;; 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-beginner-reader.ss" "lang")((modname 04consp) (read-case-sensitive #t) (teachpacks ((lib "universe.rkt" "teachpack" "2htdp") (lib "image.rkt" "teachpack" "2htdp"))) (htdp-settings #(#t constructor repeating-decimal #f #t none #f ((lib "universe.rkt" "teachpack" "2htdp") (lib "image.rkt" "teachpack" "2htdp")))))
; DEMO: How deep is a conspiracy? (October 2)
#|
**Data description**\
A _person is a structure:

    (make-person first last)

where `first` and `last` are strings

A _conspiracy_ is either
  - A structure:
          (make-cell head recruits1 recruits2)
    where
      - `head` is a person
      - `recruits1` is a conspiracy
      - `recruits2` is a conspiracy
  - A structure
          (make-no-recruits)
|#
(define-struct person (first last))
(define-struct cell (head recruits1 recruits2))
(define-struct no-recruits ())

(define NR (make-person "Norman" "Ramsey"))
(define AB (make-person "Ali" "Boreiko"))

;; depth : conspiracy -> number
;; return the max number of relays to reach any leaf in the conspiracy
(define (depth c)
  (cond [(no-recruits? c) 0]
        [(cell? c) (add1
                        (larger (depth (cell-recruits1 c))
                                (depth (cell-recruits2 c))))]))

; larger : number number -> number
; reutrn the larger of the two numbers
(define (larger n m)
  (max n m))
     



(check-expect (depth (make-no-recruits)) 0)
(check-expect 
    (depth (make-cell NR (make-no-recruits) (make-no-recruits))) 
    1)
(check-expect (depth (make-cell NR (make-cell AB (make-no-recruits) (make-no-recruits))
           (make-no-recruits))) 2)