#lang racket
(provide 2nd-max)

;; -------------------------------------------------------------------
;; A recursive solution, with the choices among the cases made
;; explicitly using a cond expression.  It is O(n), with one pass.

(define (2nd-max lon)
  (2nd-max-tr
    (max (first lon) (second lon))
    (min (first lon) (second lon))
    (rest (rest lon))))

(define (2nd-max-tr largest 2nd-largest lon)
  (if (null? lon)
      2nd-largest
      (cond ((> (first lon) largest)
               (2nd-max-tr (first lon) largest (rest lon)))
            ((> (first lon) 2nd-largest)
               (2nd-max-tr largest (first lon) (rest lon)))
            (else
               (2nd-max-tr largest 2nd-largest (rest lon))))))

;; -------------------------------------------------------------------
;; This is a tail-recursive version of the helper function.
;; It is more functional and a bit more elegant,
;;   with a single recursive call in the else clause.
;; It uses functions to compute the new arguments to pass,
;;   rather than a cond expression.

;; (define (2nd-max-tr largest 2nd-largest lon)
;;   (if (null? lon)
;;       2nd-largest
;;       (2nd-max-tr
;;         (max largest (first lon))
;;         (max 2nd-largest (min largest (first lon)))
;;         (rest lon))))

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

(require rackunit)

(check-equal? (2nd-max '(2 3))                        2)
(check-equal? (2nd-max '(2 -1))                      -1)
(check-equal? (2nd-max '(2 3 8 6 6 75 38 3 2))       38)
(check-equal? (2nd-max '(6 1 2 -3 9 4 -1 2 8 1 2 4))  8)

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