mirror of
https://github.com/TheAlgorithms/Python.git
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320 lines
9.3 KiB
Python
320 lines
9.3 KiB
Python
"""
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This is pure python implementation of binary search algorithms
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For doctests run following command:
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python -m doctest -v binary_search.py
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or
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python3 -m doctest -v binary_search.py
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For manual testing run:
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python binary_search.py
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"""
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import bisect
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def bisect_left(sorted_collection, item, lo=0, hi=None):
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"""
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Locates the first element in a sorted array that is larger or equal to a given value.
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It has the same interface as 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 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 is None:
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hi = len(sorted_collection)
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while lo < hi:
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mid = (lo + hi) // 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(sorted_collection, item, lo=0, hi=None):
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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 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 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 is None:
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hi = len(sorted_collection)
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while lo < hi:
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mid = (lo + hi) // 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(sorted_collection, item, lo=0, hi=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 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(sorted_collection, item, lo=0, hi=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 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, item):
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"""Pure implementation of binary search algorithm in Python
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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 found item or None if 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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"""
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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 None
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def binary_search_std_lib(sorted_collection, item):
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"""Pure implementation of binary search algorithm in Python using stdlib
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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 found item or None if 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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"""
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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 None
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def binary_search_by_recursion(sorted_collection, item, left, right):
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"""Pure implementation of binary search algorithm in Python by recursion
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Be careful collection must be ascending sorted, otherwise 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 found item or None if 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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"""
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if right < left:
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return None
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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 __assert_sorted(collection):
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"""Check if collection is ascending sorted, if not - raises :py:class:`ValueError`
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:param collection: collection
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:return: True if collection is ascending sorted
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:raise: :py:class:`ValueError` if collection is not ascending sorted
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Examples:
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>>> __assert_sorted([0, 1, 2, 4])
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True
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>>> __assert_sorted([10, -1, 5])
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Traceback (most recent call last):
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...
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ValueError: Collection must be ascending sorted
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"""
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if collection != sorted(collection):
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raise ValueError("Collection must be ascending sorted")
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return True
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if __name__ == "__main__":
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import sys
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user_input = input("Enter numbers separated by comma:\n").strip()
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collection = [int(item) for item in user_input.split(",")]
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try:
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__assert_sorted(collection)
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except ValueError:
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sys.exit("Sequence must be ascending sorted to apply binary search")
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target_input = input("Enter a single number to be found in the list:\n")
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target = int(target_input)
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result = binary_search(collection, target)
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if result is not None:
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print(f"{target} found at positions: {result}")
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else:
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print("Not found")
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