find the max of Collatz sequence from a giving list

Question

i'm new in scheme syntax. this is the last part of the project i've been working on. i was able to find the max from a giving Collatz sequence, but this part of the project requires finding the max length from a multiple Collatz sequences lists. So for example giving this list : '((1 10) (10 200) (201 210) (900 1000) and the output should be like this : ‘(20 125 89 174) i need to find the maximum length between the number 1 to 10 and then from 10 to 200 ets here is my code :

#lang racket
; Part I
(define (sequence n)
  (cond  [(= n 1)
      (list n)]
  [(even? n)
   ( cons n(sequence( / n 2)))]
  [(odd? n) 
   ( cons n(sequence (+(* n 3) 1))) ] ))

(sequence 10)

; Part II
(define (find-length items)
  (if (null? items)          
  (list )                   
  (cons                  
   (length (sequence(car items)))        
   (find-length (rest items))))
   )
 (find-length (list 10 16 22 90 123 169))


;Part III
(define max-in-list (lambda (ls)
(let ( (head (car ls)) (tail (cdr ls)))
  (if (null? tail)
    ; list contains only one item, return it
    head
    ; else find largest item in tail
    (let ((max-in-tail (max-in-list tail)))
      ; return the larger of 'head' and 'max-in-tail'
      (if (> head max-in-tail)
        head
        max-in-tail
      )
    )
  )
)
  ))

(define (find-max i j)
 ( if (= i j)
   (list)
  (cons
  (max-in-list (find-length(sequence i)))
  (find-max (+ 1 i ) j)
  )) 
)
(max-in-list(find-max 1 10))

(define (max-length-list items )
  (if (null? items)
  (list)

  (cons
  (find-max ? ?) ) ; how i can call this function ?
  (max-length-list (?) ) ; how i can call this function ?
  )))

(max-length-list  '((1 10) (10 200) (201 210) (900 1000) ))

1. You have not told us what "Collatz" sequence means. Is it some technical term of art? 2. Your functions do not have contracts, so it is difficult to tell whether functions like `max-in-list` are well formed. (E.g. does it need to handle the empty list?). But of course, 3. You have not written any data definitions, so it is hard to tell what the classes of data are that your program is intended to operate on. (Lists of numbers? Lists of tuples of numbers?) You'll need to write those data definitions before you can write many contracts, I'm guessing. — pnkfelix, Feb 25 '13 at 09:46

score 0 · Accepted Answer · answered Feb 25 '13 at 12:58

Each item in the list you pass to max-length-list is a list with two numbers and a nil, e.g. (cons 1 (cons 2 '())).
The first number is (car (car items)).
The second is (car (cdr (car items))).

Or, if you let ((head (car items)), then they are (car head) and (car (cdr head)).

The recursive call is trivial; you've processed the first element with find-max, now you just need to process the rest of them. You obviously already know how to accomplish that, since you've done it.

Thank you i was confused in the second element and this (car (cdr (car items))) did the magic — Muhsag, Feb 25 '13 at 13:31

find the max of Collatz sequence from a giving list

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