mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-11-24 05:21:09 +00:00
fcf82a1eda
* Implemented Exponential Search with binary search for improved performance on large sorted arrays. * [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci * Added type hints and doctests for binary_search and exponential_search functions. Improved code documentation and ensured testability. * [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci * Update and rename Exponential_Search.py to exponential_search.py * [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>
114 lines
3.6 KiB
Python
114 lines
3.6 KiB
Python
#!/usr/bin/env python3
|
|
|
|
"""
|
|
Pure Python implementation of exponential search algorithm
|
|
|
|
For more information, see the Wikipedia page:
|
|
https://en.wikipedia.org/wiki/Exponential_search
|
|
|
|
For doctests run the following command:
|
|
python3 -m doctest -v exponential_search.py
|
|
|
|
For manual testing run:
|
|
python3 exponential_search.py
|
|
"""
|
|
|
|
from __future__ import annotations
|
|
|
|
|
|
def binary_search_by_recursion(
|
|
sorted_collection: list[int], item: int, left: int = 0, right: int = -1
|
|
) -> int:
|
|
"""Pure implementation of binary search algorithm in Python using recursion
|
|
|
|
Be careful: the collection must be ascending sorted otherwise, the result will be
|
|
unpredictable.
|
|
|
|
:param sorted_collection: some ascending sorted collection with comparable items
|
|
:param item: item value to search
|
|
:param left: starting index for the search
|
|
:param right: ending index for the search
|
|
:return: index of the found item or -1 if the 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)
|
|
-1
|
|
"""
|
|
if right < 0:
|
|
right = len(sorted_collection) - 1
|
|
if list(sorted_collection) != sorted(sorted_collection):
|
|
raise ValueError("sorted_collection must be sorted in ascending order")
|
|
if right < left:
|
|
return -1
|
|
|
|
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)
|
|
|
|
|
|
def exponential_search(sorted_collection: list[int], item: int) -> int:
|
|
"""
|
|
Pure implementation of an exponential search algorithm in Python.
|
|
For more information, refer to:
|
|
https://en.wikipedia.org/wiki/Exponential_search
|
|
|
|
Be careful: the collection must be ascending sorted, otherwise the result will be
|
|
unpredictable.
|
|
|
|
:param sorted_collection: some ascending sorted collection with comparable items
|
|
:param item: item value to search
|
|
:return: index of the found item or -1 if the item is not found
|
|
|
|
The time complexity of this algorithm is O(log i) where i is the index of the item.
|
|
|
|
Examples:
|
|
>>> exponential_search([0, 5, 7, 10, 15], 0)
|
|
0
|
|
>>> exponential_search([0, 5, 7, 10, 15], 15)
|
|
4
|
|
>>> exponential_search([0, 5, 7, 10, 15], 5)
|
|
1
|
|
>>> exponential_search([0, 5, 7, 10, 15], 6)
|
|
-1
|
|
"""
|
|
if list(sorted_collection) != sorted(sorted_collection):
|
|
raise ValueError("sorted_collection must be sorted in ascending order")
|
|
|
|
if sorted_collection[0] == item:
|
|
return 0
|
|
|
|
bound = 1
|
|
while bound < len(sorted_collection) and sorted_collection[bound] < item:
|
|
bound *= 2
|
|
|
|
left = bound // 2
|
|
right = min(bound, len(sorted_collection) - 1)
|
|
return binary_search_by_recursion(sorted_collection, item, left, right)
|
|
|
|
|
|
if __name__ == "__main__":
|
|
import doctest
|
|
|
|
doctest.testmod()
|
|
|
|
# Manual testing
|
|
user_input = input("Enter numbers separated by commas: ").strip()
|
|
collection = sorted(int(item) for item in user_input.split(","))
|
|
target = int(input("Enter a number to search for: "))
|
|
result = exponential_search(sorted_collection=collection, item=target)
|
|
if result == -1:
|
|
print(f"{target} was not found in {collection}.")
|
|
else:
|
|
print(f"{target} was found at index {result} in {collection}.")
|