usrbinenv python3 pure python implementations of binary search algorithms for doctests run the following command python3 m doctest v binarysearch py for manual testing run python3 binarysearch py 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 org3librarybisect htmlbisect bisectleft param sortedcollection some ascending sorted collection with comparable items param item item to bisect param lo lowest index to consider as in sortedcollectionlo hi param hi past the highest index to consider as in sortedcollectionlo hi return index i such that all values in sortedcollectionlo i are item and all values in sortedcollectioni hi are item examples bisectleft0 5 7 10 15 0 0 bisectleft0 5 7 10 15 6 2 bisectleft0 5 7 10 15 20 5 bisectleft0 5 7 10 15 15 1 3 3 bisectleft0 5 7 10 15 6 2 2 locates the first element in a sorted array that is larger than a given value it has the same interface as https docs python org3librarybisect htmlbisect bisectright param sortedcollection some ascending sorted collection with comparable items param item item to bisect param lo lowest index to consider as in sortedcollectionlo hi param hi past the highest index to consider as in sortedcollectionlo hi return index i such that all values in sortedcollectionlo i are item and all values in sortedcollectioni hi are item examples bisectright0 5 7 10 15 0 1 bisectright0 5 7 10 15 15 5 bisectright0 5 7 10 15 6 2 bisectright0 5 7 10 15 15 1 3 3 bisectright0 5 7 10 15 6 2 2 inserts a given value into a sorted array before other values with the same value it has the same interface as https docs python org3librarybisect htmlbisect insortleft param sortedcollection some ascending sorted collection with comparable items param item item to insert param lo lowest index to consider as in sortedcollectionlo hi param hi past the highest index to consider as in sortedcollectionlo hi examples sortedcollection 0 5 7 10 15 insortleftsortedcollection 6 sortedcollection 0 5 6 7 10 15 sortedcollection 0 0 5 5 7 7 10 10 15 15 item 5 5 insortleftsortedcollection item sortedcollection 0 0 5 5 5 5 7 7 10 10 15 15 item is sortedcollection1 true item is sortedcollection2 false sortedcollection 0 5 7 10 15 insortleftsortedcollection 20 sortedcollection 0 5 7 10 15 20 sortedcollection 0 5 7 10 15 insortleftsortedcollection 15 1 3 sortedcollection 0 5 7 15 10 15 inserts a given value into a sorted array after other values with the same value it has the same interface as https docs python org3librarybisect htmlbisect insortright param sortedcollection some ascending sorted collection with comparable items param item item to insert param lo lowest index to consider as in sortedcollectionlo hi param hi past the highest index to consider as in sortedcollectionlo hi examples sortedcollection 0 5 7 10 15 insortrightsortedcollection 6 sortedcollection 0 5 6 7 10 15 sortedcollection 0 0 5 5 7 7 10 10 15 15 item 5 5 insortrightsortedcollection item sortedcollection 0 0 5 5 5 5 7 7 10 10 15 15 item is sortedcollection1 false item is sortedcollection2 true sortedcollection 0 5 7 10 15 insortrightsortedcollection 20 sortedcollection 0 5 7 10 15 20 sortedcollection 0 5 7 10 15 insortrightsortedcollection 15 1 3 sortedcollection 0 5 7 15 10 15 pure implementation of a binary search algorithm in python be careful collection must be ascending sorted otherwise the result will be unpredictable param sortedcollection 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 examples binarysearch0 5 7 10 15 0 0 binarysearch0 5 7 10 15 15 4 binarysearch0 5 7 10 15 5 1 binarysearch0 5 7 10 15 6 1 pure implementation of a binary search algorithm in python using stdlib be careful collection must be ascending sorted otherwise the result will be unpredictable param sortedcollection 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 examples binarysearchstdlib0 5 7 10 15 0 0 binarysearchstdlib0 5 7 10 15 15 4 binarysearchstdlib0 5 7 10 15 5 1 binarysearchstdlib0 5 7 10 15 6 1 pure implementation of a binary search algorithm in python by recursion be careful collection must be ascending sorted otherwise the result will be unpredictable first recursion should be started with left0 and rightlensortedcollection1 param sortedcollection 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 examples binarysearchbyrecursion0 5 7 10 15 0 0 4 0 binarysearchbyrecursion0 5 7 10 15 15 0 4 4 binarysearchbyrecursion0 5 7 10 15 5 0 4 1 binarysearchbyrecursion0 5 7 10 15 6 0 4 1 pure implementation of an exponential search algorithm in python resources used https en wikipedia orgwikiexponentialsearch be careful collection must be ascending sorted otherwise result will be unpredictable param sortedcollection 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 order of this algorithm is olg i where i is index position of item if exist examples exponentialsearch0 5 7 10 15 0 0 exponentialsearch0 5 7 10 15 15 4 exponentialsearch0 5 7 10 15 5 1 exponentialsearch0 5 7 10 15 6 1 usr bin env python3 pure python implementations of binary search algorithms for doctests run the following command python3 m doctest v binary_search py for manual testing run python3 binary_search py 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 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 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 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 pure implementation of a binary search algorithm in python be careful 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 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 1 pure implementation of a binary search algorithm in python using stdlib be careful 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 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 1 pure implementation of a binary search algorithm in python by recursion be careful collection must be ascending sorted otherwise the 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 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 pure implementation of an exponential search algorithm in python resources used https en wikipedia org wiki exponential_search 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 the found item or 1 if the item is not found the order of this algorithm is o lg i where i is index position of item if exist 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 fastest to slowest type ignore operator
from __future__ import annotations

import bisect


def bisect_left(
    sorted_collection: list[int], item: int, lo: int = 0, hi: int = -1
) -> int:
    
    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:
    
    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:
    
    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:
    
    sorted_collection.insert(bisect_right(sorted_collection, item, lo, hi), item)


def binary_search(sorted_collection: list[int], item: int) -> int:
    
    if list(sorted_collection) != sorted(sorted_collection):
        raise ValueError("sorted_collection must be sorted in ascending order")
    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 -1


def binary_search_std_lib(sorted_collection: list[int], item: int) -> int:
    
    if list(sorted_collection) != sorted(sorted_collection):
        raise ValueError("sorted_collection must be sorted in ascending order")
    index = bisect.bisect_left(sorted_collection, item)
    if index != len(sorted_collection) and sorted_collection[index] == item:
        return index
    return -1


def binary_search_by_recursion(
    sorted_collection: list[int], item: int, left: int = 0, right: int = -1
) -> int:
    
    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:
    
    if list(sorted_collection) != sorted(sorted_collection):
        raise ValueError("sorted_collection must be sorted in ascending order")
    bound = 1
    while bound < len(sorted_collection) and sorted_collection[bound] < item:
        bound *= 2
    left = bound // 2
    right = min(bound, len(sorted_collection) - 1)
    last_result = binary_search_by_recursion(
        sorted_collection=sorted_collection, item=item, left=left, right=right
    )
    if last_result is None:
        return -1
    return last_result


searches = (  
    binary_search_std_lib,
    binary_search,
    exponential_search,
    binary_search_by_recursion,
)


if __name__ == "__main__":
    import doctest
    import timeit

    doctest.testmod()
    for search in searches:
        name = f"{search.__name__:>26}"
        print(f"{name}: {search([0, 5, 7, 10, 15], 10) = }")  

    print("\nBenchmarks...")
    setup = "collection = range(1000)"
    for search in searches:
        name = search.__name__
        print(
            f"{name:>26}:",
            timeit.timeit(
                f"{name}(collection, 500)", setup=setup, number=5_000, globals=globals()
            ),
        )

    user_input = input("\nEnter numbers separated by comma: ").strip()
    collection = sorted(int(item) for item in user_input.split(","))
    target = int(input("Enter a single number to be found in the list: "))
    result = binary_search(sorted_collection=collection, item=target)
    if result == -1:
        print(f"{target} was not found in {collection}.")
    else:
        print(f"{target} was found at position {result} of {collection}.")