;; The first three lines of this file were inserted by DrRacket. They record metadata
;; about the language level of this file in a form that our tools can easily process.
#reader(lib "htdp-intermediate-lambda-reader.ss" "lang")((modname week8_m_full) (read-case-sensitive #t) (teachpacks ((lib "image.ss" "teachpack" "2htdp"))) (htdp-settings #(#t constructor repeating-decimal #f #t none #f ((lib "image.ss" "teachpack" "2htdp")))))
; a nat is an integer greater than or equal to 0.

; make-secret : nat -> (nat -> symbol)
; returns a secret g
(define (make-secret n)
  (local [(define secret (random n))]
    (lambda (guess) 
      (cond [(< guess secret) 'too-low]
            [(= guess secret) 'just-right]
            [(> guess secret) 'too-high]))))

(define my-secret (make-secret 400))

; guess-secret : (nat -> symbol) -> nat
; finds secret value for secret
(define (guess-secret secret) 
  (guess-helper-binary-search secret 0 399)
  )

; guess-helper : (nat -> symbol) nat -> nat
; finds secret value for secret assuming secret is at least n
(define (guess-helper secret n) 
  (cond [(symbol=? 'just-right (secret n)) n]
        [else (guess-helper secret (+ n 1))]))


; guess-helper-binary-search : (nat -> symbol) nat nat -> nat
; finds secret value for secret using binary search
;  assuming number is less than or equal to above
;  and is greater than or equal to below
(define (guess-helper-binary-search secret below above)
  (local [(define guess (quotient (+ below above) 2))
           (define ans (secret guess))]
    (cond [(symbol=? ans 'just-right) guess]
          [(symbol=? ans 'too-low) 
               (guess-helper-binary-search secret (+ 1 guess) above)]
          [(symbol=? ans 'too-high)
                (guess-helper-binary-search secret below (- guess 1))])))