mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-11-27 23:11:09 +00:00
c909da9b08
* pre-commit: Upgrade psf/black for stable style 2023 Updating https://github.com/psf/black ... updating 22.12.0 -> 23.1.0 for their `2023 stable style`. * https://github.com/psf/black/blob/main/CHANGES.md#2310 > This is the first [psf/black] release of 2023, and following our stability policy, it comes with a number of improvements to our stable style… Also, add https://github.com/tox-dev/pyproject-fmt and https://github.com/abravalheri/validate-pyproject to pre-commit. I only modified `.pre-commit-config.yaml` and all other files were modified by pre-commit.ci and psf/black. * [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci --------- Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
309 lines
8.9 KiB
Python
309 lines
8.9 KiB
Python
#!/usr/bin/env python3
|
|
|
|
"""
|
|
This is pure Python implementation of binary search algorithms
|
|
|
|
For doctests run following command:
|
|
python3 -m doctest -v binary_search.py
|
|
|
|
For manual testing run:
|
|
python3 binary_search.py
|
|
"""
|
|
from __future__ import annotations
|
|
|
|
import bisect
|
|
|
|
|
|
def bisect_left(
|
|
sorted_collection: list[int], item: int, lo: int = 0, hi: int = -1
|
|
) -> int:
|
|
"""
|
|
Locates the first element in a sorted array that is larger or equal to a given
|
|
value.
|
|
|
|
It has the same interface as
|
|
https://docs.python.org/3/library/bisect.html#bisect.bisect_left .
|
|
|
|
:param sorted_collection: some ascending sorted collection with comparable items
|
|
:param item: item to bisect
|
|
:param lo: lowest index to consider (as in sorted_collection[lo:hi])
|
|
:param hi: past the highest index to consider (as in sorted_collection[lo:hi])
|
|
:return: index i such that all values in sorted_collection[lo:i] are < item and all
|
|
values in sorted_collection[i:hi] are >= item.
|
|
|
|
Examples:
|
|
>>> bisect_left([0, 5, 7, 10, 15], 0)
|
|
0
|
|
|
|
>>> bisect_left([0, 5, 7, 10, 15], 6)
|
|
2
|
|
|
|
>>> bisect_left([0, 5, 7, 10, 15], 20)
|
|
5
|
|
|
|
>>> bisect_left([0, 5, 7, 10, 15], 15, 1, 3)
|
|
3
|
|
|
|
>>> bisect_left([0, 5, 7, 10, 15], 6, 2)
|
|
2
|
|
"""
|
|
if hi < 0:
|
|
hi = len(sorted_collection)
|
|
|
|
while lo < hi:
|
|
mid = lo + (hi - lo) // 2
|
|
if sorted_collection[mid] < item:
|
|
lo = mid + 1
|
|
else:
|
|
hi = mid
|
|
|
|
return lo
|
|
|
|
|
|
def bisect_right(
|
|
sorted_collection: list[int], item: int, lo: int = 0, hi: int = -1
|
|
) -> int:
|
|
"""
|
|
Locates the first element in a sorted array that is larger than a given value.
|
|
|
|
It has the same interface as
|
|
https://docs.python.org/3/library/bisect.html#bisect.bisect_right .
|
|
|
|
:param sorted_collection: some ascending sorted collection with comparable items
|
|
:param item: item to bisect
|
|
:param lo: lowest index to consider (as in sorted_collection[lo:hi])
|
|
:param hi: past the highest index to consider (as in sorted_collection[lo:hi])
|
|
:return: index i such that all values in sorted_collection[lo:i] are <= item and
|
|
all values in sorted_collection[i:hi] are > item.
|
|
|
|
Examples:
|
|
>>> bisect_right([0, 5, 7, 10, 15], 0)
|
|
1
|
|
|
|
>>> bisect_right([0, 5, 7, 10, 15], 15)
|
|
5
|
|
|
|
>>> bisect_right([0, 5, 7, 10, 15], 6)
|
|
2
|
|
|
|
>>> bisect_right([0, 5, 7, 10, 15], 15, 1, 3)
|
|
3
|
|
|
|
>>> bisect_right([0, 5, 7, 10, 15], 6, 2)
|
|
2
|
|
"""
|
|
if hi < 0:
|
|
hi = len(sorted_collection)
|
|
|
|
while lo < hi:
|
|
mid = lo + (hi - lo) // 2
|
|
if sorted_collection[mid] <= item:
|
|
lo = mid + 1
|
|
else:
|
|
hi = mid
|
|
|
|
return lo
|
|
|
|
|
|
def insort_left(
|
|
sorted_collection: list[int], item: int, lo: int = 0, hi: int = -1
|
|
) -> None:
|
|
"""
|
|
Inserts a given value into a sorted array before other values with the same value.
|
|
|
|
It has the same interface as
|
|
https://docs.python.org/3/library/bisect.html#bisect.insort_left .
|
|
|
|
:param sorted_collection: some ascending sorted collection with comparable items
|
|
:param item: item to insert
|
|
:param lo: lowest index to consider (as in sorted_collection[lo:hi])
|
|
:param hi: past the highest index to consider (as in sorted_collection[lo:hi])
|
|
|
|
Examples:
|
|
>>> sorted_collection = [0, 5, 7, 10, 15]
|
|
>>> insort_left(sorted_collection, 6)
|
|
>>> sorted_collection
|
|
[0, 5, 6, 7, 10, 15]
|
|
|
|
>>> sorted_collection = [(0, 0), (5, 5), (7, 7), (10, 10), (15, 15)]
|
|
>>> item = (5, 5)
|
|
>>> insort_left(sorted_collection, item)
|
|
>>> sorted_collection
|
|
[(0, 0), (5, 5), (5, 5), (7, 7), (10, 10), (15, 15)]
|
|
>>> item is sorted_collection[1]
|
|
True
|
|
>>> item is sorted_collection[2]
|
|
False
|
|
|
|
>>> sorted_collection = [0, 5, 7, 10, 15]
|
|
>>> insort_left(sorted_collection, 20)
|
|
>>> sorted_collection
|
|
[0, 5, 7, 10, 15, 20]
|
|
|
|
>>> sorted_collection = [0, 5, 7, 10, 15]
|
|
>>> insort_left(sorted_collection, 15, 1, 3)
|
|
>>> sorted_collection
|
|
[0, 5, 7, 15, 10, 15]
|
|
"""
|
|
sorted_collection.insert(bisect_left(sorted_collection, item, lo, hi), item)
|
|
|
|
|
|
def insort_right(
|
|
sorted_collection: list[int], item: int, lo: int = 0, hi: int = -1
|
|
) -> None:
|
|
"""
|
|
Inserts a given value into a sorted array after other values with the same value.
|
|
|
|
It has the same interface as
|
|
https://docs.python.org/3/library/bisect.html#bisect.insort_right .
|
|
|
|
:param sorted_collection: some ascending sorted collection with comparable items
|
|
:param item: item to insert
|
|
:param lo: lowest index to consider (as in sorted_collection[lo:hi])
|
|
:param hi: past the highest index to consider (as in sorted_collection[lo:hi])
|
|
|
|
Examples:
|
|
>>> sorted_collection = [0, 5, 7, 10, 15]
|
|
>>> insort_right(sorted_collection, 6)
|
|
>>> sorted_collection
|
|
[0, 5, 6, 7, 10, 15]
|
|
|
|
>>> sorted_collection = [(0, 0), (5, 5), (7, 7), (10, 10), (15, 15)]
|
|
>>> item = (5, 5)
|
|
>>> insort_right(sorted_collection, item)
|
|
>>> sorted_collection
|
|
[(0, 0), (5, 5), (5, 5), (7, 7), (10, 10), (15, 15)]
|
|
>>> item is sorted_collection[1]
|
|
False
|
|
>>> item is sorted_collection[2]
|
|
True
|
|
|
|
>>> sorted_collection = [0, 5, 7, 10, 15]
|
|
>>> insort_right(sorted_collection, 20)
|
|
>>> sorted_collection
|
|
[0, 5, 7, 10, 15, 20]
|
|
|
|
>>> sorted_collection = [0, 5, 7, 10, 15]
|
|
>>> insort_right(sorted_collection, 15, 1, 3)
|
|
>>> sorted_collection
|
|
[0, 5, 7, 15, 10, 15]
|
|
"""
|
|
sorted_collection.insert(bisect_right(sorted_collection, item, lo, hi), item)
|
|
|
|
|
|
def binary_search(sorted_collection: list[int], item: int) -> int | None:
|
|
"""Pure implementation of binary search algorithm in Python
|
|
|
|
Be careful collection must be ascending sorted, otherwise result will be
|
|
unpredictable
|
|
|
|
:param sorted_collection: some ascending sorted collection with comparable items
|
|
:param item: item value to search
|
|
:return: index of found item or None if item is not found
|
|
|
|
Examples:
|
|
>>> binary_search([0, 5, 7, 10, 15], 0)
|
|
0
|
|
|
|
>>> binary_search([0, 5, 7, 10, 15], 15)
|
|
4
|
|
|
|
>>> binary_search([0, 5, 7, 10, 15], 5)
|
|
1
|
|
|
|
>>> binary_search([0, 5, 7, 10, 15], 6)
|
|
|
|
"""
|
|
left = 0
|
|
right = len(sorted_collection) - 1
|
|
|
|
while left <= right:
|
|
midpoint = left + (right - left) // 2
|
|
current_item = sorted_collection[midpoint]
|
|
if current_item == item:
|
|
return midpoint
|
|
elif item < current_item:
|
|
right = midpoint - 1
|
|
else:
|
|
left = midpoint + 1
|
|
return None
|
|
|
|
|
|
def binary_search_std_lib(sorted_collection: list[int], item: int) -> int | None:
|
|
"""Pure implementation of binary search algorithm in Python using stdlib
|
|
|
|
Be careful collection must be ascending sorted, otherwise result will be
|
|
unpredictable
|
|
|
|
:param sorted_collection: some ascending sorted collection with comparable items
|
|
:param item: item value to search
|
|
:return: index of found item or None if item is not found
|
|
|
|
Examples:
|
|
>>> binary_search_std_lib([0, 5, 7, 10, 15], 0)
|
|
0
|
|
|
|
>>> binary_search_std_lib([0, 5, 7, 10, 15], 15)
|
|
4
|
|
|
|
>>> binary_search_std_lib([0, 5, 7, 10, 15], 5)
|
|
1
|
|
|
|
>>> binary_search_std_lib([0, 5, 7, 10, 15], 6)
|
|
|
|
"""
|
|
index = bisect.bisect_left(sorted_collection, item)
|
|
if index != len(sorted_collection) and sorted_collection[index] == item:
|
|
return index
|
|
return None
|
|
|
|
|
|
def binary_search_by_recursion(
|
|
sorted_collection: list[int], item: int, left: int, right: int
|
|
) -> int | None:
|
|
"""Pure implementation of binary search algorithm in Python by recursion
|
|
|
|
Be careful collection must be ascending sorted, otherwise result will be
|
|
unpredictable
|
|
First recursion should be started with left=0 and right=(len(sorted_collection)-1)
|
|
|
|
:param sorted_collection: some ascending sorted collection with comparable items
|
|
:param item: item value to search
|
|
:return: index of found item or None if item is not found
|
|
|
|
Examples:
|
|
>>> binary_search_by_recursion([0, 5, 7, 10, 15], 0, 0, 4)
|
|
0
|
|
|
|
>>> binary_search_by_recursion([0, 5, 7, 10, 15], 15, 0, 4)
|
|
4
|
|
|
|
>>> binary_search_by_recursion([0, 5, 7, 10, 15], 5, 0, 4)
|
|
1
|
|
|
|
>>> binary_search_by_recursion([0, 5, 7, 10, 15], 6, 0, 4)
|
|
|
|
"""
|
|
if right < left:
|
|
return None
|
|
|
|
midpoint = left + (right - left) // 2
|
|
|
|
if sorted_collection[midpoint] == item:
|
|
return midpoint
|
|
elif sorted_collection[midpoint] > item:
|
|
return binary_search_by_recursion(sorted_collection, item, left, midpoint - 1)
|
|
else:
|
|
return binary_search_by_recursion(sorted_collection, item, midpoint + 1, right)
|
|
|
|
|
|
if __name__ == "__main__":
|
|
user_input = input("Enter numbers separated by comma:\n").strip()
|
|
collection = sorted(int(item) for item in user_input.split(","))
|
|
target = int(input("Enter a single number to be found in the list:\n"))
|
|
result = binary_search(collection, target)
|
|
if result is None:
|
|
print(f"{target} was not found in {collection}.")
|
|
else:
|
|
print(f"{target} was found at position {result} in {collection}.")
|