/
sortedlistwithkey.py
1525 lines (1169 loc) · 46.8 KB
/
sortedlistwithkey.py
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# -*- coding: utf-8 -*-
#
# Sorted list implementation.
from __future__ import print_function
from sys import hexversion
from .sortedlist import recursive_repr
from bisect import bisect_left, bisect_right, insort
from itertools import chain, repeat, starmap
from collections import MutableSequence, Sequence
import operator as op
from operator import iadd, add
from functools import wraps
from math import log
if hexversion < 0x03000000:
from itertools import izip as zip
from itertools import imap as map
else:
from functools import reduce
def identity(value):
return value
class SortedListWithKey(MutableSequence):
"""
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 a list but
keeps the items in sorted order.
An optional *iterable* provides an initial series of items to populate
the 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.
"""
self._len, self._maxes, self._lists, self._keys, self._index = 0, [], [], [], []
self._key, self._load, self._twice, self._half = key, load, load * 2, load >> 1
self._offset = 0
if iterable is not None:
self.update(iterable)
def clear(self):
"""Remove all the elements from the list."""
self._len = 0
del self._maxes[:]
del self._lists[:]
del self._keys[:]
del self._index[:]
def add(self, val):
"""Add the element *val* to the list."""
_maxes, _lists, _keys = self._maxes, self._lists, self._keys
key = self._key(val)
if _maxes:
pos = bisect_right(_maxes, key)
if pos == len(_maxes):
pos -= 1
_maxes[pos] = key
_keys[pos].append(key)
_lists[pos].append(val)
else:
idx = bisect_right(_keys[pos], key)
_keys[pos].insert(idx, key)
_lists[pos].insert(idx, val)
self._expand(pos)
else:
_maxes.append(key)
_keys.append([key])
_lists.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, _keys, _index = self._lists, self._keys, self._index
if len(_keys[pos]) > self._twice:
_maxes, _load = self._maxes, self._load
half = _keys[pos][_load:]
half_list = _lists[pos][_load:]
del _keys[pos][_load:]
del _lists[pos][_load:]
_maxes[pos] = _keys[pos][-1]
_maxes.insert(pos + 1, half[-1])
_keys.insert(pos + 1, half)
_lists.insert(pos + 1, half_list)
del _index[:]
else:
if len(_index) > 0:
child = self._offset + pos
while child > 0:
_index[child] += 1
child = (child - 1) >> 1
_index[0] += 1
def update(self, iterable):
"""Update the list by adding all elements from *iterable*."""
_maxes, _lists, _keys = self._maxes, self._lists, self._keys
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, _index = self._load, self._index
_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 _index[:]
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
_keys = self._keys
_lists = self._lists
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
_keys = self._keys
_lists = self._lists
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)))
_keys = self._keys
_lists = self._lists
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.
"""
_maxes, _lists, _keys, _index = self._maxes, self._lists, self._keys, 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 len(_index) > 0:
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 _keys[pos]
del _lists[pos]
del _maxes[pos]
del _index[:]
self._expand(prev)
elif len_keys_pos:
_maxes[pos] = keys_pos[-1]
else:
del _keys[pos]
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 len(_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(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 _slice(self, slc):
start, stop, step = slc.start, slc.stop, slc.step
if step == 0:
raise ValueError('slice step cannot be zero')
# Set defaults for missing values.
if step is None:
step = 1
if step > 0:
if start is None:
start = 0
if stop is None:
stop = len(self)
elif stop < 0:
stop += len(self)
else:
if start is None:
start = len(self) - 1
if stop is None:
stop = -1
elif stop < 0:
stop += len(self)
if start < 0:
start += len(self)
# Fix indices that are too big or too small.
# Slice notation is surprisingly permissive
# where normal indexing would raise IndexError.
if step > 0:
if start < 0:
start = 0
elif start > len(self):
start = len(self)
if stop < 0:
stop = 0
elif stop > len(self):
stop = len(self)
else:
if start < 0:
start = -1
elif start >= len(self):
start = len(self) - 1
if stop < 0:
stop = -1
elif stop > len(self):
stop = len(self)
return start, stop, step
def __delitem__(self, idx):
"""Remove the element at *idx*. Supports slicing."""
if isinstance(idx, slice):
start, stop, step = self._slice(idx)
if ((step == 1) and (start < stop)
and ((stop - start) * 8 >= self._len)):
values = self[:start]
if stop < self._len:
values += self[stop:]
self.clear()
self.update(values)
return
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)
def __getitem__(self, idx):
"""Return the element at *idx*. Supports slicing."""
_lists = self._lists
if isinstance(idx, slice):
start, stop, step = self._slice(idx)
if step == 1 and start < stop:
if start == 0 and stop == self._len:
return self.as_list()
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[(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[index] for index in indices)
else:
pos, idx = self._pos(idx)
return _lists[pos][idx]
def _check_order(self, idx, key, val):
_keys, _len = self._keys, self._len
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.
"""
_maxes, _lists, _keys, _pos = self._maxes, self._lists, self._keys, self._pos
_check_order = self._check_order
if isinstance(index, slice):
start, stop, step = self._slice(index)
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:
# Test ordering using indexing. If the value given
# doesn't support getitem, convert it to a list.
if not hasattr(value, '__getitem__'):
value = list(value)
# Check that the given values are ordered properly.
keys = list(map(self._key, value))
ordered = all(keys[pos - 1] <= keys[pos]
for pos in range(1, len(keys)))
if not ordered:
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.
del self[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)
_keys[pos][loc] = key
_lists[pos][loc] = value
if len(_lists[pos]) == (loc + 1):
_maxes[pos] = key
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, step = self._slice(slice(start, stop))
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`.
"""
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: