from collections import Mapping, Sequence, OrderedDict
from fractions import Fraction
from portability import reprlib
from util import contains_duplicates, measure_stride, minmax


class CatalogBuilder:
    """Use a catalog builder to construct optimised, immutable mappings.

    A CatalogBuilder is useful when, depending on the particular keys and
    values used, a more compact or efficient representation of the mapping
    is possible than, say, a regular dictionary. The CatalogBuilder
    accumulates values and then, once all values have been added, analyzes
    the keys and values to produce a more optimized representation of the
    mapping.
    """

    def __init__(self, mapping=None):
        """Initialize a Catalog Builder.

        Args:
            mapping: An optional mapping (such as a dictionary) of items.
        """
        self._catalog = []
        if mapping is not None:
            for key, value in mapping.items():
                self.add(key, value)

    def add(self, index, value):
        """Add an item.

        Each index must be unique if create() is to be subsequently
        called successfully, although duplicate index values will be
        accepted by this call without complaint.

        """
        self._catalog.append((index, value))

    def create(self):
        """Create a possibly more optimized representation of the mapping.

        In this worst case, this method returns an object which is
        essentially an immutable dictionary. In the best case, the
        space savings can be vast.

        Returns:
            A mapping, if a unique mapping from indexes to values is
            possible, otherwise None.

        """

        # This method examines the contents of the mapping using
        # various heuristics to come up with a better representation.

        if len(self._catalog) < 2:
            return DictionaryCatalog(self._catalog)

        # In-place sort by index
        self._catalog.sort(key=lambda index_value: index_value[0])

        if contains_duplicates(index for index, value in self._catalog):
            return None

        if all(isinstance(index, Sequence) and (len(index) == 2)
               for index, value in self._catalog):
            return self._create_catalog_2()

        return self._create_catalog_1()

    def _create_catalog_1(self):
        """Create a catalog for one-dimensional integer keys (i.e. scalars)
        """
        index_min = self._catalog[0][0]
        index_max = self._catalog[-1][0]
        index_stride = measure_stride(index for index, value in self._catalog)

        if index_stride is None:
            # Dictionary strategy - arbitrary keys and values
            return DictionaryCatalog(self._catalog)

        self._catalog.sort(key=lambda index_value: index_value[1])
        value_min = self._catalog[0][1]
        value_max = self._catalog[-1][1]
        value_stride = measure_stride(value for index, value in self._catalog)

        if index_stride is not None and value_stride == 0:
            assert value_min == value_max
            return RegularConstantCatalog(index_min,
                                          index_max,
                                          index_stride,
                                          value_min)

        if index_stride is None and value_stride == 0:
            assert value_min == value_max
            return ConstantCatalog(
                    (index for index, value in self._catalog),
                    value_min)

        if index_stride is not None and value_stride is None:
            # Regular index - regular keys and arbitrary values
            return RegularCatalog(index_min,
                                  index_max,
                                  index_stride,
                                  (value for index, value in self._catalog))

        assert (index_stride is not None) and (value_stride is not None)
        catalog = LinearRegularCatalog(index_min,
                                       index_max,
                                       index_stride,
                                       value_min,
                                       value_max,
                                       value_stride)
        return catalog

    def _create_catalog_2(self):
        """Create a catalog for two-dimensional integer keys.

        Each key must be a two-element sequence.
        """
        i_min, i_max = minmax(i for (i, j), value in self._catalog)
        j_min, j_max = minmax(j for (i, j), value in self._catalog)

        is_rm, diff = self._is_row_major(i_min, j_min, j_max)
        if is_rm:
            return RowMajorCatalog(i_min, i_max, j_min, j_max, diff)
        return DictionaryCatalog(self._catalog)

    def _is_row_major(self, i_min, j_min, j_max):
        """Does row major ordering predict values from keys?

        Args:
            i_min: The minimum i value.
            j_min: The minimum j value.
            j_max: The maximum j value.

        Returns:
            A 2-tuple containing, in the first element True if the values can
            be predicted from the keys by assuming a row-major ordering,
            otherwise False. If True, the second element will be a constant
            offset, otherwise it can be ignored.
        """
        diff = None
        for (i, j), actual_value in self._catalog:
            proposed_value = (i - i_min) * j_max + (j - j_min)
            current_diff = actual_value - proposed_value
            if diff is None:
                diff = current_diff
            if current_diff != diff:
                return False, None
        return True, diff


class RowMajorCatalog(Mapping):
    """A mapping which assumes a row-major ordering of a two-dimensional matrix.

    This is the ordering of items in a two-dimensional matrix where in
    the (i, j) key tuple the j value changes fastest when iterating
    through the items in order.

    A RowMajorCatalog predicts the value v from the key (i, j) according to the
    following formula:

        v = (i - i_min) * j_max + (j - j_min) + c

    for
        i_min <= i <= i_max
        j_min <= j <= j_max

    and where c is an integer constant to allow zero- or one-based indexing.
    """

    def __init__(self, i_min, i_max, j_min, j_max, c):
        """Initialize a RowMajorCatalog.

        Args:
            i_min (int): The minimum i value.
            i_max (int): The maximum i value.
            j_min (int): The minimum j value.
            j_max (int): The maximum j value.
            c (int): The constant offset
        """
        self._i_min = i_min
        self._i_max = i_max
        self._j_min = j_min
        self._j_max = j_max
        self._c = c

    @property
    def i_min(self):
        """Minimum i value"""
        return self._i_min

    @property
    def i_max(self):
        """Maximum i value"""
        return self._i_max

    @property
    def j_min(self):
        """Minimum j value"""
        return self._j_min

    @property
    def j_max(self):
        """Maximum j value"""
        return self._j_max

    def min(self):
        """Minimum (i, j) value"""
        return self._i_min, self._j_min

    def max(self):
        """Maximum (i, j) value"""
        return self._j_min, self._j_max

    def __getitem__(self, key):
        i, j = key
        if not (self._i_min <= i <= self._i_max) and \
               (self._j_min <= j <= self._j_max):
            raise KeyError("{!r} key {!r} out of range".format(self, key))
        value = (i - self._i_min) * self._j_max + (j - self._j_min) + self._c
        return value

    def __contains__(self, key):
        i, j = key
        return (self._i_min <= i <= self._i_max) and \
               (self._j_min <= j <= self._j_max)

    def __len__(self):
        return (self._i_max - self._i_min) * (self._j_max - self._j_min)

    def __iter__(self):
        for i in range(self._i_min, self._i_max + 1):
            for j in range(self._j_min, self._j_max + 1):
                yield (i, j)

    def __repr__(self):
        return '{}({}, {}, {}, {}, {})'.format(
            self.__class__.__name__,
            self._i_min, self._i_max, self._j_min, self._j_max, self._c)


class DictionaryCatalog(Mapping):
    """An immutable, ordered, dictionary mapping.
    """

    def __init__(self, items):
        self._items = OrderedDict(items)

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

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

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

    def __contains__(self, item):
        return item in self._items

    def __repr__(self):
        return '{}({})'.format(
            self.__class__.__name__, reprlib.repr(self._items.items()))


class RegularConstantCatalog(Mapping):
    """Mapping with keys ordered with regular spacing along the number line.

    The values associated with the keys are constant.
    """

    def __init__(self, key_min, key_max, key_stride, value):
        """Initialize a RegularConstantCatalog.

        The catalog is initialized by a description of how the keys
        are distributed along the number line, and a value which
        corresponds with all keys.

        Args:
            key_min: The minimum key.
            key_max: The maximum key.
            key_stride: The difference between successive keys.
            value: A value associated with all keys.
        """
        key_range = key_max - key_min
        if key_range % key_stride != 0:
            raise ValueError("RegularIndex key range {!r} is not "
                             "a multiple of stride {!r}".format(
                                 key_stride, key_range))
        self._key_min = key_min
        self._key_max = key_max
        self._key_stride = key_stride
        self._value = value

    def __getitem__(self, key):
        if key not in self:
            raise KeyError("{!r} does not contain key {!r}".format(self, key))
        return self._value

    def __len__(self):
        return 1 + (self._key_max - self._key_min) / self._key_stride

    def __contains__(self, key):
        return (self._key_min <= key <= self._key_max) and \
               ((key - self._key_min) % self._key_stride == 0)

    def __iter__(self):
        return iter(range(self._key_min,
                          self._key_max + 1,
                          self._key_stride))

    def __repr__(self):
        return '{}({}, {}, {}, {})'.format(
            self.__class__.__name__,
            self._key_min,
            self._key_max,
            self._key_stride,
            self._value)


class ConstantCatalog(Mapping):
    """Mapping with keys ordered with regular spacing along the number line.

    The values associated with the keys are constant.
    """

    def __init__(self, keys, value):
        """Initialize a RegularConstantCatalog.

        The catalog is initialized by a description with an iterable series of
        keys and a constant value to be associated with all the keys.

        Args:
            keys: An iterable series of distinct keys.
            key_max: The maximum key.
            key_stride: The difference between successive keys.
            value: A value associated with all keys.
        """
        self._items = frozenset(keys)
        self._value = value

    def __getitem__(self, key):
        if key not in self:
            raise KeyError("{!r} does not contain key {!r}".format(self, key))
        return self._value

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

    def __contains__(self, key):
        return key in self._items

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

    def __repr__(self):
        return '{}({}, {})'.format(
            self.__class__.__name__,
            reprlib.repr(self._items),
            self._value)


class RegularCatalog(Mapping):
    """Mapping with keys ordered with regular spacing along the number line.

    The values associated with the keys are arbitrary.
    """

    def __init__(self, key_min, key_max, key_stride, values):
        """Initialize a RegularCatalog.

        The catalog is initialized by a description of how the keys
        are distributed along the number line, and an iterable series of
        corresponding values.

        Args:
            key_min: The minimum key.
            key_max: The maximum key.
            key_stride: The difference between successive keys.
            values: An iterable series of values corresponding to the keys.

        Raises:
            ValueError: There is any inconsistency in the keys, stride,
                and/or values.
        """
        key_range = key_max - key_min
        if key_range % key_stride != 0:
            raise ValueError("RegularIndex key range {!r} is not "
                             "a multiple of stride {!r}".format(
                                 key_stride, key_range))
        self._key_min = key_min
        self._key_max = key_max
        self._key_stride = key_stride
        self._values = list(values)
        num_keys = key_range // key_stride
        if num_keys != len(self._values):
            raise ValueError("RegularIndex key range and values inconsistent")

    def __getitem__(self, key):
        if not (self._key_min <= key <= self._key_max):
            raise KeyError("{!r} key {!r} out of range".format(self, key))
        offset = key - self._key_min
        if offset % self._key_stride != 0:
            raise KeyError("{!r} does not contain key {!r}".format(self, key))
        index = offset // self._key_stride
        return self._values[index]

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

    def __contains__(self, key):
        return (self._key_min <= key <= self._key_max) and \
               ((key - self._key_min) % self._key_stride == 0)

    def __iter__(self):
        return iter(range(self._key_min,
                          self._key_max + 1,
                          self._key_stride))

    def __repr__(self):
        return '{}({}, {}, {}, {})'.format(
            self.__class__.__name__,
            self._key_min,
            self._key_max,
            self._key_stride,
            reprlib.repr(self._values))


class LinearRegularCatalog(Mapping):
    """A mapping which assumes a linear relationship between keys and values.

    This is the ordering of items in a two-dimensional matrix where in
    the (i, j) key tuple the j value changes fastest when iterating
    through the items in order.

    A LinearRegularCatalog predicts the value v from the key according to the
    following formula:

        v = (value_max - value_min) / (key_max - key_min) * (key - key_min) + value_min
    """

    def __init__(self,
                 key_min,
                 key_max,
                 key_stride,
                 value_min,
                 value_max,
                 value_stride):
        """Initialize a LinearRegularCatalog.

        Args:
            key_min: The minimum key.
            key_max: The maximum key.
            key_stride: The difference between successive keys.
            value_min: The minimum value.
            value_max: The maximum value.

        Raises:
            ValueError: There is any inconsistency in the keys, strides,
                and/or values.
        """
        key_range = key_max - key_min
        if key_range % key_stride != 0:
            raise ValueError("{} key range {!r} is not "
                             "a multiple of key stride {!r}".format(
                                 self.__class__.__name__,
                                 key_stride,
                                 key_range))
        self._key_min = key_min
        self._key_max = key_max
        self._key_stride = key_stride

        value_range = value_max - value_min
        if value_range % value_stride != 0:
            raise ValueError("{} value range {!r} is not "
                             "a multiple of value stride {!r}".format(
                                 self.__class__.__name__,
                                 value_stride,
                                 value_range))
        self._value_min = value_min
        self._value_max = value_max
        self._value_stride = value_stride

        num_keys = (self._key_max - self._key_min) // self._key_stride
        num_values = (self._value_max - self._value_min) // self._value_stride
        if num_keys != num_values:
            raise ValueError("{} inconsistent number of "
                             "keys {} and values {}".format(
                                 self.__class__.__name__,
                                 num_keys,
                                 num_values))

        self._m = Fraction(self._value_max - self._value_min,
                           self._key_max - self._key_min)

    def __getitem__(self, key):
        if not (self._key_min <= key <= self._key_max):
            raise KeyError("{!r} key {!r} out of range".format(self, key))
        offset = key - self._key_min
        if offset % self._key_stride != 0:
            raise KeyError("{!r} does not contain key {!r}".format(self, key))

        v = self._m * (key - self._key_min) + self._value_min
        assert v.denominator == 1
        return v.numerator

    def __len__(self):
        return 1 + (self._key_max - self._key_min) // self._key_stride

    def __contains__(self, key):
        return (self._key_min <= key <= self._key_max) and \
               ((key - self._key_min) % self._key_stride == 0)

    def __iter__(self):
        return iter(range(self._key_min, self._key_max + 1, self._key_stride))

    def __repr__(self):
        return '{}({}, {}, {}, {}, {}, {})'.format(
            self.__class__.__name__,
            self._key_min,
            self._key_max,
            self._key_stride,
            self._value_min,
            self._value_max,
            self._value_stride)