55 lines
1.8 KiB
Python
55 lines
1.8 KiB
Python
"""
|
|
Given a list of integers, made up of (hopefully) a small number of long runs
|
|
of consecutive integers, compute a representation of the form
|
|
((start1, end1), (start2, end2) ...). Then answer the question "was x present
|
|
in the original list?" in time O(log(# runs)).
|
|
"""
|
|
|
|
import bisect
|
|
from typing import List, Tuple
|
|
|
|
def intranges_from_list(list_: List[int]) -> Tuple[int, ...]:
|
|
"""Represent a list of integers as a sequence of ranges:
|
|
((start_0, end_0), (start_1, end_1), ...), such that the original
|
|
integers are exactly those x such that start_i <= x < end_i for some i.
|
|
|
|
Ranges are encoded as single integers (start << 32 | end), not as tuples.
|
|
"""
|
|
|
|
sorted_list = sorted(list_)
|
|
ranges = []
|
|
last_write = -1
|
|
for i in range(len(sorted_list)):
|
|
if i+1 < len(sorted_list):
|
|
if sorted_list[i] == sorted_list[i+1]-1:
|
|
continue
|
|
current_range = sorted_list[last_write+1:i+1]
|
|
ranges.append(_encode_range(current_range[0], current_range[-1] + 1))
|
|
last_write = i
|
|
|
|
return tuple(ranges)
|
|
|
|
def _encode_range(start: int, end: int) -> int:
|
|
return (start << 32) | end
|
|
|
|
def _decode_range(r: int) -> Tuple[int, int]:
|
|
return (r >> 32), (r & ((1 << 32) - 1))
|
|
|
|
|
|
def intranges_contain(int_: int, ranges: Tuple[int, ...]) -> bool:
|
|
"""Determine if `int_` falls into one of the ranges in `ranges`."""
|
|
tuple_ = _encode_range(int_, 0)
|
|
pos = bisect.bisect_left(ranges, tuple_)
|
|
# we could be immediately ahead of a tuple (start, end)
|
|
# with start < int_ <= end
|
|
if pos > 0:
|
|
left, right = _decode_range(ranges[pos-1])
|
|
if left <= int_ < right:
|
|
return True
|
|
# or we could be immediately behind a tuple (int_, end)
|
|
if pos < len(ranges):
|
|
left, _ = _decode_range(ranges[pos])
|
|
if left == int_:
|
|
return True
|
|
return False
|