#!/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 """ 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: """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 """ 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: """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 """ 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: """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 """ 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 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 """ 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 = ( # Fastest to slowest... 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) = }") # type: ignore[operator] 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}.")