我们都爱尾递归

一个女服务生走向有四个客人的桌子。“你们要什么？” 她问。“我要特餐，” 第一个客人说。 “我也是，” 第二个客人说。“听起来不错，” 第三个客人说。每个人看着第四个客人。 “我要一个香菜蛋奶酥，” 他小声地说。瞬息之间，女服务生就转身踩着高跟鞋走回柜台去了。“三个特餐”，她大声对厨师说，“还有一个香菜蛋奶酥。”

; Sequence: 
;
; (1 1 1 0 1 0 0 0 0 1) => ((3 1) 0 1 (4 0) 1)
;
; →     1 1 1 0 1 0 0 0 0 1
; →  1    1 1 0 1 0 0 0 0 1
; →  2,1    1 0 1 0 0 0 0 1
; →  3,1      0 1 0 0 0 0 1
; →  3,1 0      1 0 0 0 0 1
; →  3,1 0 1      0 0 0 0 1
; →  3,1 0 1 0      0 0 0 1
; →  3,1 0 1 2,0      0 0 1
; →  3,1 0 1 3,0        0 1
; →  3,1 0 1 4,0          1
; →  3,1 0 1 4,0 1         
;
; Procedure: 
; 
; seq                  n  x  last-seq
; ()                   1  1  (1 1 0 1 0 0 0 0 1)
; ()                   2  1    (1 0 1 0 0 0 0 1)
; ()                   3  1      (0 1 0 0 0 0 1)
; ((3 1))              1  0        (1 0 0 0 0 1)
; ((3 1) 0)            1  1          (0 0 0 0 1)
; ((3 1) 0 1)          1  0            (0 0 0 1)
; ((3 1) 0 1)          2  0              (0 0 1)
; ((3 1) 0 1)          3  0                (0 1)
; ((3 1) 0 1)          4  0                  (1)
; ((3 1) 0 1 (4 0))    1  1                   ()
; ((3 1) 0 1 (4 0) 1)  1  1                   ()
;
; Sequence: 
;
; ((3 1) 0 1 (3 0) 0 1) => (1 1 1 0 1 0 0 0 0 1)
;
; Procedure: 
;
; seq                   it    last-seq
; (1 1 1)               (3 1) (0 1 (4 0) 1)
; (1 1 1 0)             0       (1 (4 0) 1)
; (1 1 1 0 1)           1         ((4 0) 1)
; (1 1 1 0 1 0 0 0 0)   (4 0)           (1)
; (1 1 1 0 1 0 0 0 0 1) 1                ()

                   
(define it-n
  (lambda (x n)
    (if (> n 1)
      (list (list n x)) ; ((3 1))
      (list x))))       ; (1)

(define compare
  (lambda (seq last-seq n x)
    (if (eq? last-seq '())
      (append seq (it-n x n))
      (let ((i (car last-seq)))
        (if (= x i)
          (compare seq (cdr last-seq) (+ n 1) i)  
          (compare (append seq (it-n x n)) (cdr last-seq) 1 i))))))

(define compress
  (lambda (seq)
    (if (list? seq)
      (compare '() (cdr seq) 1 (car seq))
      seq)))

(define unof
  (lambda (lst n x)
    (if (> n 0)
      (unof (append lst (list x)) (- n 1) x)
      lst)))                                 

(define unlice
  (lambda (seq it last-seq)
    (if (eq? last-seq '())
      (if (list? it)
        (let ((n (car it)) (x (car (cdr it))))
          (append seq (unof '() n x)))
        (append seq (list it)))
      (if (list? it)
        (let ((n (car it)) (x (car (cdr it))))
          (unlice (append seq (unof '() n x)) (car last-seq) (cdr last-seq)))
        (unlice (append seq (list it)) (car last-seq) (cdr last-seq))))))

(define uncompress
  (lambda (seq)
    (if (list? seq)
      (unlice '() (car seq) (cdr seq))
      seq)))

; (1 1 1 0 1 0 0 0 0 1) => ((3 1) 0 1 (3 0) 0 1)
(display "(1 1 1 0 1 0 0 0 0 1) => ") 
(display (compress '(1 1 1 0 1 0 0 0 0 1)))
(newline)
; ((3 1) 0 1 (3 0) 0 1) => (1 1 1 0 1 0 0 0 0 1)
(display "((3 1) 0 1 (3 0) 0 1) => ")
(display (uncompress '((3 1) 0 1 (3 0) 0 1)))
(newline)
; (0 0 1 0 1 0 0 0 0 0 0) => ((2 0) 1 0 1 (6 0)) 
(display "(0 0 1 0 1 0 0 0 0 0 0) => ")
(display (compress '(0 0 1 0 1 0 0 0 0 0 0)))
(newline)
; ((2 0) 1 0 1 (6 0)) => (0 0 1 0 1 0 0 0 0 0 0)
(display "((2 0) 1 0 1 (6 0)) => ")
(display (uncompress '((2 0) 1 0 1 (6 0))))