapters
            will be automatically added to the logbook.
            ::

                >>> fit_stats = Statistics(key=attrgetter("fitness.values"))
                >>> size_stats = Statistics(key=len)
                >>> mstats = MultiStatistics(fitness=fit_stats, size=size_stats)
                >>> # [...]
                >>> record = mstats.compile(population)
                >>> logbook.record(**record)
                >>> print logbook
                  fitness          length
                ------------    ------------
                max     mean    max     mean
                2       1       4       3

            """

            self.columns_len = None
            self.header = None
            """Order of the columns to print when using the :data:`stream` and
            :meth:`__str__` methods. The syntax is a single iterable containing
            string elements. For example, with the previously
            defined statistics class, one can print the generation and the
            fitness average, and maximum with
            ::

                logbook.header = ("gen", "mean", "max")

            If not set the header is built with all fields, in arbitrary order
            on insertion of the first data. The header can be removed by setting
            it to :data:`None`.
            """

            self.log_header = True
            """Tells the log book to output or not the header when streaming the
            first line or getting its entire string representation. This defaults
            :data:`True`.
            """

        def record(self, **infos):
            """Enter a record of event in the logbook as a list of key-value pairs.
            The information are appended chronologically to a list as a dictionary.
            When the value part of a pair is a dictionary, the information contained
            in the dictionary are recorded in a chapter entitled as the name of the
            key part of the pair. Chapters are also Logbook.
            """
            apply_to_all = {k: v for k, v in infos.items() if not isinstance(v, dict)}
            for key, value in list(infos.items()):
                if isinstance(value, dict):
                    chapter_infos = value.copy()
                    chapter_infos.update(apply_to_all)
                    self.chapters[key].record(**chapter_infos)
                    del infos[key]
            self.append(infos)

        def select(self, *names):
            """Return a list of values associated to the *names* provided
            in argument in each dictionary of the Statistics object list.
            One list per name is returned in order.
            ::

                >>> log = Logbook()
                >>> log.record(gen=0, mean=5.4, max=10.0)
                >>> log.record(gen=1, mean=9.4, max=15.0)
                >>> log.select("mean")
                [5.4, 9.4]
                >>> log.select("gen", "max")
                ([0, 1], [10.0, 15.0])

            With a :class:`MultiStatistics` object, the statistics for each
            measurement can be retrieved using the :data:`chapters` member :
            ::

                >>> log = Logbook()
                >>> log.record(**{'gen': 0, 'fit': {'mean': 0.8, 'max': 1.5},
                ... 'size': {'mean': 25.4, 'max': 67}})
                >>> log.record(**{'gen': 1, 'fit': {'mean': 0.95, 'max': 1.7},
                ... 'size': {'mean': 28.1, 'max': 71}})
                >>> log.chapters['size'].select("mean")
                [25.4, 28.1]
                >>> log.chapters['fit'].select("gen", "max")
                ([0, 1], [1.5, 1.7])
            """
            if len(names) == 1:
                return [entry.get(names[0], None) for entry in self]
            return tuple([entry.get(name, None) for entry in self] for name in names)

        @property
        def stream(self):
            """Retrieve the formatted not streamed yet entries of the database
            including the headers.
            ::

                >>> log = Logbook()
                >>> log.append({'gen' : 0})
                >>> print log.stream  # doctest: +NORMALIZE_WHITESPACE
                gen
                0
                >>> log.append({'gen' : 1})
                >>> print log.stream  # doctest: +NORMALIZE_WHITESPACE
                1
            """
            startindex, self.buffindex = self.buffindex, len(self)
            return self.__str__(startindex)

        def __delitem__(self, key):
            if isinstance(key, slice):
                for i, in range(*key.indices(len(self))):
                    self.pop(i)
                    for chapter in self.chapters.values():
                        chapter.pop(i)
            else:
                self.pop(key)
                for chapter in self.chapters.values():
                    chapter.pop(key)

        def pop(self, index=0):
            """Retrieve and delete element *index*. The header and stream will be
            adjusted to follow the modification.

            :param item: The index of the element to remove, optional. It defaults
                         to the first element.

            You can also use the following syntax to delete elements.
            ::

                del log[0]
                del log[1::5]
            """
            if index < self.buffindex:
                self.buffindex -= 1
            return super(self.__class__, self).pop(index)

        def __txt__(self, startindex):
            columns = self.header
            if not columns:
                columns = sorted(self[0].keys()) + sorted(self.chapters.keys())
            if not self.columns_len or len(self.columns_len) != len(columns):
                self.columns_len = [len(c) for c in columns]

            chapters_txt = {}
            offsets = defaultdict(int)
            for name, chapter in self.chapters.items():
                chapters_txt[name] = chapter.__txt__(startindex)
                if startindex == 0:
                    offsets[name] = len(chapters_txt[name]) - len(self)

            str_matrix = []
            for i, line in enumerate(self[startindex:]):
                str_line = []
                for j, name in enumerate(columns):
                    if name in chapters_txt:
                        column = chapters_txt[name][i + offsets[name]]
                    else:
                        value = line.get(name, "")
                        string = "{0:n}" if isinstance(value, float) else "{0}"
                        column = string.format(value)
                    self.columns_len[j] = max(self.columns_len[j], len(column))
                    str_line.append(column)
                str_matrix.append(str_line)

            if startindex == 0 and self.log_header:
                header = []
                nlines = 1
                if len(self.chapters) > 0:
                    nlines += max(map(len, chapters_txt.values())) - len(self) + 1
                header = [[] for i in range(nlines)]
                for j, name in enumerate(columns):
                    if name in chapters_txt:
                        length = max(len(line.expandtabs()) for line in chapters_txt[name])
                        blanks = nlines - 2 - offsets[name]
                        for i in range(blanks):
                            header[i].append(" " * length)
                        header[blanks].append(name.center(length))
                        header[blanks + 1].append("-" * length)
                        for i in range(offsets[name]):
                            header[blanks + 2 + i].append(chapters_txt[name][i])
                    else:
                        length = max(len(line[j].expandtabs()) for line in str_matrix)
                        for line in header[:-1]:
                            line.append(" " * length)
                        header[-1].append(name)
                str_matrix = chain(header, str_matrix)

            template = "\t".join("{%i:<%i}" % (i, l) for i, l in enumerate(self.columns_len))
            text = [template.format(*line) for line in str_matrix]

            return text

        def __str__(self, startindex=0):
            text = self.__txt__(startindex)
            return "\n".join(text)

    class HallOfFame(object):
        """The hall of fame contains the best individual that ever lived in the
        population during the evolution. It is lexicographically sorted at all
        time so that the first element of the hall of fame is the individual that
        has the best first fitness value ever seen, according to the weights
        provided to the fitness at creation time.

        The insertion is made so that old individuals have priority on new
        individuals. A single copy of each individual is kept at all time, the
        equivalence between two individuals is made by the operator passed to the
        *similar* argument.

        :param maxsize: The maximum number of individual to keep in the hall of
                        fame.
        :param similar: An equivalence operator between two individuals, optional.
                        It defaults to operator :func:`operator.eq`.

        The class :class:`HallOfFame` provides an interface similar to a list
        (without being one completely). It is possible to retrieve its length, to
        iterate on it forward and backward and to get an item or a slice from it.
        """
        def __init__(self, maxsize, similar=eq):
            self.maxsize = maxsize
            self.keys = list()
            self.items = list()
            self.similar = similar

        def update(self, population):
            """Update the hall of fame with the *population* by replacing the
            worst individuals in it by the best individuals present in
            *population* (if they are better). The size of the hall of fame is
            kept constant.

            :param population: A list of individual with a fitness attribute to
                               update the hall of fame with.
            """
            for ind in population:
                if len(self) == 0 and self.maxsize != 0:
                    # Working on an empty hall of fame is problematic for the
                    # "for else"
                    self.insert(population[0])
                    continue
                if ind.fitness > self[-1].fitness or len(self) < self.maxsize:
                    for hofer in self:
                        # Loop through the hall of fame to check for any
                        # similar individual
                        if self.similar(ind, hofer):
                            break
                    else:
                        # The individual is unique and strictly better than
                        # the worst
                        if len(self) >= self.maxsize:
                            self.remove(-1)
                        self.insert(ind)

        def insert(self, item):
            """Insert a new individual in the hall of fame using the
            :func:`~bisect.bisect_right` function. The inserted individual is
            inserted on the right side of an equal individual. Inserting a new
            individual in the hall of fame also preserve the hall of fame's order.
            This method **does not** check for the size of the hall of fame, in a
            way that inserting a new individual in a full hall of fame will not
            remove the worst individual to maintain a constant size.

            :param item: The individual with a fitness attribute to insert in the
                         hall of fame.
            """
            item = deepcopy(item)
            i = bisect_right(self.keys, item.fitness)
            self.items.insert(len(self) - i, item)
            self.keys.insert(i, item.fitness)

        def remove(self, index):
            """Remove the specified *index* from the hall of fame.

            :param index: An integer giving which item to remove.
            """
            del self.keys[len(self) - (index % len(self) + 1)]
            del self.items[index]

        def clear(self):
            """Clear the hall of fame."""
            del self.items[:]
            del self.keys[:]

        def __len__(self):
            return len(self.items)

        def __getitem__(self, i):
            return self.items[i]

        def __iter__(self):
            return iter(self.items)

        def __reversed__(self):
            return reversed(self.items)

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

    class ParetoFront(HallOfFame):
        """The Pareto front hall of fame contains all the non-dominated individuals
        that ever lived in the population. That means that the Pareto front hall of
        fame can contain an infinity of different individuals.

        :param similar: A function that tells the Pareto front whether or not two
                        individuals are similar, optional.

        The size of the front may become very large if it is used for example on
        a continuous function with a continuous domain. In order to limit the number
        of individuals, it is possible to specify a similarity function that will
        return :data:`True` if the genotype of two individuals are similar. In that
        case only one of the two individuals will be added to the hall of fame. By
        default the similarity function is :func:`operator.eq`.

        Since, the Pareto front hall of fame inherits from the :class:`HallOfFame`,
        it is sorted lexicographically at every moment.
        """
        def __init__(self, similar=eq):
            HallOfFame.__init__(self, None, similar)

        def update(self, population):
            """Update the Pareto front hall of fame with the *population* by adding
            the individuals from the population that are not dominated by the hall
            of fame. If any individual in the hall of fame is dominated it is
            removed.

            :param population: A list of individual with a fitness attribute to
                               update the hall of fame with.
            """
            for ind in population:
                is_dominated = False
                dominates_one = False
                has_twin = False
                to_remove = []
                for i, hofer in enumerate(self):    # hofer = hall of famer
                    if not dominates_one and hofer.fitness.dominates(ind.fitness):
                        is_dominated = True
                        break
                    elif ind.fitness.dominates(hofer.fitness):
                        dominates_one = True
                        to_remove.append(i)
                    elif ind.fitness == hofer.fitness and self.similar(ind, hofer):
                        has_twin = True
                        break

                for i in reversed(to_remove):       # Remove the dominated hofer
                    self.remove(i)
                if not is_dominated and not has_twin:
                    self.insert(ind)

    __all__ = ['HallOfFame', 'ParetoFront', 'History', 'Statistics', 'MultiStatistics', 'Logbook']

    if __name__ == "__main__":
        import doctest

        doctest.run_docstring_examples(Statistics, globals())
        doctest.run_docstring_examples(Statistics.register, globals())
        doctest.run_docstring_examples(Statistics.compile, globals())

        doctest.run_docstring_examples(MultiStatistics, globals())
        doctest.run_docstring_examples(MultiStatistics.register, globals())
        doctest.run_docstring_examples(MultiStatistics.compile, globals())