from __future__ import annotations
from functools import total_ordering
-from typing import Any, Optional, Union
+from typing import Any, Generator, Optional, Union
from overrides import overrides
@total_ordering
class NumericRange(object):
+ """Essentially a tuple of numbers denoting a range with some added
+ helper methods on it."""
+
def __init__(self, low: Numeric, high: Numeric):
+ """Creates a NumericRange.
+
+ Args:
+ low: the lowest point in the range (inclusive).
+ high: the highest point in the range (inclusive).
+
+ .. warning::
+
+ If low > high this code swaps the parameters and keeps the range
+ rather than raising.
+
+ """
if low > high:
temp: Numeric = low
low = high
self.highest_in_subtree: Numeric = high
def __lt__(self, other: NumericRange) -> bool:
+ """
+ Returns:
+ True is this range is less than (lower low) other, else False.
+ """
return self.low < other.low
@overrides
def __eq__(self, other: object) -> bool:
+ """
+ Returns:
+ True if this is the same range as other, else False.
+ """
if not isinstance(other, NumericRange):
return False
return self.low == other.low and self.high == other.high
def overlaps_with(self, other: NumericRange) -> bool:
+ """
+ Returns:
+ True if this NumericRange overlaps with other, else False.
+ """
return self.low <= other.high and self.high >= other.low
def __repr__(self) -> str:
class AugmentedIntervalTree(bst.BinarySearchTree):
- def __init__(self):
- super().__init__()
-
@staticmethod
- def assert_value_must_be_range(value: Any) -> None:
+ def _assert_value_must_be_range(value: Any) -> None:
if not isinstance(value, NumericRange):
raise Exception(
"AugmentedIntervalTree expects to use NumericRanges, see bst for a "
@overrides
def _on_insert(self, parent: Optional[bst.Node], new: bst.Node) -> None:
- AugmentedIntervalTree.assert_value_must_be_range(new.value)
+ AugmentedIntervalTree._assert_value_must_be_range(new.value)
for ancestor in self.parent_path(new):
assert ancestor
if new.value.high > ancestor.value.highest_in_subtree:
@overrides
def _on_delete(self, parent: Optional[bst.Node], deleted: bst.Node) -> None:
if parent:
- new_highest_candidates = []
- if deleted.left:
- new_highest_candidates.append(deleted.left.value.highest_in_subtree)
- if deleted.right:
- new_highest_candidates.append(deleted.right.value.highest_in_subtree)
- if len(new_highest_candidates):
- parent.value.highest_in_subtree = max(
- parent.value.high, max(new_highest_candidates)
- )
- else:
- parent.value.highest_in_subtree = parent.value.high
-
- def find_overlaps(self, x: NumericRange):
- """Yields ranges previously added to the tree that x overlaps with.
+ new_highest_candidates = [parent.value.high]
+ if parent.left:
+ new_highest_candidates.append(parent.left.value.highest_in_subtree)
+ if parent.right:
+ new_highest_candidates.append(parent.right.value.highest_in_subtree)
+ parent.value.highest_in_subtree = max(new_highest_candidates)
+
+ def find_one_overlap(self, to_find: NumericRange) -> Optional[NumericRange]:
+ """Identify and return one overlapping node from the tree.
+
+ Args:
+ to_find: the interval with which to find an overlap.
+
+ Returns:
+ An overlapping range from the tree or None if no such
+ ranges exist in the tree at present.
>>> tree = AugmentedIntervalTree()
>>> tree.insert(NumericRange(20, 24))
>>> tree.insert(NumericRange(13, 18))
>>> tree.insert(NumericRange(16, 28))
>>> tree.insert(NumericRange(21, 27))
- >>> for x in tree.find_overlaps(NumericRange(19, 21)):
+ >>> tree.find_one_overlap(NumericRange(6, 7))
+ 1..30
+
+ """
+ return self._find_one_overlap(self.root, to_find)
+
+ def _find_one_overlap(
+ self, root: bst.Node, x: NumericRange
+ ) -> Optional[NumericRange]:
+ if root is None:
+ return None
+
+ if root.value.overlaps_with(x):
+ return root.value
+
+ if root.left:
+ if root.left.value.highest_in_subtree >= x.low:
+ return self._find_one_overlap(root.left, x)
+
+ if root.right:
+ return self._find_one_overlap(root.right, x)
+ return None
+
+ def find_all_overlaps(
+ self, to_find: NumericRange
+ ) -> Generator[NumericRange, None, None]:
+ """Yields ranges previously added to the tree that overlaps with
+ to_find argument.
+
+ Args:
+ to_find: the interval with which to find all overlaps.
+
+ Returns:
+ A (potentially empty) sequence of all ranges in the tree
+ that overlap with the argument.
+
+ >>> tree = AugmentedIntervalTree()
+ >>> tree.insert(NumericRange(20, 24))
+ >>> tree.insert(NumericRange(18, 22))
+ >>> tree.insert(NumericRange(14, 16))
+ >>> tree.insert(NumericRange(1, 30))
+ >>> tree.insert(NumericRange(25, 30))
+ >>> tree.insert(NumericRange(29, 33))
+ >>> tree.insert(NumericRange(5, 12))
+ >>> tree.insert(NumericRange(1, 6))
+ >>> tree.insert(NumericRange(13, 18))
+ >>> tree.insert(NumericRange(16, 28))
+ >>> tree.insert(NumericRange(21, 27))
+ >>> for x in tree.find_all_overlaps(NumericRange(19, 21)):
... print(x)
20..24
18..22
1..30
16..28
21..27
+
+ >>> del tree[NumericRange(1, 30)]
+ >>> for x in tree.find_all_overlaps(NumericRange(19, 21)):
+ ... print(x)
+ 20..24
+ 18..22
+ 16..28
+ 21..27
+
"""
if self.root is None:
return
- yield from self._find_overlaps(self.root, x)
-
- def _find_overlaps(self, root: bst.Node, x: NumericRange):
- """It's known that two intervals A and B overlap only
- when both A.low <= B.high and A.high >= B.low. When
- searching the trees for nodes overlapping with a given
- interval, we can immediately skip:
-
- * all nodes to the right of nodes whose low value is past
- the end of the given interval and
- * all nodes that have their maximum high value below the
- start of the given interval.
- """
+ yield from self._find_all_overlaps(self.root, to_find)
+
+ def _find_all_overlaps(
+ self, root: bst.Node, x: NumericRange
+ ) -> Generator[NumericRange, None, None]:
if root is None:
- return
+ return None
if root.value.overlaps_with(x):
yield root.value
if root.left:
if root.left.value.highest_in_subtree >= x.low:
- yield from self._find_overlaps(root.left, x)
+ yield from self._find_all_overlaps(root.left, x)
- if root.value.low <= x.high:
- if root.right:
- yield from self._find_overlaps(root.right, x)
+ if root.right:
+ if root.right.value.highest_in_subtree >= x.low:
+ yield from self._find_all_overlaps(root.right, x)
if __name__ == "__main__":
projects / pyutils.git / blobdiff