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"""

Pure Python implementation of the jump search algorithm.

This algorithm iterates through a sorted collection with a step of n^(1/2),

until the element compared is bigger than the one searched.

It will then perform a linear search until it matches the wanted number.

If not found, it returns -1.

"""

import math

def jump_search(arr: list, x: int) -> int:

"""

Pure Python implementation of the jump search algorithm.

Examples:

>>> jump_search([0, 1, 2, 3, 4, 5], 3)

>>> jump_search([-5, -2, -1], -1)

>>> jump_search([0, 5, 10, 20], 8)

-1

>>> jump_search([0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610], 55)

"""

n = len(arr)

step = int(math.floor(math.sqrt(n)))

prev = 0

while arr[min(step, n) - 1] < x:

prev = step

step += int(math.floor(math.sqrt(n)))

if prev >= n:

return -1

while arr[prev] < x:

prev = prev + 1

if prev == min(step, n):

return -1

if arr[prev] == x:

return prev

return -1

if __name__ == "__main__":

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

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

x = int(input("Enter the number to be searched:\n"))

res = jump_search(arr, x)

if res == -1:

print("Number not found!")

else:

print(f"Number {x} is at index {res}")

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