SICP Exercise 3.38

SICP Exercise 3.38

a) I list all the orders of the three process, and then determine the value of balance. For simplicity, I use 1, 2, 3 , instead of Peter, Paul, Mary.

123	$45
132	$35
213	$45
231	$50
312	$40
321	$40

b) If the system allows the processes to be interleaved, there are some other values that could be produced, eg. $30, $55, $60, $80, $90, $110. Here I want to show you how to get these values systematicly, I won't draw the digrams.(please refer to http://wqzhang.wordpress.com/2009/07/30/sicp-exercise-3-38/ for digrams).

We need pay attention to the time of access balance and the time of set balance. I will use the following shortcut notations:

• a1:  access balance time of Peter.
• a2:  access balance time of Paul.
• a3: access balance time of Mary.
• s1: set balance time of Peter.
• s2: set balance time of Paul.
• s3: set balance time of Mary.

Note: the following precedure assume that, there has interleaved parts between the three processess.

(cond ((< (max a1 a2 a3) (min s1 s2 s3))
       (cond ((= (max s1 s2 s3) s1) '$110)
             ((= (max s1 s2 s3) s2) '$80)
             ((= (max s1 s2 s3) s3) '$50)))
      ;;If s1 is big than some access time.
      ((and (> a2 s1) (> a3 s1))
       (cond ((> s2 s3) '$90)
             ((> s3 s2) '$55)))
      ((and (> a2 s1) (< a3 s1))
       (cond ((> s2 s3) '$90)
             ((> s3 s2) '$50)))
      ((and (< a2 s1) (> a2 s1))
       (cond ((> s2 s3) '$80)
             ((> s3 s2) '$55)))
      ;;If s2 is big than some access time.
      ((and (> a1 s2) (> a3 s2))
       (cond ((> s1 s3) '$90)
             ((> s3 s1) '$40)))
      ((and (> a1 s2) (< a3 s2))
       (cond ((> s1 s3) '$90)
             ((> s3 s1) '$50)))
      ((and (< a1 s2) (> a3 s2))
       (cond ((> s1 s3) '$110)
             ((> s3 s1) '$40)))
      ;;If s3 is big than some access time.
       ((and (> a1 s3) (> a2 s3))
       (cond ((> s1 s2) '$60)
             ((> s2 s1) '$30)))
      ((and (> a1 s3) (< a2 s3))
       (cond ((> s1 s2) '$60)
             ((> s2 s1) '$80)))
      ((and (< a1 s3) (> a2 s3))
       (cond ((> s1 s2) '$110)
             ((> s2 s1) '$30))))