Based on the Heron-adapted algorithm, what is the complexity class of theperfect square problem? Show your reasoning.

The Heron-adapted algorithm is used to determine whether a given number is a perfect square. The algorithm works by iteratively improving the estimate of the square root of a number until the estimate is good enough.

The complexity of this algorithm is O(log n). Here's why:

1. The algorithm starts with an initial guess for the square root. This guess is typically the number itself or some part of it.

2. In each iteration, the algorithm improves the guess by averaging the guess and the quotient of the number and the guess.

3. The number of iterations required to get a good enough estimate is proportional to the number of digits in the number. This is because each iteration roughly doubles the number of correct digits in the estimate.

4. Therefore, the time complexity of the algorithm is proportional to the logarithm of the number, which is O(log n).

So, based on the Heron-adapted algorithm, the complexity class of the perfect square problem is O(log n).