;; 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 lec18) (read-case-sensitive #t) (teachpacks ()) (htdp-settings #(#t constructor repeating-decimal #f #t none #f ())))

;; is-sequence? : list-of-num -> boolean?
(define (is-sequence? l)
  (is-sequence-starting-from? l 0))

;; is-sequence? : list-of-num num -> boolean?
;;  n accumulateds how many items we have seen
(define (is-sequence-starting-from? l n)
  (cond
    [(empty? l) true]
    [(cons? l)  (and (= n (first l))
                     (is-sequence-starting-from? (rest l)
                                                 (add1 n)))]))

(check-expect (is-sequence-starting-from? empty 5) true)
(check-expect (is-sequence-starting-from? '(1 2 3) 0) false)
(check-expect (is-sequence-starting-from? '(1 2 3) 1) true)

(check-expect (is-sequence? empty) true)
(check-expect (is-sequence? '(0 1 2 3)) true)
(check-expect (is-sequence? '(1 2 3)) false)
(check-expect (is-sequence? '(0 1 2 4)) false)
(check-expect (is-sequence? '(0 1 2 1)) false)

;; --------------------------------------------------

;; A maze
;;  - num
;;  - (make-branch num maze maze)
(define-struct branch (spells left right))

;; Score is total number of spells seen at branches
;; times amount of gold at end

(define always-lose 10)
(define always-four (make-branch 2 2 2))
(define sometimes-four (make-branch 1 4 0))
(define bigger (make-branch 5 always-four sometimes-four))

;; max-score : maze num -> num
(define (max-score-for-spells m num-spells)
  (cond
    [(number? m) (* m num-spells)]
    [(branch? m) (local [(define new-num-spells (+ num-spells
                                                   (branch-spells m)))]
                   (max (max-score-for-spells (branch-left m)
                                              new-num-spells)
                        (max-score-for-spells (branch-right m)
                                              new-num-spells)))]))

;; max-score : maze -> num
(define (max-score m)
  (max-score-for-spells m 0))
  
(check-expect (max-score always-lose) 0)
(check-expect (max-score always-four) 4)
(check-expect (max-score sometimes-four) 4)
(check-expect (max-score bigger) 24)