from collections import Counter
from itertools import islice
-from typing import Any, Iterator, List, Mapping, Sequence
+from typing import Any, Iterator, List, Mapping, Sequence, Tuple
def shard(lst: List[Any], size: int) -> Iterator[Any]:
return lst
-def population_counts(lst: List[Any]) -> Mapping[Any, int]:
+def population_counts(lst: Sequence[Any]) -> Counter:
"""
Return a population count mapping for the list (i.e. the keys are
list items and the values are the number of occurrances of that
['an', 'awesome', 'test']
"""
for i in range(len(lst) - n + 1):
- yield lst[i:i + n]
+ yield lst[i : i + n]
+
+
+def permute(seq: str):
+ """
+ Returns all permutations of a sequence; takes O(N!) time.
+
+ >>> for x in permute('cat'):
+ ... print(x)
+ cat
+ cta
+ act
+ atc
+ tca
+ tac
+
+ """
+ yield from _permute(seq, "")
+
+
+def _permute(seq: str, path: str):
+ seq_len = len(seq)
+ if seq_len == 0:
+ yield path
+
+ for i in range(seq_len):
+ car = seq[i]
+ left = seq[0:i]
+ right = seq[i + 1 :]
+ cdr = left + right
+ yield from _permute(cdr, path + car)
+
+
+def binary_search(
+ lst: Sequence[Any], target: Any, *, sanity_check=False
+) -> Tuple[bool, int]:
+ """Performs a binary search on lst (which must already be sorted).
+ Returns a Tuple composed of a bool which indicates whether the
+ target was found and an int which indicates the index closest to
+ target whether it was found or not.
+
+ >>> a = [1, 4, 5, 6, 7, 9, 10, 11]
+ >>> binary_search(a, 4)
+ (True, 1)
+
+ >>> binary_search(a, 12)
+ (False, 8)
+
+ >>> binary_search(a, 3)
+ (False, 1)
+
+ >>> binary_search(a, 2)
+ (False, 1)
+
+ >>> a.append(9)
+ >>> binary_search(a, 4, sanity_check=True)
+ Traceback (most recent call last):
+ ...
+ AssertionError
+
+ """
+ if sanity_check:
+ last = None
+ for x in lst:
+ if last is not None:
+ assert x >= last # This asserts iff the list isn't sorted
+ last = x # in ascending order.
+ return _binary_search(lst, target, 0, len(lst) - 1)
+
+
+def _binary_search(
+ lst: Sequence[Any], target: Any, low: int, high: int
+) -> Tuple[bool, int]:
+ if high >= low:
+ mid = (high + low) // 2
+ if lst[mid] == target:
+ return (True, mid)
+ elif lst[mid] > target:
+ return _binary_search(lst, target, low, mid - 1)
+ else:
+ return _binary_search(lst, target, mid + 1, high)
+ else:
+ return (False, low)
if __name__ == '__main__':
import doctest
+
doctest.testmod()