# This file is part of Hypothesis, which may be found at
# https://github.com/HypothesisWorks/hypothesis/
#
# Copyright the Hypothesis Authors.
# Individual contributors are listed in AUTHORS.rst and the git log.
#
# This Source Code Form is subject to the terms of the Mozilla Public License,
# v. 2.0. If a copy of the MPL was not distributed with this file, You can
# obtain one at https://mozilla.org/MPL/2.0/.
from collections.abc import Iterable, Sequence
from typing import TYPE_CHECKING, Union, cast, final
if TYPE_CHECKING:
from typing import TypeAlias
from typing_extensions import Self
IntervalsT: "TypeAlias" = tuple[tuple[int, int], ...]
# @final makes mypy happy with the Self return annotations. We otherwise run
# afoul of:
# > You should not use Self as the return annotation if the method is not
# > guaranteed to return an instance of a subclass when the class is subclassed
# > https://docs.python.org/3/library/typing.html#typing.Self
[docs]
@final
class IntervalSet:
"""
A compact and efficient representation of a set of ``(a, b)`` intervals. Can
be treated like a set of integers, in that ``n in intervals`` will return
``True`` if ``n`` is contained in any of the ``(a, b)`` intervals, and
``False`` otherwise.
"""
@classmethod
def from_string(cls, s: str) -> "Self":
"""Return a tuple of intervals, covering the codepoints of characters in `s`.
>>> IntervalSet.from_string('abcdef0123456789')
((48, 57), (97, 102))
"""
x = cls([(ord(c), ord(c)) for c in sorted(s)])
return x.union(x)
def __init__(self, intervals: Iterable[Sequence[int]] = ()) -> None:
self.intervals: IntervalsT = cast(
IntervalsT, tuple(tuple(v) for v in intervals)
)
# cast above is validated by this length assertion. check here instead of
# before to not exhaust generators before we create intervals from it
assert all(len(v) == 2 for v in self.intervals)
self.offsets: list[int] = [0]
for u, v in self.intervals:
self.offsets.append(self.offsets[-1] + v - u + 1)
self.size = self.offsets.pop()
self._idx_of_zero = self.index_above(ord("0"))
self._idx_of_Z = min(self.index_above(ord("Z")), len(self) - 1)
def __len__(self) -> int:
return self.size
def __iter__(self) -> Iterable[int]:
for u, v in self.intervals:
yield from range(u, v + 1)
def __getitem__(self, i: int) -> int:
if i < 0:
i = self.size + i
if i < 0 or i >= self.size:
raise IndexError(f"Invalid index {i} for [0, {self.size})")
# Want j = maximal such that offsets[j] <= i
j = len(self.intervals) - 1
if self.offsets[j] > i:
hi = j
lo = 0
# Invariant: offsets[lo] <= i < offsets[hi]
while lo + 1 < hi:
mid = (lo + hi) // 2
if self.offsets[mid] <= i:
lo = mid
else:
hi = mid
j = lo
t = i - self.offsets[j]
u, v = self.intervals[j]
r = u + t
assert r <= v
return r
def __contains__(self, elem: Union[str, int]) -> bool:
if isinstance(elem, str):
elem = ord(elem)
assert 0 <= elem <= 0x10FFFF
return any(start <= elem <= end for start, end in self.intervals)
def __repr__(self) -> str:
return f"IntervalSet({self.intervals!r})"
def index(self, value: int) -> int:
for offset, (u, v) in zip(self.offsets, self.intervals):
if u == value:
return offset
elif u > value:
raise ValueError(f"{value} is not in list")
if value <= v:
return offset + (value - u)
raise ValueError(f"{value} is not in list")
def index_above(self, value: int) -> int:
for offset, (u, v) in zip(self.offsets, self.intervals):
if u >= value:
return offset
if value <= v:
return offset + (value - u)
return self.size
def __or__(self, other: "Self") -> "Self":
return self.union(other)
def __sub__(self, other: "Self") -> "Self":
return self.difference(other)
def __and__(self, other: "Self") -> "Self":
return self.intersection(other)
def __eq__(self, other: object) -> bool:
return isinstance(other, IntervalSet) and (other.intervals == self.intervals)
def __hash__(self) -> int:
return hash(self.intervals)
def union(self, other: "Self") -> "Self":
"""Merge two sequences of intervals into a single tuple of intervals.
Any integer bounded by `x` or `y` is also bounded by the result.
>>> union([(3, 10)], [(1, 2), (5, 17)])
((1, 17),)
"""
assert isinstance(other, type(self))
x = self.intervals
y = other.intervals
if not x:
return IntervalSet(y)
if not y:
return IntervalSet(x)
intervals = sorted(x + y, reverse=True)
result = [intervals.pop()]
while intervals:
# 1. intervals is in descending order
# 2. pop() takes from the RHS.
# 3. (a, b) was popped 1st, then (u, v) was popped 2nd
# 4. Therefore: a <= u
# 5. We assume that u <= v and a <= b
# 6. So we need to handle 2 cases of overlap, and one disjoint case
# | u--v | u----v | u--v |
# | a----b | a--b | a--b |
u, v = intervals.pop()
a, b = result[-1]
if u <= b + 1:
# Overlap cases
result[-1] = (a, max(v, b))
else:
# Disjoint case
result.append((u, v))
return IntervalSet(result)
def difference(self, other: "Self") -> "Self":
"""Set difference for lists of intervals. That is, returns a list of
intervals that bounds all values bounded by x that are not also bounded by
y. x and y are expected to be in sorted order.
For example difference([(1, 10)], [(2, 3), (9, 15)]) would
return [(1, 1), (4, 8)], removing the values 2, 3, 9 and 10 from the
interval.
"""
assert isinstance(other, type(self))
x = self.intervals
y = other.intervals
if not y:
return IntervalSet(x)
x = list(map(list, x))
i = 0
j = 0
result: list[Iterable[int]] = []
while i < len(x) and j < len(y):
# Iterate in parallel over x and y. j stays pointing at the smallest
# interval in the left hand side that could still overlap with some
# element of x at index >= i.
# Similarly, i is not incremented until we know that it does not
# overlap with any element of y at index >= j.
xl, xr = x[i]
assert xl <= xr
yl, yr = y[j]
assert yl <= yr
if yr < xl:
# The interval at y[j] is strictly to the left of the interval at
# x[i], so will not overlap with it or any later interval of x.
j += 1
elif yl > xr:
# The interval at y[j] is strictly to the right of the interval at
# x[i], so all of x[i] goes into the result as no further intervals
# in y will intersect it.
result.append(x[i])
i += 1
elif yl <= xl:
if yr >= xr:
# x[i] is contained entirely in y[j], so we just skip over it
# without adding it to the result.
i += 1
else:
# The beginning of x[i] is contained in y[j], so we update the
# left endpoint of x[i] to remove this, and increment j as we
# now have moved past it. Note that this is not added to the
# result as is, as more intervals from y may intersect it so it
# may need updating further.
x[i][0] = yr + 1
j += 1
else:
# yl > xl, so the left hand part of x[i] is not contained in y[j],
# so there are some values we should add to the result.
result.append((xl, yl - 1))
if yr + 1 <= xr:
# If y[j] finishes before x[i] does, there may be some values
# in x[i] left that should go in the result (or they may be
# removed by a later interval in y), so we update x[i] to
# reflect that and increment j because it no longer overlaps
# with any remaining element of x.
x[i][0] = yr + 1
j += 1
else:
# Every element of x[i] other than the initial part we have
# already added is contained in y[j], so we move to the next
# interval.
i += 1
# Any remaining intervals in x do not overlap with any of y, as if they did
# we would not have incremented j to the end, so can be added to the result
# as they are.
result.extend(x[i:])
return IntervalSet(map(tuple, result))
def intersection(self, other: "Self") -> "Self":
"""Set intersection for lists of intervals."""
assert isinstance(other, type(self)), other
intervals = []
i = j = 0
while i < len(self.intervals) and j < len(other.intervals):
u, v = self.intervals[i]
U, V = other.intervals[j]
if u > V:
j += 1
elif U > v:
i += 1
else:
intervals.append((max(u, U), min(v, V)))
if v < V:
i += 1
else:
j += 1
return IntervalSet(intervals)
def char_in_shrink_order(self, i: int) -> str:
# We would like it so that, where possible, shrinking replaces
# characters with simple ascii characters, so we rejig this
# bit so that the smallest values are 0, 1, 2, ..., Z.
#
# Imagine that numbers are laid out as abc0yyyZ...
# this rearranges them so that they are laid out as
# 0yyyZcba..., which gives a better shrinking order.
if i <= self._idx_of_Z:
# We want to rewrite the integers [0, n] inclusive
# to [zero_point, Z_point].
n = self._idx_of_Z - self._idx_of_zero
if i <= n:
i += self._idx_of_zero
else:
# We want to rewrite the integers [n + 1, Z_point] to
# [zero_point, 0] (reversing the order so that codepoints below
# zero_point shrink upwards).
i = self._idx_of_zero - (i - n)
assert i < self._idx_of_zero
assert 0 <= i <= self._idx_of_Z
return chr(self[i])
def index_from_char_in_shrink_order(self, c: str) -> int:
"""
Inverse of char_in_shrink_order.
"""
assert len(c) == 1
i = self.index(ord(c))
if i <= self._idx_of_Z:
n = self._idx_of_Z - self._idx_of_zero
# Rewrite [zero_point, Z_point] to [0, n].
if self._idx_of_zero <= i <= self._idx_of_Z:
i -= self._idx_of_zero
assert 0 <= i <= n
# Rewrite [zero_point, 0] to [n + 1, Z_point].
else:
i = self._idx_of_zero - i + n
assert n + 1 <= i <= self._idx_of_Z
assert 0 <= i <= self._idx_of_Z
return i