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"""

This is a type of divide and conquer algorithm which divides the search space into

3 parts and finds the target value based on the property of the array or list

(usually monotonic property).

Time Complexity : O(log3 N)

Space Complexity : O(1)

"""

from typing import List

# This is the precision for this function which can be altered.

# It is recommended for users to keep this number greater than or equal to 10.

precision = 10

# This is the linear search that will occur after the search space has become smaller.

def lin_search(left: int, right: int, array: List[int], target: int) -> int:

"""Perform linear search in list. Returns -1 if element is not found.

Parameters

----------

left : int

left index bound.

right : int

right index bound.

array : List[int]

List of elements to be searched on

target : int

Element that is searched

Returns

-------

int

index of element that is looked for.

Examples

--------

>>> lin_search(0, 4, [4, 5, 6, 7], 7)

>>> lin_search(0, 3, [4, 5, 6, 7], 7)

-1

>>> lin_search(0, 2, [-18, 2], -18)

>>> lin_search(0, 1, [5], 5)

>>> lin_search(0, 3, ['a', 'c', 'd'], 'c')

>>> lin_search(0, 3, [.1, .4 , -.1], .1)

>>> lin_search(0, 3, [.1, .4 , -.1], -.1)

"""

for i in range(left, right):

if array[i] == target:

return i

return -1

def ite_ternary_search(array: List[int], target: int) -> int:

"""Iterative method of the ternary search algorithm.

>>> test_list = [0, 1, 2, 8, 13, 17, 19, 32, 42]

>>> ite_ternary_search(test_list, 3)

-1

>>> ite_ternary_search(test_list, 13)

>>> ite_ternary_search([4, 5, 6, 7], 4)

>>> ite_ternary_search([4, 5, 6, 7], -10)

-1

>>> ite_ternary_search([-18, 2], -18)

>>> ite_ternary_search([5], 5)

>>> ite_ternary_search(['a', 'c', 'd'], 'c')

>>> ite_ternary_search(['a', 'c', 'd'], 'f')

-1

>>> ite_ternary_search([], 1)

-1

>>> ite_ternary_search([.1, .4 , -.1], .1)

"""

left = 0

right = len(array)

while left <= right:

if right - left < precision:

return lin_search(left, right, array, target)

one_third = (left + right) / 3 + 1

two_third = 2 * (left + right) / 3 + 1

if array[one_third] == target:

return one_third

elif array[two_third] == target:

return two_third

elif target < array[one_third]:

right = one_third - 1

elif array[two_third] < target:

left = two_third + 1

else:

left = one_third + 1

right = two_third - 1

else:

return -1

def rec_ternary_search(left: int, right: int, array: List[int], target: int) -> int:

"""Recursive method of the ternary search algorithm.

>>> test_list = [0, 1, 2, 8, 13, 17, 19, 32, 42]

>>> rec_ternary_search(0, len(test_list), test_list, 3)

-1

>>> rec_ternary_search(4, len(test_list), test_list, 42)

>>> rec_ternary_search(0, 2, [4, 5, 6, 7], 4)

>>> rec_ternary_search(0, 3, [4, 5, 6, 7], -10)

-1

>>> rec_ternary_search(0, 1, [-18, 2], -18)

>>> rec_ternary_search(0, 1, [5], 5)

>>> rec_ternary_search(0, 2, ['a', 'c', 'd'], 'c')

>>> rec_ternary_search(0, 2, ['a', 'c', 'd'], 'f')

-1

>>> rec_ternary_search(0, 0, [], 1)

-1

>>> rec_ternary_search(0, 3, [.1, .4 , -.1], .1)

"""

if left < right:

if right - left < precision:

return lin_search(left, right, array, target)

one_third = (left + right) / 3 + 1

two_third = 2 * (left + right) / 3 + 1

if array[one_third] == target:

return one_third

elif array[two_third] == target:

return two_third

elif target < array[one_third]:

return rec_ternary_search(left, one_third - 1, array, target)

elif array[two_third] < target:

return rec_ternary_search(two_third + 1, right, array, target)

else:

return rec_ternary_search(one_third + 1, two_third - 1, array, target)

else:

return -1

if __name__ == "__main__":

user_input = input("Enter numbers separated by comma:\n").strip()

collection = [int(item.strip()) for item in user_input.split(",")]

assert collection == sorted(collection), f"List must be ordered.\n{collection}."

target = int(input("Enter the number to be found in the list:\n").strip())

result1 = ite_ternary_search(collection, target)

result2 = rec_ternary_search(0, len(collection) - 1, collection, target)

if result2 != -1:

print(f"Iterative search: {target} found at positions: {result1}")

print(f"Recursive search: {target} found at positions: {result2}")

else:

print("Not found")

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