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134 lines
2.9 KiB
Python
134 lines
2.9 KiB
Python
"""
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This is pure Python implementation of fibonacci search.
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Resources used:
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https://en.wikipedia.org/wiki/Fibonacci_search_technique
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For doctests run following command:
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python3 -m doctest -v fibonacci_search.py
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For manual testing run:
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python3 fibonacci_search.py
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"""
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from functools import lru_cache
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@lru_cache
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def fibonacci(k: int) -> int:
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"""Finds fibonacci number in index k.
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Parameters
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----------
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k :
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Index of fibonacci.
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Returns
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-------
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int
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Fibonacci number in position k.
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>>> fibonacci(0)
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0
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>>> fibonacci(2)
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1
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>>> fibonacci(5)
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5
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>>> fibonacci(15)
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610
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>>> fibonacci('a')
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Traceback (most recent call last):
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TypeError: k must be an integer.
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>>> fibonacci(-5)
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Traceback (most recent call last):
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ValueError: k integer must be greater or equal to zero.
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"""
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if not isinstance(k, int):
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raise TypeError("k must be an integer.")
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if k < 0:
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raise ValueError("k integer must be greater or equal to zero.")
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if k == 0:
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return 0
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elif k == 1:
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return 1
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else:
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return fibonacci(k - 1) + fibonacci(k - 2)
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def fibonacci_search(arr: list, val: int) -> int:
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"""A pure Python implementation of a fibonacci search algorithm.
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Parameters
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----------
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arr
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List of sorted elements.
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val
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Element to search in list.
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Returns
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-------
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int
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The index of the element in the array.
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-1 if the element is not found.
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>>> fibonacci_search([4, 5, 6, 7], 4)
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0
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>>> fibonacci_search([4, 5, 6, 7], -10)
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-1
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>>> fibonacci_search([-18, 2], -18)
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0
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>>> fibonacci_search([5], 5)
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0
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>>> fibonacci_search(['a', 'c', 'd'], 'c')
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1
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>>> fibonacci_search(['a', 'c', 'd'], 'f')
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-1
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>>> fibonacci_search([], 1)
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-1
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>>> fibonacci_search([.1, .4 , 7], .4)
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1
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>>> fibonacci_search([], 9)
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-1
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>>> fibonacci_search(list(range(100)), 63)
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63
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>>> fibonacci_search(list(range(100)), 99)
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99
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>>> fibonacci_search(list(range(-100, 100, 3)), -97)
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1
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>>> fibonacci_search(list(range(-100, 100, 3)), 0)
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-1
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>>> fibonacci_search(list(range(-100, 100, 5)), 0)
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20
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>>> fibonacci_search(list(range(-100, 100, 5)), 95)
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39
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"""
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len_list = len(arr)
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# Find m such that F_m >= n where F_i is the i_th fibonacci number.
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i = 0
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while True:
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if fibonacci(i) >= len_list:
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fibb_k = i
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break
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i += 1
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offset = 0
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while fibb_k > 0:
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index_k = min(
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offset + fibonacci(fibb_k - 1), len_list - 1
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) # Prevent out of range
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item_k_1 = arr[index_k]
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if item_k_1 == val:
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return index_k
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elif val < item_k_1:
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fibb_k -= 1
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elif val > item_k_1:
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offset += fibonacci(fibb_k - 1)
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fibb_k -= 2
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else:
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return -1
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if __name__ == "__main__":
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import doctest
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doctest.testmod()
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