Answer must be in racket

;************************************************************ ; ** problem 3 ** (10 points) ; Write one procedure

; (total-order? compare? domain)

; that takes a predicate (compare? x y) and a list of values domain ; such that whenever x and y are values from domain, (compare? x y) ; returns either #t or #f. ; The procedure returns #t if compare? is a total order on domain ; (that is, satisfies the four properties above for all x, y, z from domain), ; and #f otherwise.

; Hint: it might be helpful to write a procedure to check these conditions ; one pair x, y at a time.

; QUESTION: What is the running time of your procedure in terms of n, ; the number of elements in the domain. Assume compare? takes time O(1). ; Give your answer in terms of O, Theta, or Omega, as appropriate and ; explain why it is correct. Replace "replace" in total-order-runtime ; with your answer.

; Examples ;> (total-order? <= '(1 3 5 4)) ;#t ;> (total-order? < '(1 3 5 4)) ;#f ;> (total-order? >= '(3 2 4 5 1)) ;#t ;> (total-order? string<=? (list "hi" "hey" "hello")) ;#t ;> (total-order? equal? (list "hi" "hey" "hello")) ;#f ;************************************************************

(define total-order-runtime "replace") ; Explain your answer here.

(define (total-order? compare? domain) "total-order? is not defined yet")

;************************************************************