Source code for sortedcontainers.sortedlist

"""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  # pylint: disable=no-name-in-module
    from itertools import imap as map  # pylint: disable=no-name-in-module
    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

LOAD = 1000

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

[docs]class SortedList(MutableSequence): """ SortedList provides most of the same methods as a list but keeps the items in sorted order. """ # pylint: disable=too-many-ancestors def __init__(self, iterable=None): """ 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. """ self._len = 0 self._lists = [] self._maxes = [] self._index = [] self._load = LOAD self._half = LOAD >> 1 self._dual = LOAD << 1 self._offset = 0 if iterable is not None: self._update(iterable) def __new__(cls, iterable=None, key=None): """ 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. """ # 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') @property def key(self): """Key function used to extract comparison key for sorting.""" return None def _reset(self, load): """ Reset sorted list load. The *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. """ values = reduce(iadd, self._lists, []) self._clear() self._load = load self._half = load >> 1 self._dual = load << 1 self._update(values) 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._dual: _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. """ # pylint: disable=arguments-differ _maxes = self._maxes if not _maxes: raise ValueError('{0!r} not in list'.format(val)) pos = bisect_left(_maxes, val) if pos == len(_maxes): raise ValueError('{0!r} not in list'.format(val)) _lists = self._lists idx = bisect_left(_lists[pos], val) if _lists[pos][idx] == val: self._delete(pos, idx) else: raise ValueError('{0!r} not in list'.format(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!r} not in sort order at index {1}'.format(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!r} not in sort order at index {1}'.format(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 = '{0!r} not in sort order at index {1}'.format( values[0], start) raise ValueError(message) if stop != _len and self._getitem(stop) < values[-1]: message = '{0!r} not in sort order at index {1}'.format( 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 reverse(self): """Raise NotImplementedError SortedList maintains values in ascending sort order. Values may not be reversed in-place. Use ``reversed(sorted_list)`` for a reverse iterator over values in descending sort order. Implemented to override MutableSequence.reverse which provides an erroneous default implementation. """ raise NotImplementedError('.reverse() not defined') 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], ) 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.""" # pylint: disable=arguments-differ _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) __copy__ = copy def append(self, val): """ Append the element *val* to the list. Raises a ValueError if the *val* would violate the sort order. """ # pylint: disable=arguments-differ _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!r} not in sort order at index {1}'.format(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!r} not in sort order at index {1}'.format(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. """ # pylint: disable=arguments-differ _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!r} not in sort order at index {1}'.format(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!r} not in sort order at index {1}'.format(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!r} not in sort order at index {1}'.format(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. """ # pylint: disable=arguments-differ 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!r} is not in list'.format(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!r} is not in list'.format(val)) _maxes = self._maxes pos_left = bisect_left(_maxes, val) if pos_left == len(_maxes): raise ValueError('{0!r} is not in list'.format(val)) _lists = self._lists idx_left = bisect_left(_lists[pos_left], val) if _lists[pos_left][idx_left] != val: raise ValueError('{0!r} is not in list'.format(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!r} is not in list'.format(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) 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) 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.""" return '{0}({1!r})'.format(type(self).__name__, list(self)) def _check(self): try: # Check load parameters. assert self._load >= 4 assert self._half == (self._load >> 1) assert self._dual == (self._load << 1) # Check empty sorted list case. if self._maxes == []: assert self._lists == [] return assert self._maxes and self._lists # 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 _dual. assert all(len(sublist) <= self._dual 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 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._dual) 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
[docs]class SortedListWithKey(SortedList): """ SortedListWithKey provides most of the same methods as a list but keeps the items in sorted order. """ # pylint: disable=too-many-ancestors,abstract-method def __init__(self, iterable=None, key=identity): """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. """ # pylint: disable=super-init-not-called self._len = 0 self._lists = [] self._keys = [] self._maxes = [] self._index = [] self._key = key self._load = LOAD self._half = LOAD >> 1 self._dual = LOAD << 1 self._offset = 0 if iterable is not None: self._update(iterable) def __new__(cls, iterable=None, key=identity): return object.__new__(cls) @property def key(self): """Key function used to extract comparison key for sorting.""" return self._key 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._dual: _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!r} not in list'.format(val)) key = self._key(val) pos = bisect_left(_maxes, key) if pos == len(_maxes): raise ValueError('{0!r} not in list'.format(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!r} not in list'.format(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!r} not in list'.format(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!r} not in sort order at index {1}'.format(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!r} not in sort order at index {1}'.format(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. """ # pylint: disable=too-many-locals _lists = self._lists _keys = self._keys _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) 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(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. keys = tuple(map(self._key, values)) alphas = iter(keys) betas = iter(keys) 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: pos, loc = _pos(start - 1) if _keys[pos][loc] > keys[0]: msg = '{0!r} not in sort order at index {1}'.format( values[0], start) raise ValueError(msg) if stop != _len: pos, loc = _pos(stop) if _keys[pos][loc] < keys[-1]: msg = '{0!r} not in sort order at index {1}'.format( values[-1], stop) raise ValueError(msg) # 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) 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) __copy__ = copy def append(self, val): """ Append the element *val* to the list. Raises a ValueError if the *val* would violate the sort order. """ # pylint: disable=arguments-differ _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!r} not in sort order at index {1}'.format(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!r} not in sort order at index {1}'.format(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!r} not in sort order at index {1}'.format(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!r} not in sort order at index {1}'.format(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!r} not in sort order at index {1}'.format(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!r} is not in list'.format(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!r} is not in list'.format(val)) _maxes = self._maxes key = self._key(val) pos = bisect_left(_maxes, key) if pos == len(_maxes): raise ValueError('{0!r} is not in list'.format(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!r} is not in list'.format(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!r} is not in list'.format(val)) len_sublist = len(_keys[pos]) idx = 0 raise ValueError('{0!r} is not in list'.format(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) 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) 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.""" name = type(self).__name__ values = list(self) _key = self._key return '{0}({1!r}, key={2!r})'.format(name, values, _key) def _check(self): try: # Check load parameters. assert self._load >= 4 assert self._half == (self._load >> 1) assert self._dual == (self._load << 1) # Check empty sorted list case. if self._maxes == []: assert self._keys == [] assert self._lists == [] return assert self._maxes and self._keys and self._lists # 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 _dual. assert all(len(sublist) <= self._dual 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 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._dual) 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