#### Interpolation Search

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```"""
This is pure Python implementation of interpolation search algorithm
"""

def interpolation_search(sorted_collection, item):
"""Pure implementation of interpolation search algorithm in Python
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 found item or None if item is not found
"""
left = 0
right = len(sorted_collection) - 1

while left <= right:
# avoid divided by 0 during interpolation
if sorted_collection[left] == sorted_collection[right]:
if sorted_collection[left] == item:
return left
else:
return None

point = left + ((item - sorted_collection[left]) * (right - left)) // (
sorted_collection[right] - sorted_collection[left]
)

# out of range check
if point < 0 or point >= len(sorted_collection):
return None

current_item = sorted_collection[point]
if current_item == item:
return point
else:
if point < left:
right = left
left = point
elif point > right:
left = right
right = point
else:
if item < current_item:
right = point - 1
else:
left = point + 1
return None

def interpolation_search_by_recursion(sorted_collection, item, left, right):

"""Pure implementation of interpolation search algorithm in Python by recursion
Be careful collection must be ascending sorted, otherwise 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 found item or None if item is not found
"""

# avoid divided by 0 during interpolation
if sorted_collection[left] == sorted_collection[right]:
if sorted_collection[left] == item:
return left
else:
return None

point = left + ((item - sorted_collection[left]) * (right - left)) // (
sorted_collection[right] - sorted_collection[left]
)

# out of range check
if point < 0 or point >= len(sorted_collection):
return None

if sorted_collection[point] == item:
return point
elif point < left:
return interpolation_search_by_recursion(sorted_collection, item, point, left)
elif point > right:
return interpolation_search_by_recursion(sorted_collection, item, right, left)
else:
if sorted_collection[point] > item:
return interpolation_search_by_recursion(
sorted_collection, item, left, point - 1
)
else:
return interpolation_search_by_recursion(
sorted_collection, item, point + 1, right
)

def __assert_sorted(collection):
"""Check if collection is ascending sorted, if not - raises :py:class:`ValueError`
:param collection: collection
:return: True if collection is ascending sorted
:raise: :py:class:`ValueError` if collection is not ascending sorted
Examples:
>>> __assert_sorted([0, 1, 2, 4])
True
>>> __assert_sorted([10, -1, 5])
Traceback (most recent call last):
...
ValueError: Collection must be ascending sorted
"""
if collection != sorted(collection):
raise ValueError("Collection must be ascending sorted")
return True

if __name__ == "__main__":
import sys

"""
user_input = input('Enter numbers separated by comma:\n').strip()
collection = [int(item) for item in user_input.split(',')]
try:
__assert_sorted(collection)
except ValueError:
sys.exit('Sequence must be ascending sorted to apply interpolation search')

target_input = input('Enter a single number to be found in the list:\n')
target = int(target_input)
"""

debug = 0
if debug == 1:
collection = [10, 30, 40, 45, 50, 66, 77, 93]
try:
__assert_sorted(collection)
except ValueError:
sys.exit("Sequence must be ascending sorted to apply interpolation search")
target = 67

result = interpolation_search(collection, target)
if result is not None:
print(f"{target} found at positions: {result}")
else: