#lang racket 

; the above line tells Racket to use the standard language subset

; CS 42 Homework 1, Problem 3
; Author(s): [your name here]
; Time spent: [enter the time spent on this homework here]

; You should ALWAYS include the above information.

; Additional comments (optional):
;
; You may add your definitions to this file and load it as Racket code.
; When run as is, many tests will fail. By replacing the definitions
; with correct ones, you should get more tests succeeding, and eventually
; all tests should succeed.

; You should use this file as a template for your hw1pr4.rkt file and for
; all future Racket files.

(require htdp/testing)   ; this enables the unit-testing interface.

; (generate-report)  ;; this command (when uncommented) outputs the test 
                     ;; results so far.  Generally, you only want one
                     ;; call to generate-report, at the very end.

; Right now, we provide at least one unit test for every function. You should add
; more of your own, to check yourself. You should leave your unit tests in 
; the submitted file. We will be using some unit tests that you haven't seen
; yet in evaluating your solutions, and we may evaulate your unit tests.
;
; You do not have to worry about checking for malformed input. We will not be
; using any test cases such as that.
;
; You should pay attention to elegance, readability, and comments where needed.
; Formatting should be straightforward if you use Dr. Racket, since it indents
; for you.
;
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
; All answers MUST be done using functional programming. Do not use assignment!;
; Do not use conventional iteration. It isn't needed.                          ;
; The emphasis here is on constructing and composing functions. Non-compliant  ;
; solutions will be counted as wrong. If you don't know how to approach a      ;
; problem in the prescribed way, please seek help at your earliest opportunity.;
;                                                                              ; 
; Include comments and use meaningful identifiers where possible.              ; 
; Make your solutions elegant and clear as possible.                           ;
; We are interested in style, rather than simply answers.                      ;
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;

; Problem 3.1
;
; Function: erdos
; Input: 
;    N - a non-negative integer
; Output: 
;    Computes the Erdos number of the input: 3N+1 if N is odd; N/2 if N is even

(define (erdos N) 0)  ;; Replace with the correct definition

; Unit tests for erdos

;             EXPRESSION   EXPECTED RESULT
(check-expect (erdos 3)                 10)
(check-expect (erdos 10)                 5)


; Problem 3.2

; Function: erdosCount
; Input: 
;    N - a non-negative integer
; Output:
;    The smallest number of times erdos must be iterated, when started with an 
;    input of N, in order to arrive at a value of 1

(define (erdosCount N) 0) ;; Replace with the correct definition

(check-expect (erdosCount 26) 10)
(check-expect (erdosCount 27) 111)

; Problem 3.3
;
; Function: removeAll
; Input: 
;    e - an element
;    L - a list
; Output:
;    A list that is identical to L except with top-level instances of e removed.

(define (removeAll e L) '())   ;; Replace with the correct definition

(check-expect (removeAll "i" '("a" "l" "i" "i" "i" "e" "n")) '("a" "l" "e" "n"))
(check-expect (removeAll "i" '( ("a" "l" "i") "i" "i" "e" "n" )) '(("a" "l" "i") "e" "n"))
(check-expect (removeAll 0 '(1 0 1 0 1 0)) '(1 1 1))


; Problem 3.4
; 
; Function: find
; Input:
;    L - A list
;    M - A list that may or may not contain L as a sublist
; Output:
;    #t if L is a sublist of M, #f otherwise

(define (find L M) #f)

(check-expect (find '(1 2 3) '(0 1 2 3 4)) #t)
(check-expect (find '(1 2 3) '(0 1 2 2 3 4)) #f)

; And a few more
(check-expect (find '() '(1 2 3)) #t)
(check-expect (find '(1) '()) #f)
(check-expect (find '(1 2) '(2 1 1 1)) #f)
(check-expect (find '(1 2) '(2 1 1 (1 2))) #f) ;; an element is not a sub-list
(check-expect (find '(1 1 3) '(2 1 1 2 3 1)) #f)


; The following will give the overall number of tests correct and incorrect.
(generate-report)