#### Ternary Search

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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 __future__ import annotations

# 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)
3
>>> lin_search(0, 3, [4, 5, 6, 7], 7)
-1
>>> lin_search(0, 2, [-18, 2], -18)
0
>>> lin_search(0, 1, [5], 5)
0
>>> lin_search(0, 3, ['a', 'c', 'd'], 'c')
1
>>> lin_search(0, 3, [.1, .4 , -.1], .1)
0
>>> lin_search(0, 3, [.1, .4 , -.1], -.1)
2
"""
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)
4
>>> ite_ternary_search([4, 5, 6, 7], 4)
0
>>> ite_ternary_search([4, 5, 6, 7], -10)
-1
>>> ite_ternary_search([-18, 2], -18)
0
>>> ite_ternary_search([5], 5)
0
>>> ite_ternary_search(['a', 'c', 'd'], 'c')
1
>>> ite_ternary_search(['a', 'c', 'd'], 'f')
-1
>>> ite_ternary_search([], 1)
-1
>>> ite_ternary_search([.1, .4 , -.1], .1)
0
"""

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
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)
8
>>> rec_ternary_search(0, 2, [4, 5, 6, 7], 4)
0
>>> rec_ternary_search(0, 3, [4, 5, 6, 7], -10)
-1
>>> rec_ternary_search(0, 1, [-18, 2], -18)
0
>>> rec_ternary_search(0, 1, [5], 5)
0
>>> rec_ternary_search(0, 2, ['a', 'c', 'd'], 'c')
1
>>> 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)
0
"""
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__":
import doctest

doctest.testmod()

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: