"""Sorted list implementation.
"""
# pylint: disable=redefined-builtin, ungrouped-imports
from __future__ import print_function
from bisect import bisect_left, bisect_right, insort
from collections import Sequence, MutableSequence
from functools import wraps
from itertools import chain, repeat, starmap
from math import log as log_e
import operator as op
from operator import iadd, add
from sys import hexversion
if hexversion < 0x03000000:
from itertools import izip as zip
from itertools import imap as map
try:
from thread import get_ident
except ImportError:
from dummy_thread import get_ident
else:
from functools import reduce
try:
from _thread import get_ident
except ImportError:
from _dummy_thread import get_ident # pylint: disable=import-error
def recursive_repr(func):
"""Decorator to prevent infinite repr recursion."""
repr_running = set()
@wraps(func)
def wrapper(self):
"Return ellipsis on recursive re-entry to function."
key = id(self), get_ident()
if key in repr_running:
return '...'
repr_running.add(key)
try:
return func(self)
finally:
repr_running.discard(key)
return wrapper
class SortedList(MutableSequence):
"""
SortedList provides most of the same methods as a list but keeps the items
in sorted order.
"""
def __init__(self, iterable=None, load=1000):
"""
SortedList provides most of the same methods as a list but keeps the
items in sorted order.
An optional *iterable* provides an initial series of items to populate
the SortedList.
An optional *load* specifies the load-factor of the list. The default
load factor of '1000' works well for lists from tens to tens of millions
of elements. Good practice is to use a value that is the cube root of
the list size. With billions of elements, the best load factor depends
on your usage. It's best to leave the load factor at the default until
you start benchmarking.
"""
self._len = 0
self._lists = []
self._maxes = []
self._index = []
self._load = load
self._twice = load * 2
self._half = load >> 1
self._offset = 0
if iterable is not None:
self._update(iterable)
def __new__(cls, iterable=None, key=None, load=1000):
"""
SortedList provides most of the same methods as a list but keeps the
items in sorted order.
An optional *iterable* provides an initial series of items to populate
the SortedList.
An optional *key* argument will return an instance of subtype
SortedListWithKey.
An optional *load* specifies the load-factor of the list. The default
load factor of '1000' works well for lists from tens to tens of millions
of elements. Good practice is to use a value that is the cube root of
the list size. With billions of elements, the best load factor depends
on your usage. It's best to leave the load factor at the default until
you start benchmarking.
"""
# pylint: disable=unused-argument
if key is None:
return object.__new__(cls)
else:
if cls is SortedList:
return object.__new__(SortedListWithKey)
else:
raise TypeError('inherit SortedListWithKey for key argument')
def clear(self):
"""Remove all the elements from the list."""
self._len = 0
del self._lists[:]
del self._maxes[:]
del self._index[:]
_clear = clear
def add(self, val):
"""Add the element *val* to the list."""
_lists = self._lists
_maxes = self._maxes
if _maxes:
pos = bisect_right(_maxes, val)
if pos == len(_maxes):
pos -= 1
_lists[pos].append(val)
_maxes[pos] = val
else:
insort(_lists[pos], val)
self._expand(pos)
else:
_lists.append([val])
_maxes.append(val)
self._len += 1
def _expand(self, pos):
"""Splits sublists that are more than double the load level.
Updates the index when the sublist length is less than double the load
level. This requires incrementing the nodes in a traversal from the
leaf node to the root. For an example traversal see self._loc.
"""
_lists = self._lists
_index = self._index
if len(_lists[pos]) > self._twice:
_maxes = self._maxes
_load = self._load
_lists_pos = _lists[pos]
half = _lists_pos[_load:]
del _lists_pos[_load:]
_maxes[pos] = _lists_pos[-1]
_lists.insert(pos + 1, half)
_maxes.insert(pos + 1, half[-1])
del _index[:]
else:
if _index:
child = self._offset + pos
while child:
_index[child] += 1
child = (child - 1) >> 1
_index[0] += 1
def update(self, iterable):
"""Update the list by adding all elements from *iterable*."""
_lists = self._lists
_maxes = self._maxes
values = sorted(iterable)
if _maxes:
if len(values) * 4 >= self._len:
values.extend(chain.from_iterable(_lists))
values.sort()
self._clear()
else:
_add = self.add
for val in values:
_add(val)
return
_load = self._load
_lists.extend(values[pos:(pos + _load)]
for pos in range(0, len(values), _load))
_maxes.extend(sublist[-1] for sublist in _lists)
self._len = len(values)
del self._index[:]
_update = update
def __contains__(self, val):
"""Return True if and only if *val* is an element in the list."""
_maxes = self._maxes
if not _maxes:
return False
pos = bisect_left(_maxes, val)
if pos == len(_maxes):
return False
_lists = self._lists
idx = bisect_left(_lists[pos], val)
return _lists[pos][idx] == val
def discard(self, val):
"""
Remove the first occurrence of *val*.
If *val* is not a member, does nothing.
"""
_maxes = self._maxes
if not _maxes:
return
pos = bisect_left(_maxes, val)
if pos == len(_maxes):
return
_lists = self._lists
idx = bisect_left(_lists[pos], val)
if _lists[pos][idx] == val:
self._delete(pos, idx)
def remove(self, val):
"""
Remove first occurrence of *val*.
Raises ValueError if *val* is not present.
"""
_maxes = self._maxes
if not _maxes:
raise ValueError('{0} not in list'.format(repr(val)))
pos = bisect_left(_maxes, val)
if pos == len(_maxes):
raise ValueError('{0} not in list'.format(repr(val)))
_lists = self._lists
idx = bisect_left(_lists[pos], val)
if _lists[pos][idx] == val:
self._delete(pos, idx)
else:
raise ValueError('{0} not in list'.format(repr(val)))
def _delete(self, pos, idx):
"""Delete the item at the given (pos, idx).
Combines lists that are less than half the load level.
Updates the index when the sublist length is more than half the load
level. This requires decrementing the nodes in a traversal from the leaf
node to the root. For an example traversal see self._loc.
"""
_lists = self._lists
_maxes = self._maxes
_index = self._index
_lists_pos = _lists[pos]
del _lists_pos[idx]
self._len -= 1
len_lists_pos = len(_lists_pos)
if len_lists_pos > self._half:
_maxes[pos] = _lists_pos[-1]
if _index:
child = self._offset + pos
while child > 0:
_index[child] -= 1
child = (child - 1) >> 1
_index[0] -= 1
elif len(_lists) > 1:
if not pos:
pos += 1
prev = pos - 1
_lists[prev].extend(_lists[pos])
_maxes[prev] = _lists[prev][-1]
del _lists[pos]
del _maxes[pos]
del _index[:]
self._expand(prev)
elif len_lists_pos:
_maxes[pos] = _lists_pos[-1]
else:
del _lists[pos]
del _maxes[pos]
del _index[:]
def _loc(self, pos, idx):
"""Convert an index pair (alpha, beta) into a single index that corresponds to
the position of the value in the sorted list.
Most queries require the index be built. Details of the index are
described in self._build_index.
Indexing requires traversing the tree from a leaf node to the root. The
parent of each node is easily computable at (pos - 1) // 2.
Left-child nodes are always at odd indices and right-child nodes are
always at even indices.
When traversing up from a right-child node, increment the total by the
left-child node.
The final index is the sum from traversal and the index in the sublist.
For example, using the index from self._build_index:
_index = 14 5 9 3 2 4 5
_offset = 3
Tree:
14
5 9
3 2 4 5
Converting index pair (2, 3) into a single index involves iterating like
so:
1. Starting at the leaf node: offset + alpha = 3 + 2 = 5. We identify
the node as a left-child node. At such nodes, we simply traverse to
the parent.
2. At node 9, position 2, we recognize the node as a right-child node
and accumulate the left-child in our total. Total is now 5 and we
traverse to the parent at position 0.
3. Iteration ends at the root.
Computing the index is the sum of the total and beta: 5 + 3 = 8.
"""
if not pos:
return idx
_index = self._index
if not _index:
self._build_index()
total = 0
# Increment pos to point in the index to len(self._lists[pos]).
pos += self._offset
# Iterate until reaching the root of the index tree at pos = 0.
while pos:
# Right-child nodes are at odd indices. At such indices
# account the total below the left child node.
if not pos & 1:
total += _index[pos - 1]
# Advance pos to the parent node.
pos = (pos - 1) >> 1
return total + idx
def _pos(self, idx):
"""Convert an index into a pair (alpha, beta) that can be used to access
the corresponding _lists[alpha][beta] position.
Most queries require the index be built. Details of the index are
described in self._build_index.
Indexing requires traversing the tree to a leaf node. Each node has
two children which are easily computable. Given an index, pos, the
left-child is at pos * 2 + 1 and the right-child is at pos * 2 + 2.
When the index is less than the left-child, traversal moves to the
left sub-tree. Otherwise, the index is decremented by the left-child
and traversal moves to the right sub-tree.
At a child node, the indexing pair is computed from the relative
position of the child node as compared with the offset and the remaining
index.
For example, using the index from self._build_index:
_index = 14 5 9 3 2 4 5
_offset = 3
Tree:
14
5 9
3 2 4 5
Indexing position 8 involves iterating like so:
1. Starting at the root, position 0, 8 is compared with the left-child
node (5) which it is greater than. When greater the index is
decremented and the position is updated to the right child node.
2. At node 9 with index 3, we again compare the index to the left-child
node with value 4. Because the index is the less than the left-child
node, we simply traverse to the left.
3. At node 4 with index 3, we recognize that we are at a leaf node and
stop iterating.
4. To compute the sublist index, we subtract the offset from the index
of the leaf node: 5 - 3 = 2. To compute the index in the sublist, we
simply use the index remaining from iteration. In this case, 3.
The final index pair from our example is (2, 3) which corresponds to
index 8 in the sorted list.
"""
if idx < 0:
last_len = len(self._lists[-1])
if (-idx) <= last_len:
return len(self._lists) - 1, last_len + idx
idx += self._len
if idx < 0:
raise IndexError('list index out of range')
elif idx >= self._len:
raise IndexError('list index out of range')
if idx < len(self._lists[0]):
return 0, idx
_index = self._index
if not _index:
self._build_index()
pos = 0
child = 1
len_index = len(_index)
while child < len_index:
index_child = _index[child]
if idx < index_child:
pos = child
else:
idx -= index_child
pos = child + 1
child = (pos << 1) + 1
return (pos - self._offset, idx)
def _build_index(self):
"""Build an index for indexing the sorted list.
Indexes are represented as binary trees in a dense array notation
similar to a binary heap.
For example, given a _lists representation storing integers:
[0]: 1 2 3
[1]: 4 5
[2]: 6 7 8 9
[3]: 10 11 12 13 14
The first transformation maps the sub-lists by their length. The
first row of the index is the length of the sub-lists.
[0]: 3 2 4 5
Each row after that is the sum of consecutive pairs of the previous row:
[1]: 5 9
[2]: 14
Finally, the index is built by concatenating these lists together:
_index = 14 5 9 3 2 4 5
An offset storing the start of the first row is also stored:
_offset = 3
When built, the index can be used for efficient indexing into the list.
See the comment and notes on self._pos for details.
"""
row0 = list(map(len, self._lists))
if len(row0) == 1:
self._index[:] = row0
self._offset = 0
return
head = iter(row0)
tail = iter(head)
row1 = list(starmap(add, zip(head, tail)))
if len(row0) & 1:
row1.append(row0[-1])
if len(row1) == 1:
self._index[:] = row1 + row0
self._offset = 1
return
size = 2 ** (int(log_e(len(row1) - 1, 2)) + 1)
row1.extend(repeat(0, size - len(row1)))
tree = [row0, row1]
while len(tree[-1]) > 1:
head = iter(tree[-1])
tail = iter(head)
row = list(starmap(add, zip(head, tail)))
tree.append(row)
reduce(iadd, reversed(tree), self._index)
self._offset = size * 2 - 1
def __delitem__(self, idx):
"""Remove the element at *idx*. Supports slicing."""
if isinstance(idx, slice):
start, stop, step = idx.indices(self._len)
if step == 1 and start < stop:
if start == 0 and stop == self._len:
return self._clear()
elif self._len <= 8 * (stop - start):
values = self._getitem(slice(None, start))
if stop < self._len:
values += self._getitem(slice(stop, None))
self._clear()
return self._update(values)
indices = range(start, stop, step)
# Delete items from greatest index to least so
# that the indices remain valid throughout iteration.
if step > 0:
indices = reversed(indices)
_pos, _delete = self._pos, self._delete
for index in indices:
pos, idx = _pos(index)
_delete(pos, idx)
else:
pos, idx = self._pos(idx)
self._delete(pos, idx)
_delitem = __delitem__
def __getitem__(self, idx):
"""Return the element at *idx*. Supports slicing."""
_lists = self._lists
if isinstance(idx, slice):
start, stop, step = idx.indices(self._len)
if step == 1 and start < stop:
if start == 0 and stop == self._len:
return reduce(iadd, self._lists, [])
start_pos, start_idx = self._pos(start)
if stop == self._len:
stop_pos = len(_lists) - 1
stop_idx = len(_lists[stop_pos])
else:
stop_pos, stop_idx = self._pos(stop)
if start_pos == stop_pos:
return _lists[start_pos][start_idx:stop_idx]
prefix = _lists[start_pos][start_idx:]
middle = _lists[(start_pos + 1):stop_pos]
result = reduce(iadd, middle, prefix)
result += _lists[stop_pos][:stop_idx]
return result
if step == -1 and start > stop:
result = self._getitem(slice(stop + 1, start + 1))
result.reverse()
return result
# Return a list because a negative step could
# reverse the order of the items and this could
# be the desired behavior.
indices = range(start, stop, step)
return list(self._getitem(index) for index in indices)
else:
if self._len:
if idx == 0:
return _lists[0][0]
elif idx == -1:
return _lists[-1][-1]
else:
raise IndexError('list index out of range')
if 0 <= idx < len(_lists[0]):
return _lists[0][idx]
len_last = len(_lists[-1])
if -len_last < idx < 0:
return _lists[-1][len_last + idx]
pos, idx = self._pos(idx)
return _lists[pos][idx]
_getitem = __getitem__
def _check_order(self, idx, val):
_len = self._len
_lists = self._lists
pos, loc = self._pos(idx)
if idx < 0:
idx += _len
# Check that the inserted value is not less than the
# previous value.
if idx > 0:
idx_prev = loc - 1
pos_prev = pos
if idx_prev < 0:
pos_prev -= 1
idx_prev = len(_lists[pos_prev]) - 1
if _lists[pos_prev][idx_prev] > val:
msg = '{0} not in sort order at index {1}'.format(repr(val), idx)
raise ValueError(msg)
# Check that the inserted value is not greater than
# the previous value.
if idx < (_len - 1):
idx_next = loc + 1
pos_next = pos
if idx_next == len(_lists[pos_next]):
pos_next += 1
idx_next = 0
if _lists[pos_next][idx_next] < val:
msg = '{0} not in sort order at index {1}'.format(repr(val), idx)
raise ValueError(msg)
def __setitem__(self, index, value):
"""Replace item at position *index* with *value*.
Supports slice notation. Raises :exc:`ValueError` if the sort order
would be violated. When used with a slice and iterable, the
:exc:`ValueError` is raised before the list is mutated if the sort
order would be violated by the operation.
"""
_lists = self._lists
_maxes = self._maxes
_check_order = self._check_order
_pos = self._pos
if isinstance(index, slice):
_len = self._len
start, stop, step = index.indices(_len)
indices = range(start, stop, step)
# Copy value to avoid aliasing issues with self and cases where an
# iterator is given.
values = tuple(value)
if step != 1:
if len(values) != len(indices):
raise ValueError(
'attempt to assign sequence of size %s'
' to extended slice of size %s'
% (len(values), len(indices)))
# Keep a log of values that are set so that we can
# roll back changes if ordering is violated.
log = []
_append = log.append
for idx, val in zip(indices, values):
pos, loc = _pos(idx)
_append((idx, _lists[pos][loc], val))
_lists[pos][loc] = val
if len(_lists[pos]) == (loc + 1):
_maxes[pos] = val
try:
# Validate ordering of new values.
for idx, _, newval in log:
_check_order(idx, newval)
except ValueError:
# Roll back changes from log.
for idx, oldval, _ in log:
pos, loc = _pos(idx)
_lists[pos][loc] = oldval
if len(_lists[pos]) == (loc + 1):
_maxes[pos] = oldval
raise
else:
if start == 0 and stop == _len:
self._clear()
return self._update(values)
if stop < start:
# When calculating indices, stop may be less than start.
# For example: ...[5:3:1] results in slice(5, 3, 1) which
# is a valid but not useful stop index.
stop = start
if values:
# Check that given values are ordered properly.
alphas = iter(values)
betas = iter(values)
next(betas)
pairs = zip(alphas, betas)
if not all(alpha <= beta for alpha, beta in pairs):
raise ValueError('given values not in sort order')
# Check ordering in context of sorted list.
if start and self._getitem(start - 1) > values[0]:
message = '%s not in sort order at index %s' % (
repr(values[0]), start)
raise ValueError(message)
if stop != _len and self._getitem(stop) < values[-1]:
message = '%s not in sort order at index %s' % (
repr(values[-1]), stop)
raise ValueError(message)
# Delete the existing values.
self._delitem(index)
# Insert the new values.
_insert = self.insert
for idx, val in enumerate(values):
_insert(start + idx, val)
else:
pos, loc = _pos(index)
_check_order(index, value)
_lists[pos][loc] = value
if len(_lists[pos]) == (loc + 1):
_maxes[pos] = value
def __iter__(self):
"""
Return an iterator over the Sequence.
Iterating the Sequence while adding or deleting values may raise a
`RuntimeError` or fail to iterate over all entries.
"""
return chain.from_iterable(self._lists)
def __reversed__(self):
"""
Return an iterator to traverse the Sequence in reverse.
Iterating the Sequence while adding or deleting values may raise a
`RuntimeError` or fail to iterate over all entries.
"""
return chain.from_iterable(map(reversed, reversed(self._lists)))
def islice(self, start=None, stop=None, reverse=False):
"""
Returns an iterator that slices `self` from `start` to `stop` index,
inclusive and exclusive respectively.
When `reverse` is `True`, values are yielded from the iterator in
reverse order.
Both `start` and `stop` default to `None` which is automatically
inclusive of the beginning and end.
"""
_len = self._len
if not _len:
return iter(())
start, stop, _ = slice(start, stop).indices(self._len)
if start >= stop:
return iter(())
_pos = self._pos
min_pos, min_idx = _pos(start)
if stop == _len:
max_pos = len(self._lists) - 1
max_idx = len(self._lists[-1])
else:
max_pos, max_idx = _pos(stop)
return self._islice(min_pos, min_idx, max_pos, max_idx, reverse)
def _islice(self, min_pos, min_idx, max_pos, max_idx, reverse):
"""
Returns an iterator that slices `self` using two index pairs,
`(min_pos, min_idx)` and `(max_pos, max_idx)`; the first inclusive
and the latter exclusive. See `_pos` for details on how an index
is converted to an index pair.
When `reverse` is `True`, values are yielded from the iterator in
reverse order.
"""
_lists = self._lists
if min_pos > max_pos:
return iter(())
elif min_pos == max_pos and not reverse:
return iter(_lists[min_pos][min_idx:max_idx])
elif min_pos == max_pos and reverse:
return reversed(_lists[min_pos][min_idx:max_idx])
elif min_pos + 1 == max_pos and not reverse:
return chain(_lists[min_pos][min_idx:], _lists[max_pos][:max_idx])
elif min_pos + 1 == max_pos and reverse:
return chain(
reversed(_lists[max_pos][:max_idx]),
reversed(_lists[min_pos][min_idx:]),
)
elif not reverse:
return chain(
_lists[min_pos][min_idx:],
chain.from_iterable(_lists[(min_pos + 1):max_pos]),
_lists[max_pos][:max_idx],
)
else:
temp = map(reversed, reversed(_lists[(min_pos + 1):max_pos]))
return chain(
reversed(_lists[max_pos][:max_idx]),
chain.from_iterable(temp),
reversed(_lists[min_pos][min_idx:]),
)
def irange(self, minimum=None, maximum=None, inclusive=(True, True),
reverse=False):
"""
Create an iterator of values between `minimum` and `maximum`.
`inclusive` is a pair of booleans that indicates whether the minimum
and maximum ought to be included in the range, respectively. The
default is (True, True) such that the range is inclusive of both
minimum and maximum.
Both `minimum` and `maximum` default to `None` which is automatically
inclusive of the start and end of the list, respectively.
When `reverse` is `True` the values are yielded from the iterator in
reverse order; `reverse` defaults to `False`.
"""
_maxes = self._maxes
if not _maxes:
return iter(())
_lists = self._lists
# Calculate the minimum (pos, idx) pair. By default this location
# will be inclusive in our calculation.
if minimum is None:
min_pos = 0
min_idx = 0
else:
if inclusive[0]:
min_pos = bisect_left(_maxes, minimum)
if min_pos == len(_maxes):
return iter(())
min_idx = bisect_left(_lists[min_pos], minimum)
else:
min_pos = bisect_right(_maxes, minimum)
if min_pos == len(_maxes):
return iter(())
min_idx = bisect_right(_lists[min_pos], minimum)
# Calculate the maximum (pos, idx) pair. By default this location
# will be exclusive in our calculation.
if maximum is None:
max_pos = len(_maxes) - 1
max_idx = len(_lists[max_pos])
else:
if inclusive[1]:
max_pos = bisect_right(_maxes, maximum)
if max_pos == len(_maxes):
max_pos -= 1
max_idx = len(_lists[max_pos])
else:
max_idx = bisect_right(_lists[max_pos], maximum)
else:
max_pos = bisect_left(_maxes, maximum)
if max_pos == len(_maxes):
max_pos -= 1
max_idx = len(_lists[max_pos])
else:
max_idx = bisect_left(_lists[max_pos], maximum)
return self._islice(min_pos, min_idx, max_pos, max_idx, reverse)
def __len__(self):
"""Return the number of elements in the list."""
return self._len
def bisect_left(self, val):
"""
Similar to the *bisect* module in the standard library, this returns an
appropriate index to insert *val*. If *val* is already present, the
insertion point will be before (to the left of) any existing entries.
"""
_maxes = self._maxes
if not _maxes:
return 0
pos = bisect_left(_maxes, val)
if pos == len(_maxes):
return self._len
idx = bisect_left(self._lists[pos], val)
return self._loc(pos, idx)
def bisect_right(self, val):
"""
Same as *bisect_left*, but if *val* is already present, the insertion
point will be after (to the right of) any existing entries.
"""
_maxes = self._maxes
if not _maxes:
return 0
pos = bisect_right(_maxes, val)
if pos == len(_maxes):
return self._len
idx = bisect_right(self._lists[pos], val)
return self._loc(pos, idx)
bisect = bisect_right
_bisect_right = bisect_right
def count(self, val):
"""Return the number of occurrences of *val* in the list."""
_maxes = self._maxes
if not _maxes:
return 0
pos_left = bisect_left(_maxes, val)
if pos_left == len(_maxes):
return 0
_lists = self._lists
idx_left = bisect_left(_lists[pos_left], val)
pos_right = bisect_right(_maxes, val)
if pos_right == len(_maxes):
return self._len - self._loc(pos_left, idx_left)
idx_right = bisect_right(_lists[pos_right], val)
if pos_left == pos_right:
return idx_right - idx_left
right = self._loc(pos_right, idx_right)
left = self._loc(pos_left, idx_left)
return right - left
def copy(self):
"""Return a shallow copy of the sorted list."""
return self.__class__(self, load=self._load)
__copy__ = copy
def append(self, val):
"""
Append the element *val* to the list. Raises a ValueError if the *val*
would violate the sort order.
"""
_lists = self._lists
_maxes = self._maxes
if not _maxes:
_maxes.append(val)
_lists.append([val])
self._len = 1
return
pos = len(_lists) - 1
if val < _lists[pos][-1]:
msg = '{0} not in sort order at index {1}'.format(repr(val), self._len)
raise ValueError(msg)
_maxes[pos] = val
_lists[pos].append(val)
self._len += 1
self._expand(pos)
def extend(self, values):
"""
Extend the list by appending all elements from the *values*. Raises a
ValueError if the sort order would be violated.
"""
_lists = self._lists
_maxes = self._maxes
_load = self._load
if not isinstance(values, list):
values = list(values)
if not values:
return
if any(values[pos - 1] > values[pos]
for pos in range(1, len(values))):
raise ValueError('given sequence not in sort order')
offset = 0
if _maxes:
if values[0] < _lists[-1][-1]:
msg = '{0} not in sort order at index {1}'.format(repr(values[0]), self._len)
raise ValueError(msg)
if len(_lists[-1]) < self._half:
_lists[-1].extend(values[:_load])
_maxes[-1] = _lists[-1][-1]
offset = _load
len_lists = len(_lists)
for idx in range(offset, len(values), _load):
_lists.append(values[idx:(idx + _load)])
_maxes.append(_lists[-1][-1])
_index = self._index
if len_lists == len(_lists):
len_index = len(_index)
if len_index > 0:
len_values = len(values)
child = len_index - 1
while child:
_index[child] += len_values
child = (child - 1) >> 1
_index[0] += len_values
else:
del _index[:]
self._len += len(values)
def insert(self, idx, val):
"""
Insert the element *val* into the list at *idx*. Raises a ValueError if
the *val* at *idx* would violate the sort order.
"""
_len = self._len
_lists = self._lists
_maxes = self._maxes
if idx < 0:
idx += _len
if idx < 0:
idx = 0
if idx > _len:
idx = _len
if not _maxes:
# The idx must be zero by the inequalities above.
_maxes.append(val)
_lists.append([val])
self._len = 1
return
if not idx:
if val > _lists[0][0]:
msg = '{0} not in sort order at index {1}'.format(repr(val), 0)
raise ValueError(msg)
else:
_lists[0].insert(0, val)
self._expand(0)
self._len += 1
return
if idx == _len:
pos = len(_lists) - 1
if _lists[pos][-1] > val:
msg = '{0} not in sort order at index {1}'.format(repr(val), _len)
raise ValueError(msg)
else:
_lists[pos].append(val)
_maxes[pos] = _lists[pos][-1]
self._expand(pos)
self._len += 1
return
pos, idx = self._pos(idx)
idx_before = idx - 1
if idx_before < 0:
pos_before = pos - 1
idx_before = len(_lists[pos_before]) - 1
else:
pos_before = pos
before = _lists[pos_before][idx_before]
if before <= val <= _lists[pos][idx]:
_lists[pos].insert(idx, val)
self._expand(pos)
self._len += 1
else:
msg = '{0} not in sort order at index {1}'.format(repr(val), idx)
raise ValueError(msg)
def pop(self, idx=-1):
"""
Remove and return item at *idx* (default last). Raises IndexError if
list is empty or index is out of range. Negative indices are supported,
as for slice indices.
"""
if not self._len:
raise IndexError('pop index out of range')
_lists = self._lists
if idx == 0:
val = _lists[0][0]
self._delete(0, 0)
return val
if idx == -1:
pos = len(_lists) - 1
loc = len(_lists[pos]) - 1
val = _lists[pos][loc]
self._delete(pos, loc)
return val
if 0 <= idx < len(_lists[0]):
val = _lists[0][idx]
self._delete(0, idx)
return val
len_last = len(_lists[-1])
if -len_last < idx < 0:
pos = len(_lists) - 1
loc = len_last + idx
val = _lists[pos][loc]
self._delete(pos, loc)
return val
pos, idx = self._pos(idx)
val = _lists[pos][idx]
self._delete(pos, idx)
return val
def index(self, val, start=None, stop=None):
"""
Return the smallest *k* such that L[k] == val and i <= k < j`. Raises
ValueError if *val* is not present. *stop* defaults to the end of the
list. *start* defaults to the beginning. Negative indices are supported,
as for slice indices.
"""
# pylint: disable=arguments-differ
_len = self._len
if not _len:
raise ValueError('{0} is not in list'.format(repr(val)))
if start is None:
start = 0
if start < 0:
start += _len
if start < 0:
start = 0
if stop is None:
stop = _len
if stop < 0:
stop += _len
if stop > _len:
stop = _len
if stop <= start:
raise ValueError('{0} is not in list'.format(repr(val)))
_maxes = self._maxes
pos_left = bisect_left(_maxes, val)
if pos_left == len(_maxes):
raise ValueError('{0} is not in list'.format(repr(val)))
_lists = self._lists
idx_left = bisect_left(_lists[pos_left], val)
if _lists[pos_left][idx_left] != val:
raise ValueError('{0} is not in list'.format(repr(val)))
stop -= 1
left = self._loc(pos_left, idx_left)
if start <= left:
if left <= stop:
return left
else:
right = self._bisect_right(val) - 1
if start <= right:
return start
raise ValueError('{0} is not in list'.format(repr(val)))
def __add__(self, that):
"""
Return a new sorted list containing all the elements in *self* and
*that*. Elements in *that* do not need to be properly ordered with
respect to *self*.
"""
values = reduce(iadd, self._lists, [])
values.extend(that)
return self.__class__(values, load=self._load)
def __iadd__(self, that):
"""
Update *self* to include all values in *that*. Elements in *that* do not
need to be properly ordered with respect to *self*.
"""
self._update(that)
return self
def __mul__(self, that):
"""
Return a new sorted list containing *that* shallow copies of each item
in SortedList.
"""
values = reduce(iadd, self._lists, []) * that
return self.__class__(values, load=self._load)
def __imul__(self, that):
"""
Increase the length of the list by appending *that* shallow copies of
each item.
"""
values = reduce(iadd, self._lists, []) * that
self._clear()
self._update(values)
return self
def _make_cmp(self, seq_op, doc):
"Make comparator method."
def comparer(self, that):
"Compare method for sorted list and sequence."
# pylint: disable=protected-access
if not isinstance(that, Sequence):
return NotImplemented
self_len = self._len
len_that = len(that)
if self_len != len_that:
if seq_op is op.eq:
return False
if seq_op is op.ne:
return True
for alpha, beta in zip(self, that):
if alpha != beta:
return seq_op(alpha, beta)
return seq_op(self_len, len_that)
comparer.__name__ = '__{0}__'.format(seq_op.__name__)
doc_str = 'Return `True` if and only if Sequence is {0} `that`.'
comparer.__doc__ = doc_str.format(doc)
return comparer
__eq__ = _make_cmp(None, op.eq, 'equal to')
__ne__ = _make_cmp(None, op.ne, 'not equal to')
__lt__ = _make_cmp(None, op.lt, 'less than')
__gt__ = _make_cmp(None, op.gt, 'greater than')
__le__ = _make_cmp(None, op.le, 'less than or equal to')
__ge__ = _make_cmp(None, op.ge, 'greater than or equal to')
@recursive_repr
def __repr__(self):
"""Return string representation of sequence."""
temp = '{0}({1}, load={2})'
return temp.format(
self.__class__.__name__,
repr(list(self)),
repr(self._load)
)
def _check(self):
try:
# Check load parameters.
assert self._load >= 4
assert self._half == (self._load >> 1)
assert self._twice == (self._load * 2)
# Check empty sorted list case.
if self._maxes == []:
assert self._lists == []
return
assert len(self._maxes) > 0 and len(self._lists) > 0
# Check all sublists are sorted.
assert all(sublist[pos - 1] <= sublist[pos]
for sublist in self._lists
for pos in range(1, len(sublist)))
# Check beginning/end of sublists are sorted.
for pos in range(1, len(self._lists)):
assert self._lists[pos - 1][-1] <= self._lists[pos][0]
# Check length of _maxes and _lists match.
assert len(self._maxes) == len(self._lists)
# Check _maxes is a map of _lists.
assert all(self._maxes[pos] == self._lists[pos][-1]
for pos in range(len(self._maxes)))
# Check load level is less than _twice.
assert all(len(sublist) <= self._twice for sublist in self._lists)
# Check load level is greater than _half for all
# but the last sublist.
assert all(len(self._lists[pos]) >= self._half
for pos in range(0, len(self._lists) - 1))
# Check length.
assert self._len == sum(len(sublist) for sublist in self._lists)
# Check index.
if len(self._index):
assert len(self._index) == self._offset + len(self._lists)
assert self._len == self._index[0]
def test_offset_pos(pos):
"Test positional indexing offset."
from_index = self._index[self._offset + pos]
return from_index == len(self._lists[pos])
assert all(test_offset_pos(pos)
for pos in range(len(self._lists)))
for pos in range(self._offset):
child = (pos << 1) + 1
if child >= len(self._index):
assert self._index[pos] == 0
elif child + 1 == len(self._index):
assert self._index[pos] == self._index[child]
else:
child_sum = self._index[child] + self._index[child + 1]
assert self._index[pos] == child_sum
except:
import sys
import traceback
traceback.print_exc(file=sys.stdout)
print('len', self._len)
print('load', self._load, self._half, self._twice)
print('offset', self._offset)
print('len_index', len(self._index))
print('index', self._index)
print('len_maxes', len(self._maxes))
print('maxes', self._maxes)
print('len_lists', len(self._lists))
print('lists', self._lists)
raise
def identity(value):
"Identity function."
return value
class SortedListWithKey(SortedList):
"""
SortedListWithKey provides most of the same methods as a list but keeps
the items in sorted order.
"""
def __init__(self, iterable=None, key=identity, load=1000):
"""SortedListWithKey provides most of the same methods as list but keeps the
items in sorted order.
An optional *iterable* provides an initial series of items to populate
the SortedListWithKey.
An optional *key* argument defines a callable that, like the `key`
argument to Python's `sorted` function, extracts a comparison key from
each element. The default is the identity function.
An optional *load* specifies the load-factor of the list. The default
load factor of '1000' works well for lists from tens to tens of millions
of elements. Good practice is to use a value that is the cube root of
the list size. With billions of elements, the best load factor depends
on your usage. It's best to leave the load factor at the default until
you start benchmarking.
"""
# pylint: disable=super-init-not-called
self._len = 0
self._lists = []
self._keys = []
self._maxes = []
self._index = []
self._key = key
self._load = load
self._twice = load * 2
self._half = load >> 1
self._offset = 0
if iterable is not None:
self._update(iterable)
def __new__(cls, iterable=None, key=identity, load=1000):
return object.__new__(cls)
def clear(self):
"""Remove all the elements from the list."""
self._len = 0
del self._lists[:]
del self._keys[:]
del self._maxes[:]
del self._index[:]
_clear = clear
def add(self, val):
"""Add the element *val* to the list."""
_lists = self._lists
_keys = self._keys
_maxes = self._maxes
key = self._key(val)
if _maxes:
pos = bisect_right(_maxes, key)
if pos == len(_maxes):
pos -= 1
_lists[pos].append(val)
_keys[pos].append(key)
_maxes[pos] = key
else:
idx = bisect_right(_keys[pos], key)
_lists[pos].insert(idx, val)
_keys[pos].insert(idx, key)
self._expand(pos)
else:
_lists.append([val])
_keys.append([key])
_maxes.append(key)
self._len += 1
def _expand(self, pos):
"""Splits sublists that are more than double the load level.
Updates the index when the sublist length is less than double the load
level. This requires incrementing the nodes in a traversal from the
leaf node to the root. For an example traversal see self._loc.
"""
_lists = self._lists
_keys = self._keys
_index = self._index
if len(_keys[pos]) > self._twice:
_maxes = self._maxes
_load = self._load
_lists_pos = _lists[pos]
_keys_pos = _keys[pos]
half = _lists_pos[_load:]
half_keys = _keys_pos[_load:]
del _lists_pos[_load:]
del _keys_pos[_load:]
_maxes[pos] = _keys_pos[-1]
_lists.insert(pos + 1, half)
_keys.insert(pos + 1, half_keys)
_maxes.insert(pos + 1, half_keys[-1])
del _index[:]
else:
if _index:
child = self._offset + pos
while child:
_index[child] += 1
child = (child - 1) >> 1
_index[0] += 1
def update(self, iterable):
"""Update the list by adding all elements from *iterable*."""
_lists = self._lists
_keys = self._keys
_maxes = self._maxes
values = sorted(iterable, key=self._key)
if _maxes:
if len(values) * 4 >= self._len:
values.extend(chain.from_iterable(_lists))
values.sort(key=self._key)
self._clear()
else:
_add = self.add
for val in values:
_add(val)
return
_load = self._load
_lists.extend(values[pos:(pos + _load)]
for pos in range(0, len(values), _load))
_keys.extend(list(map(self._key, _list)) for _list in _lists)
_maxes.extend(sublist[-1] for sublist in _keys)
self._len = len(values)
del self._index[:]
_update = update
def __contains__(self, val):
"""Return True if and only if *val* is an element in the list."""
_maxes = self._maxes
if not _maxes:
return False
key = self._key(val)
pos = bisect_left(_maxes, key)
if pos == len(_maxes):
return False
_lists = self._lists
_keys = self._keys
idx = bisect_left(_keys[pos], key)
len_keys = len(_keys)
len_sublist = len(_keys[pos])
while True:
if _keys[pos][idx] != key:
return False
if _lists[pos][idx] == val:
return True
idx += 1
if idx == len_sublist:
pos += 1
if pos == len_keys:
return False
len_sublist = len(_keys[pos])
idx = 0
def discard(self, val):
"""
Remove the first occurrence of *val*.
If *val* is not a member, does nothing.
"""
_maxes = self._maxes
if not _maxes:
return
key = self._key(val)
pos = bisect_left(_maxes, key)
if pos == len(_maxes):
return
_lists = self._lists
_keys = self._keys
idx = bisect_left(_keys[pos], key)
len_keys = len(_keys)
len_sublist = len(_keys[pos])
while True:
if _keys[pos][idx] != key:
return
if _lists[pos][idx] == val:
self._delete(pos, idx)
return
idx += 1
if idx == len_sublist:
pos += 1
if pos == len_keys:
return
len_sublist = len(_keys[pos])
idx = 0
def remove(self, val):
"""
Remove first occurrence of *val*.
Raises ValueError if *val* is not present.
"""
_maxes = self._maxes
if not _maxes:
raise ValueError('{0} not in list'.format(repr(val)))
key = self._key(val)
pos = bisect_left(_maxes, key)
if pos == len(_maxes):
raise ValueError('{0} not in list'.format(repr(val)))
_lists = self._lists
_keys = self._keys
idx = bisect_left(_keys[pos], key)
len_keys = len(_keys)
len_sublist = len(_keys[pos])
while True:
if _keys[pos][idx] != key:
raise ValueError('{0} not in list'.format(repr(val)))
if _lists[pos][idx] == val:
self._delete(pos, idx)
return
idx += 1
if idx == len_sublist:
pos += 1
if pos == len_keys:
raise ValueError('{0} not in list'.format(repr(val)))
len_sublist = len(_keys[pos])
idx = 0
def _delete(self, pos, idx):
"""
Delete the item at the given (pos, idx).
Combines lists that are less than half the load level.
Updates the index when the sublist length is more than half the load
level. This requires decrementing the nodes in a traversal from the leaf
node to the root. For an example traversal see self._loc.
"""
_lists = self._lists
_keys = self._keys
_maxes = self._maxes
_index = self._index
keys_pos = _keys[pos]
lists_pos = _lists[pos]
del keys_pos[idx]
del lists_pos[idx]
self._len -= 1
len_keys_pos = len(keys_pos)
if len_keys_pos > self._half:
_maxes[pos] = keys_pos[-1]
if _index:
child = self._offset + pos
while child > 0:
_index[child] -= 1
child = (child - 1) >> 1
_index[0] -= 1
elif len(_keys) > 1:
if not pos:
pos += 1
prev = pos - 1
_keys[prev].extend(_keys[pos])
_lists[prev].extend(_lists[pos])
_maxes[prev] = _keys[prev][-1]
del _lists[pos]
del _keys[pos]
del _maxes[pos]
del _index[:]
self._expand(prev)
elif len_keys_pos:
_maxes[pos] = keys_pos[-1]
else:
del _lists[pos]
del _keys[pos]
del _maxes[pos]
del _index[:]
def _check_order(self, idx, key, val):
# pylint: disable=arguments-differ
_len = self._len
_keys = self._keys
pos, loc = self._pos(idx)
if idx < 0:
idx += _len
# Check that the inserted value is not less than the
# previous value.
if idx > 0:
idx_prev = loc - 1
pos_prev = pos
if idx_prev < 0:
pos_prev -= 1
idx_prev = len(_keys[pos_prev]) - 1
if _keys[pos_prev][idx_prev] > key:
msg = '{0} not in sort order at index {1}'.format(repr(val), idx)
raise ValueError(msg)
# Check that the inserted value is not greater than
# the previous value.
if idx < (_len - 1):
idx_next = loc + 1
pos_next = pos
if idx_next == len(_keys[pos_next]):
pos_next += 1
idx_next = 0
if _keys[pos_next][idx_next] < key:
msg = '{0} not in sort order at index {1}'.format(repr(val), idx)
raise ValueError(msg)
def __setitem__(self, index, value):
"""
Replace the item at position *index* with *value*.
Supports slice notation. Raises a :exc:`ValueError` if the sort order
would be violated. When used with a slice and iterable, the
:exc:`ValueError` is raised before the list is mutated if the sort order
would be violated by the operation.
"""
_lists = self._lists
_keys = self._keys
_maxes = self._maxes
_check_order = self._check_order
_pos = self._pos
if isinstance(index, slice):
start, stop, step = index.indices(self._len)
indices = range(start, stop, step)
if step != 1:
if not hasattr(value, '__len__'):
value = list(value)
indices = list(indices)
if len(value) != len(indices):
raise ValueError(
'attempt to assign sequence of size {0}'
' to extended slice of size {1}'
.format(len(value), len(indices)))
# Keep a log of values that are set so that we can
# roll back changes if ordering is violated.
log = []
_append = log.append
for idx, val in zip(indices, value):
pos, loc = _pos(idx)
key = self._key(val)
_append((idx, _keys[pos][loc], key, _lists[pos][loc], val))
_keys[pos][loc] = key
_lists[pos][loc] = val
if len(_keys[pos]) == (loc + 1):
_maxes[pos] = key
try:
# Validate ordering of new values.
for idx, oldkey, newkey, oldval, newval in log:
_check_order(idx, newkey, newval)
except ValueError:
# Roll back changes from log.
for idx, oldkey, newkey, oldval, newval in log:
pos, loc = _pos(idx)
_keys[pos][loc] = oldkey
_lists[pos][loc] = oldval
if len(_keys[pos]) == (loc + 1):
_maxes[pos] = oldkey
raise
else:
if start == 0 and stop == self._len:
self._clear()
return self._update(value)
# Test ordering using indexing. If the given value
# isn't a Sequence, convert it to a tuple.
if not isinstance(value, Sequence):
value = tuple(value) # pylint: disable=redefined-variable-type
# Check that the given values are ordered properly.
keys = tuple(map(self._key, value))
iterator = range(1, len(keys))
if not all(keys[pos - 1] <= keys[pos] for pos in iterator):
raise ValueError('given sequence not in sort order')
# Check ordering in context of sorted list.
if not start or not len(value):
# Nothing to check on the lhs.
pass
else:
pos, loc = _pos(start - 1)
if _keys[pos][loc] > keys[0]:
msg = '{0} not in sort order at index {1}'.format(repr(value[0]), start)
raise ValueError(msg)
if stop == len(self) or not len(value):
# Nothing to check on the rhs.
pass
else:
# "stop" is exclusive so we don't need
# to add one for the index.
pos, loc = _pos(stop)
if _keys[pos][loc] < keys[-1]:
msg = '{0} not in sort order at index {1}'.format(repr(value[-1]), stop)
raise ValueError(msg)
# Delete the existing values.
self._delitem(index)
# Insert the new values.
_insert = self.insert
for idx, val in enumerate(value):
_insert(start + idx, val)
else:
pos, loc = _pos(index)
key = self._key(value)
_check_order(index, key, value)
_lists[pos][loc] = value
_keys[pos][loc] = key
if len(_lists[pos]) == (loc + 1):
_maxes[pos] = key
def irange(self, minimum=None, maximum=None, inclusive=(True, True),
reverse=False):
"""
Create an iterator of values between `minimum` and `maximum`.
`inclusive` is a pair of booleans that indicates whether the minimum
and maximum ought to be included in the range, respectively. The
default is (True, True) such that the range is inclusive of both
minimum and maximum.
Both `minimum` and `maximum` default to `None` which is automatically
inclusive of the start and end of the list, respectively.
When `reverse` is `True` the values are yielded from the iterator in
reverse order; `reverse` defaults to `False`.
"""
minimum = self._key(minimum) if minimum is not None else None
maximum = self._key(maximum) if maximum is not None else None
return self._irange_key(
min_key=minimum, max_key=maximum,
inclusive=inclusive, reverse=reverse,
)
def irange_key(self, min_key=None, max_key=None, inclusive=(True, True),
reverse=False):
"""
Create an iterator of values between `min_key` and `max_key`.
`inclusive` is a pair of booleans that indicates whether the min_key
and max_key ought to be included in the range, respectively. The
default is (True, True) such that the range is inclusive of both
`min_key` and `max_key`.
Both `min_key` and `max_key` default to `None` which is automatically
inclusive of the start and end of the list, respectively.
When `reverse` is `True` the values are yielded from the iterator in
reverse order; `reverse` defaults to `False`.
"""
_maxes = self._maxes
if not _maxes:
return iter(())
_keys = self._keys
# Calculate the minimum (pos, idx) pair. By default this location
# will be inclusive in our calculation.
if min_key is None:
min_pos = 0
min_idx = 0
else:
if inclusive[0]:
min_pos = bisect_left(_maxes, min_key)
if min_pos == len(_maxes):
return iter(())
min_idx = bisect_left(_keys[min_pos], min_key)
else:
min_pos = bisect_right(_maxes, min_key)
if min_pos == len(_maxes):
return iter(())
min_idx = bisect_right(_keys[min_pos], min_key)
# Calculate the maximum (pos, idx) pair. By default this location
# will be exclusive in our calculation.
if max_key is None:
max_pos = len(_maxes) - 1
max_idx = len(_keys[max_pos])
else:
if inclusive[1]:
max_pos = bisect_right(_maxes, max_key)
if max_pos == len(_maxes):
max_pos -= 1
max_idx = len(_keys[max_pos])
else:
max_idx = bisect_right(_keys[max_pos], max_key)
else:
max_pos = bisect_left(_maxes, max_key)
if max_pos == len(_maxes):
max_pos -= 1
max_idx = len(_keys[max_pos])
else:
max_idx = bisect_left(_keys[max_pos], max_key)
return self._islice(min_pos, min_idx, max_pos, max_idx, reverse)
_irange_key = irange_key
def bisect_left(self, val):
"""
Similar to the *bisect* module in the standard library, this returns an
appropriate index to insert *val*. If *val* is already present, the
insertion point will be before (to the left of) any existing entries.
"""
return self._bisect_key_left(self._key(val))
def bisect_right(self, val):
"""
Same as *bisect_left*, but if *val* is already present, the insertion
point will be after (to the right of) any existing entries.
"""
return self._bisect_key_right(self._key(val))
bisect = bisect_right
def bisect_key_left(self, key):
"""
Similar to the *bisect* module in the standard library, this returns an
appropriate index to insert a value with a given *key*. If values with
*key* are already present, the insertion point will be before (to the
left of) any existing entries.
"""
_maxes = self._maxes
if not _maxes:
return 0
pos = bisect_left(_maxes, key)
if pos == len(_maxes):
return self._len
idx = bisect_left(self._keys[pos], key)
return self._loc(pos, idx)
_bisect_key_left = bisect_key_left
def bisect_key_right(self, key):
"""
Same as *bisect_key_left*, but if *key* is already present, the insertion
point will be after (to the right of) any existing entries.
"""
_maxes = self._maxes
if not _maxes:
return 0
pos = bisect_right(_maxes, key)
if pos == len(_maxes):
return self._len
idx = bisect_right(self._keys[pos], key)
return self._loc(pos, idx)
bisect_key = bisect_key_right
_bisect_key_right = bisect_key_right
def count(self, val):
"""Return the number of occurrences of *val* in the list."""
_maxes = self._maxes
if not _maxes:
return 0
key = self._key(val)
pos = bisect_left(_maxes, key)
if pos == len(_maxes):
return 0
_lists = self._lists
_keys = self._keys
idx = bisect_left(_keys[pos], key)
total = 0
len_keys = len(_keys)
len_sublist = len(_keys[pos])
while True:
if _keys[pos][idx] != key:
return total
if _lists[pos][idx] == val:
total += 1
idx += 1
if idx == len_sublist:
pos += 1
if pos == len_keys:
return total
len_sublist = len(_keys[pos])
idx = 0
def copy(self):
"""Return a shallow copy of the sorted list."""
return self.__class__(self, key=self._key, load=self._load)
__copy__ = copy
def append(self, val):
"""
Append the element *val* to the list. Raises a ValueError if the *val*
would violate the sort order.
"""
_lists = self._lists
_keys = self._keys
_maxes = self._maxes
key = self._key(val)
if not _maxes:
_maxes.append(key)
_keys.append([key])
_lists.append([val])
self._len = 1
return
pos = len(_keys) - 1
if key < _keys[pos][-1]:
msg = '{0} not in sort order at index {1}'.format(repr(val), self._len)
raise ValueError(msg)
_lists[pos].append(val)
_keys[pos].append(key)
_maxes[pos] = key
self._len += 1
self._expand(pos)
def extend(self, values):
"""
Extend the list by appending all elements from the *values*. Raises a
ValueError if the sort order would be violated.
"""
_lists = self._lists
_keys = self._keys
_maxes = self._maxes
_load = self._load
if not isinstance(values, list):
values = list(values)
keys = list(map(self._key, values))
if any(keys[pos - 1] > keys[pos]
for pos in range(1, len(keys))):
raise ValueError('given sequence not in sort order')
offset = 0
if _maxes:
if keys[0] < _keys[-1][-1]:
msg = '{0} not in sort order at index {1}'.format(repr(values[0]), self._len)
raise ValueError(msg)
if len(_keys[-1]) < self._half:
_lists[-1].extend(values[:_load])
_keys[-1].extend(keys[:_load])
_maxes[-1] = _keys[-1][-1]
offset = _load
len_keys = len(_keys)
for idx in range(offset, len(keys), _load):
_lists.append(values[idx:(idx + _load)])
_keys.append(keys[idx:(idx + _load)])
_maxes.append(_keys[-1][-1])
_index = self._index
if len_keys == len(_keys):
len_index = len(_index)
if len_index > 0:
len_values = len(values)
child = len_index - 1
while child:
_index[child] += len_values
child = (child - 1) >> 1
_index[0] += len_values
else:
del _index[:]
self._len += len(values)
def insert(self, idx, val):
"""
Insert the element *val* into the list at *idx*. Raises a ValueError if
the *val* at *idx* would violate the sort order.
"""
_len = self._len
_lists = self._lists
_keys = self._keys
_maxes = self._maxes
if idx < 0:
idx += _len
if idx < 0:
idx = 0
if idx > _len:
idx = _len
key = self._key(val)
if not _maxes:
self._len = 1
_lists.append([val])
_keys.append([key])
_maxes.append(key)
return
if not idx:
if key > _keys[0][0]:
msg = '{0} not in sort order at index {1}'.format(repr(val), 0)
raise ValueError(msg)
else:
self._len += 1
_lists[0].insert(0, val)
_keys[0].insert(0, key)
self._expand(0)
return
if idx == _len:
pos = len(_keys) - 1
if _keys[pos][-1] > key:
msg = '{0} not in sort order at index {1}'.format(repr(val), _len)
raise ValueError(msg)
else:
self._len += 1
_lists[pos].append(val)
_keys[pos].append(key)
_maxes[pos] = _keys[pos][-1]
self._expand(pos)
return
pos, idx = self._pos(idx)
idx_before = idx - 1
if idx_before < 0:
pos_before = pos - 1
idx_before = len(_keys[pos_before]) - 1
else:
pos_before = pos
before = _keys[pos_before][idx_before]
if before <= key <= _keys[pos][idx]:
self._len += 1
_lists[pos].insert(idx, val)
_keys[pos].insert(idx, key)
self._expand(pos)
else:
msg = '{0} not in sort order at index {1}'.format(repr(val), idx)
raise ValueError(msg)
def index(self, val, start=None, stop=None):
"""
Return the smallest *k* such that L[k] == val and i <= k < j`. Raises
ValueError if *val* is not present. *stop* defaults to the end of the
list. *start* defaults to the beginning. Negative indices are supported,
as for slice indices.
"""
_len = self._len
if not _len:
raise ValueError('{0} is not in list'.format(repr(val)))
if start is None:
start = 0
if start < 0:
start += _len
if start < 0:
start = 0
if stop is None:
stop = _len
if stop < 0:
stop += _len
if stop > _len:
stop = _len
if stop <= start:
raise ValueError('{0} is not in list'.format(repr(val)))
_maxes = self._maxes
key = self._key(val)
pos = bisect_left(_maxes, key)
if pos == len(_maxes):
raise ValueError('{0} is not in list'.format(repr(val)))
stop -= 1
_lists = self._lists
_keys = self._keys
idx = bisect_left(_keys[pos], key)
len_keys = len(_keys)
len_sublist = len(_keys[pos])
while True:
if _keys[pos][idx] != key:
raise ValueError('{0} is not in list'.format(repr(val)))
if _lists[pos][idx] == val:
loc = self._loc(pos, idx)
if start <= loc <= stop:
return loc
elif loc > stop:
break
idx += 1
if idx == len_sublist:
pos += 1
if pos == len_keys:
raise ValueError('{0} is not in list'.format(repr(val)))
len_sublist = len(_keys[pos])
idx = 0
raise ValueError('{0} is not in list'.format(repr(val)))
def __add__(self, that):
"""
Return a new sorted list containing all the elements in *self* and
*that*. Elements in *that* do not need to be properly ordered with
respect to *self*.
"""
values = reduce(iadd, self._lists, [])
values.extend(that)
return self.__class__(values, key=self._key, load=self._load)
def __mul__(self, that):
"""
Return a new sorted list containing *that* shallow copies of each item
in SortedListWithKey.
"""
values = reduce(iadd, self._lists, []) * that
return self.__class__(values, key=self._key, load=self._load)
def __imul__(self, that):
"""
Increase the length of the list by appending *that* shallow copies of
each item.
"""
values = reduce(iadd, self._lists, []) * that
self._clear()
self._update(values)
return self
@recursive_repr
def __repr__(self):
"""Return string representation of sequence."""
temp = '{0}({1}, key={2}, load={3})'
return temp.format(
self.__class__.__name__,
repr(list(self)),
repr(self._key),
repr(self._load)
)
def _check(self):
try:
# Check load parameters.
assert self._load >= 4
assert self._half == (self._load >> 1)
assert self._twice == (self._load * 2)
# Check empty sorted list case.
if self._maxes == []:
assert self._keys == []
assert self._lists == []
return
assert len(self._maxes) > 0 and len(self._keys) > 0 and len(self._lists) > 0
# Check all sublists are sorted.
assert all(sublist[pos - 1] <= sublist[pos]
for sublist in self._keys
for pos in range(1, len(sublist)))
# Check beginning/end of sublists are sorted.
for pos in range(1, len(self._keys)):
assert self._keys[pos - 1][-1] <= self._keys[pos][0]
# Check length of _maxes and _lists match.
assert len(self._maxes) == len(self._lists) == len(self._keys)
# Check _keys matches _key mapped to _lists.
assert all(len(val_list) == len(key_list)
for val_list, key_list in zip(self._lists, self._keys))
assert all(self._key(val) == key for val, key in
zip((_val for _val_list in self._lists for _val in _val_list),
(_key for _key_list in self._keys for _key in _key_list)))
# Check _maxes is a map of _keys.
assert all(self._maxes[pos] == self._keys[pos][-1]
for pos in range(len(self._maxes)))
# Check load level is less than _twice.
assert all(len(sublist) <= self._twice for sublist in self._lists)
# Check load level is greater than _half for all
# but the last sublist.
assert all(len(self._lists[pos]) >= self._half
for pos in range(0, len(self._lists) - 1))
# Check length.
assert self._len == sum(len(sublist) for sublist in self._lists)
# Check index.
if len(self._index):
assert len(self._index) == self._offset + len(self._lists)
assert self._len == self._index[0]
def test_offset_pos(pos):
"Test positional indexing offset."
from_index = self._index[self._offset + pos]
return from_index == len(self._lists[pos])
assert all(test_offset_pos(pos)
for pos in range(len(self._lists)))
for pos in range(self._offset):
child = (pos << 1) + 1
if self._index[pos] == 0:
assert child >= len(self._index)
elif child + 1 == len(self._index):
assert self._index[pos] == self._index[child]
else:
child_sum = self._index[child] + self._index[child + 1]
assert self._index[pos] == child_sum
except:
import sys
import traceback
traceback.print_exc(file=sys.stdout)
print('len', self._len)
print('load', self._load, self._half, self._twice)
print('offset', self._offset)
print('len_index', len(self._index))
print('index', self._index)
print('len_maxes', len(self._maxes))
print('maxes', self._maxes)
print('len_keys', len(self._keys))
print('keys', self._keys)
print('len_lists', len(self._lists))
print('lists', self._lists)
raise