Identify a Hidden Number from Comparison Replies

# Identify a Hidden Number from Comparison Replies A service chooses one fixed integer from `1` through `n`, inclusive. Implement `Solution.guessNumber(n)` to return that integer using only the provided `guess(number)` API. ### Interface The reply describes your proposed number relative to the hidden number: - `-1`: your proposal is too high. - `1`: your proposal is too low. - `0`: your proposal equals the hidden number. Only propose numbers in `1..n`. For this Python practice interface, construct `Solution(guess)` with the supplied callable and invoke `guessNumber(n)`. The candidate may call that API but may not inspect its owner, attributes, closure or source. The hidden number in an example is private setup data, not an argument to `guessNumber`. ### Examples **Example 1:** With `n = 20` and private hidden number `14`, `guessNumber(20)` returns `14`. For illustration, `guess(10)` would return `1`, `guess(17)` would return `-1`, and `guess(14)` would return `0`. **Example 2:** With `n = 9` and private hidden number `9`, `guessNumber(9)` returns `9`. A proposal of `8` is too low and receives `1`. ### Constraints - `1 <= n <= 2**31 - 1`. - The hidden number lies in `1..n` and never changes during a game. - Every reply follows the sign convention above. - No particular numeric API-call cap is part of the contract. ### What a Strong Answer Covers - Interpret both nonzero replies in the correct direction. - Return the exact hidden number, including endpoint and single-number games. - Explain termination and the number of API calls. ### Follow-up Questions - Which tests would reveal an implementation that reverses the two nonzero replies? - What assumptions must hold if the same client is used for several independent games?