Given a positive integer n, write a function that returns true if it is a perfect square and false otherwise. Don’t use any built-in math functions like sqrt.

perfect_square.py

def perfect_square(n: int) -> bool:
    if n < 0 or not isinstance(n, int):
        raise ValueError(f'{n} -> must be integer and non-negative')

    return int(n ** 0.5) ** 2 == n


def perfect_square_binary_search(n: int) -> bool:
    if n < 0 or not isinstance(n, int):
        raise ValueError(f'{n} -> must be integer and non-negative')
    
    low = 0
    high = n
    while low <= high:
        mid = (high - low) // 2 + low
        if mid ** 2 > n:
            high = mid - 1
        elif mid ** 2 < n:
            low = mid + 1
        else:
            return True
    # Can't be a perfect square.
    return False


def test_cases():
    CASES = (
        (25, True),
        (10, False),
        (0, True),
        (1, True),
        (9, True),
        (49, True),
        (64, True),
        (2, False),
        (3, False),
        (15, False),
    )

    for num, expected in CASES:
        result = perfect_square_binary_search(num)
        assert result == expected, f'{result=} != {expected=}'


if __name__ == '__main__':
    test_cases()