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"""

Is Rotated String

Given two strings, determine if the second is a rotated version of the first.

Two approaches are provided: concatenation check and brute force.

Reference: https://leetcode.com/problems/rotate-string/

Complexity:

Time: O(n) for concatenation approach, O(n^2) for brute force

Space: O(n)

"""

from __future__ import annotations

def is_rotated(first: str, second: str) -> bool:

"""Check if second is a rotation of first using string concatenation.

Args:

first: The original string.

second: The string to check as a rotation.

Returns:

True if second is a rotation of first, False otherwise.

Examples:

>>> is_rotated("hello", "llohe")

True

"""

if len(first) == len(second):

return second in first + first

else:

return False

def is_rotated_v1(first: str, second: str) -> bool:

"""Check if second is a rotation of first using brute force comparison.

Args:

first: The original string.

second: The string to check as a rotation.

Returns:

True if second is a rotation of first, False otherwise.

Examples:

>>> is_rotated_v1("hello", "llohe")

True

"""

if len(first) != len(second):

return False

if len(first) == 0:

return True

for offset in range(len(first)):

if all(

first[(offset + index) % len(first)] == second[index]

for index in range(len(first))

):

return True

return False