// ============================================================================
// Number guessing game — hi/lo feedback and a binary-search solver
// ============================================================================
//
// feedback() compares a guess to the secret and returns "low" / "high" /
// "correct". auto_solve() proves the search space is exhausted in at most
// ceil(log2(range)) guesses by playing the optimal binary-search strategy.
//
// Run:  soma run guessing_game.cell --signal demo
// Test: soma test guessing_game.cell

cell GuessingGame {
    face {
        signal feedback(secret: Int, guess: Int) -> String
        signal auto_solve(secret: Int, lo: Int, hi: Int) -> Map
        signal demo() -> Map
    }

    on feedback(secret: Int, guess: Int) {
        return match true {
            _ if guess < secret -> "low"
            _ if guess > secret -> "high"
            _                   -> "correct"
        }
    }

    // Binary search the [lo, hi] interval; count guesses until "correct".
    on auto_solve(secret: Int, lo: Int, hi: Int) {
        let l = lo
        let h = hi
        let guesses = 0
        let found = -1
        while l <= h {
            let mid = floor((l + h) / 2)
            guesses = guesses + 1
            let f = feedback(secret, mid)
            if f == "correct" {
                found = mid
                l = h + 1
            } else if f == "low" {
                l = mid + 1
            } else {
                h = mid - 1
            }
        }
        return map("found", found, "guesses", guesses)
    }

    on demo() {
        return auto_solve(73, 1, 100)
    }
}

cell test GuessingTests {
    rules {
        assert feedback(50, 30) == "low"
        assert feedback(50, 80) == "high"
        assert feedback(50, 50) == "correct"
        // binary search always finds the secret
        assert auto_solve(73, 1, 100).found == 73
        // 1..100 is solved in at most 7 guesses (ceil(log2(100)) = 7)
        assert auto_solve(1, 1, 100).guesses <= 7
        assert auto_solve(100, 1, 100).guesses <= 7
        assert auto_solve(64, 1, 100).found == 64
    }
}