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361 lines
11 KiB
Python
361 lines
11 KiB
Python
#!/usr/bin/env python3
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"""
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Pure Python implementations of binary search algorithms
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For doctests run the following command:
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python3 -m doctest -v binary_search.py
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For manual testing run:
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python3 binary_search.py
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"""
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from __future__ import annotations
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import bisect
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def bisect_left(
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sorted_collection: list[int], item: int, lo: int = 0, hi: int = -1
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) -> int:
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"""
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Locates the first element in a sorted array that is larger or equal to a given
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value.
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It has the same interface as
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https://docs.python.org/3/library/bisect.html#bisect.bisect_left .
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:param sorted_collection: some ascending sorted collection with comparable items
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:param item: item to bisect
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:param lo: lowest index to consider (as in sorted_collection[lo:hi])
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:param hi: past the highest index to consider (as in sorted_collection[lo:hi])
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:return: index i such that all values in sorted_collection[lo:i] are < item and all
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values in sorted_collection[i:hi] are >= item.
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Examples:
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>>> bisect_left([0, 5, 7, 10, 15], 0)
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0
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>>> bisect_left([0, 5, 7, 10, 15], 6)
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2
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>>> bisect_left([0, 5, 7, 10, 15], 20)
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5
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>>> bisect_left([0, 5, 7, 10, 15], 15, 1, 3)
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3
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>>> bisect_left([0, 5, 7, 10, 15], 6, 2)
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2
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"""
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if hi < 0:
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hi = len(sorted_collection)
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while lo < hi:
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mid = lo + (hi - lo) // 2
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if sorted_collection[mid] < item:
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lo = mid + 1
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else:
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hi = mid
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return lo
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def bisect_right(
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sorted_collection: list[int], item: int, lo: int = 0, hi: int = -1
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) -> int:
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"""
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Locates the first element in a sorted array that is larger than a given value.
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It has the same interface as
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https://docs.python.org/3/library/bisect.html#bisect.bisect_right .
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:param sorted_collection: some ascending sorted collection with comparable items
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:param item: item to bisect
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:param lo: lowest index to consider (as in sorted_collection[lo:hi])
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:param hi: past the highest index to consider (as in sorted_collection[lo:hi])
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:return: index i such that all values in sorted_collection[lo:i] are <= item and
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all values in sorted_collection[i:hi] are > item.
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Examples:
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>>> bisect_right([0, 5, 7, 10, 15], 0)
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1
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>>> bisect_right([0, 5, 7, 10, 15], 15)
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5
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>>> bisect_right([0, 5, 7, 10, 15], 6)
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2
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>>> bisect_right([0, 5, 7, 10, 15], 15, 1, 3)
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3
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>>> bisect_right([0, 5, 7, 10, 15], 6, 2)
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2
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"""
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if hi < 0:
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hi = len(sorted_collection)
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while lo < hi:
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mid = lo + (hi - lo) // 2
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if sorted_collection[mid] <= item:
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lo = mid + 1
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else:
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hi = mid
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return lo
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def insort_left(
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sorted_collection: list[int], item: int, lo: int = 0, hi: int = -1
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) -> None:
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"""
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Inserts a given value into a sorted array before other values with the same value.
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It has the same interface as
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https://docs.python.org/3/library/bisect.html#bisect.insort_left .
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:param sorted_collection: some ascending sorted collection with comparable items
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:param item: item to insert
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:param lo: lowest index to consider (as in sorted_collection[lo:hi])
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:param hi: past the highest index to consider (as in sorted_collection[lo:hi])
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Examples:
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>>> sorted_collection = [0, 5, 7, 10, 15]
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>>> insort_left(sorted_collection, 6)
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>>> sorted_collection
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[0, 5, 6, 7, 10, 15]
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>>> sorted_collection = [(0, 0), (5, 5), (7, 7), (10, 10), (15, 15)]
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>>> item = (5, 5)
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>>> insort_left(sorted_collection, item)
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>>> sorted_collection
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[(0, 0), (5, 5), (5, 5), (7, 7), (10, 10), (15, 15)]
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>>> item is sorted_collection[1]
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True
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>>> item is sorted_collection[2]
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False
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>>> sorted_collection = [0, 5, 7, 10, 15]
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>>> insort_left(sorted_collection, 20)
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>>> sorted_collection
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[0, 5, 7, 10, 15, 20]
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>>> sorted_collection = [0, 5, 7, 10, 15]
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>>> insort_left(sorted_collection, 15, 1, 3)
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>>> sorted_collection
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[0, 5, 7, 15, 10, 15]
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"""
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sorted_collection.insert(bisect_left(sorted_collection, item, lo, hi), item)
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def insort_right(
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sorted_collection: list[int], item: int, lo: int = 0, hi: int = -1
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) -> None:
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"""
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Inserts a given value into a sorted array after other values with the same value.
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It has the same interface as
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https://docs.python.org/3/library/bisect.html#bisect.insort_right .
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:param sorted_collection: some ascending sorted collection with comparable items
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:param item: item to insert
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:param lo: lowest index to consider (as in sorted_collection[lo:hi])
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:param hi: past the highest index to consider (as in sorted_collection[lo:hi])
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Examples:
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>>> sorted_collection = [0, 5, 7, 10, 15]
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>>> insort_right(sorted_collection, 6)
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>>> sorted_collection
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[0, 5, 6, 7, 10, 15]
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>>> sorted_collection = [(0, 0), (5, 5), (7, 7), (10, 10), (15, 15)]
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>>> item = (5, 5)
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>>> insort_right(sorted_collection, item)
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>>> sorted_collection
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[(0, 0), (5, 5), (5, 5), (7, 7), (10, 10), (15, 15)]
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>>> item is sorted_collection[1]
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False
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>>> item is sorted_collection[2]
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True
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>>> sorted_collection = [0, 5, 7, 10, 15]
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>>> insort_right(sorted_collection, 20)
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>>> sorted_collection
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[0, 5, 7, 10, 15, 20]
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>>> sorted_collection = [0, 5, 7, 10, 15]
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>>> insort_right(sorted_collection, 15, 1, 3)
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>>> sorted_collection
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[0, 5, 7, 15, 10, 15]
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"""
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sorted_collection.insert(bisect_right(sorted_collection, item, lo, hi), item)
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def binary_search(sorted_collection: list[int], item: int) -> int:
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"""Pure implementation of a binary search algorithm in Python
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Be careful collection must be ascending sorted otherwise, the result will be
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unpredictable
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:param sorted_collection: some ascending sorted collection with comparable items
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:param item: item value to search
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:return: index of the found item or -1 if the item is not found
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Examples:
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>>> binary_search([0, 5, 7, 10, 15], 0)
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0
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>>> binary_search([0, 5, 7, 10, 15], 15)
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4
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>>> binary_search([0, 5, 7, 10, 15], 5)
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1
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>>> binary_search([0, 5, 7, 10, 15], 6)
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-1
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"""
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if list(sorted_collection) != sorted(sorted_collection):
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raise ValueError("sorted_collection must be sorted in ascending order")
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left = 0
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right = len(sorted_collection) - 1
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while left <= right:
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midpoint = left + (right - left) // 2
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current_item = sorted_collection[midpoint]
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if current_item == item:
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return midpoint
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elif item < current_item:
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right = midpoint - 1
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else:
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left = midpoint + 1
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return -1
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def binary_search_std_lib(sorted_collection: list[int], item: int) -> int:
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"""Pure implementation of a binary search algorithm in Python using stdlib
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Be careful collection must be ascending sorted otherwise, the result will be
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unpredictable
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:param sorted_collection: some ascending sorted collection with comparable items
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:param item: item value to search
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:return: index of the found item or -1 if the item is not found
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Examples:
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>>> binary_search_std_lib([0, 5, 7, 10, 15], 0)
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0
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>>> binary_search_std_lib([0, 5, 7, 10, 15], 15)
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4
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>>> binary_search_std_lib([0, 5, 7, 10, 15], 5)
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1
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>>> binary_search_std_lib([0, 5, 7, 10, 15], 6)
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-1
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"""
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if list(sorted_collection) != sorted(sorted_collection):
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raise ValueError("sorted_collection must be sorted in ascending order")
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index = bisect.bisect_left(sorted_collection, item)
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if index != len(sorted_collection) and sorted_collection[index] == item:
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return index
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return -1
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def binary_search_by_recursion(
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sorted_collection: list[int], item: int, left: int = 0, right: int = -1
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) -> int:
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"""Pure implementation of a binary search algorithm in Python by recursion
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Be careful collection must be ascending sorted otherwise, the result will be
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unpredictable
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First recursion should be started with left=0 and right=(len(sorted_collection)-1)
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:param sorted_collection: some ascending sorted collection with comparable items
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:param item: item value to search
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:return: index of the found item or -1 if the item is not found
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Examples:
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>>> binary_search_by_recursion([0, 5, 7, 10, 15], 0, 0, 4)
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0
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>>> binary_search_by_recursion([0, 5, 7, 10, 15], 15, 0, 4)
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4
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>>> binary_search_by_recursion([0, 5, 7, 10, 15], 5, 0, 4)
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1
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>>> binary_search_by_recursion([0, 5, 7, 10, 15], 6, 0, 4)
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-1
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"""
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if right < 0:
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right = len(sorted_collection) - 1
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if list(sorted_collection) != sorted(sorted_collection):
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raise ValueError("sorted_collection must be sorted in ascending order")
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if right < left:
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return -1
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midpoint = left + (right - left) // 2
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if sorted_collection[midpoint] == item:
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return midpoint
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elif sorted_collection[midpoint] > item:
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return binary_search_by_recursion(sorted_collection, item, left, midpoint - 1)
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else:
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return binary_search_by_recursion(sorted_collection, item, midpoint + 1, right)
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def exponential_search(sorted_collection: list[int], item: int) -> int:
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"""Pure implementation of an exponential search algorithm in Python
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Resources used:
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https://en.wikipedia.org/wiki/Exponential_search
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Be careful collection must be ascending sorted otherwise, result will be
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unpredictable
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:param sorted_collection: some ascending sorted collection with comparable items
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:param item: item value to search
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:return: index of the found item or -1 if the item is not found
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the order of this algorithm is O(lg I) where I is index position of item if exist
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Examples:
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>>> exponential_search([0, 5, 7, 10, 15], 0)
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0
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>>> exponential_search([0, 5, 7, 10, 15], 15)
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4
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>>> exponential_search([0, 5, 7, 10, 15], 5)
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1
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>>> exponential_search([0, 5, 7, 10, 15], 6)
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-1
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"""
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if list(sorted_collection) != sorted(sorted_collection):
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raise ValueError("sorted_collection must be sorted in ascending order")
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bound = 1
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while bound < len(sorted_collection) and sorted_collection[bound] < item:
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bound *= 2
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left = bound // 2
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right = min(bound, len(sorted_collection) - 1)
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last_result = binary_search_by_recursion(
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sorted_collection=sorted_collection, item=item, left=left, right=right
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)
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if last_result is None:
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return -1
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return last_result
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searches = ( # Fastest to slowest...
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binary_search_std_lib,
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binary_search,
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exponential_search,
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binary_search_by_recursion,
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)
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if __name__ == "__main__":
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import doctest
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import timeit
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doctest.testmod()
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for search in searches:
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name = f"{search.__name__:>26}"
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print(f"{name}: {search([0, 5, 7, 10, 15], 10) = }") # type: ignore[operator]
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print("\nBenchmarks...")
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setup = "collection = range(1000)"
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for search in searches:
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name = search.__name__
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print(
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f"{name:>26}:",
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timeit.timeit(
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f"{name}(collection, 500)", setup=setup, number=5_000, globals=globals()
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),
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)
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user_input = input("\nEnter numbers separated by comma: ").strip()
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collection = sorted(int(item) for item in user_input.split(","))
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target = int(input("Enter a single number to be found in the list: "))
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result = binary_search(sorted_collection=collection, item=target)
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if result == -1:
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print(f"{target} was not found in {collection}.")
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else:
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print(f"{target} was found at position {result} of {collection}.")
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