Zhao Wei

ref: chapter01

1. power(x n) where x and n are integers
   

   (defun power (x n)
     (cond ((= n 0)
            1)
           ((evenp n)
            (expt (power x (/ n 2)) 2))
           (t
            (* x (power x (- n 1))))))
   
   (power 2 13)
   

   Notice: Its execution time is not n it is log(n).
   

2. Write a function that count the number of atoms in an expression.
   

   ;; (count-atoms '(a (b) (c))) = 3
   
   (defun count-atoms (exp)
     (cond ((null exp) 0)
           ((atom exp) 1)
           (t
            (+ (count-atoms (first exp))
               (count-atoms (rest exp))))))
   
   (count-atoms '(a (b) (c (d (e (f))))))
   
   

3. Write a function that counts the number of times a expression occurs anywhere within another expression.
   

   (defun count-anywhere (item tree)
     (cond ((equal item tree) 1)
           ((atom tree) 0)
           (t
            (+ (count-anywhere item (first tree))
               (count-anywhere item (rest tree))))))
   
   (count-anywhere 'a '(a ((a) b) a (a (a (a)))))
   

4. compute dot product of two list
   

   (defun dot (xs ys)
     (if (eq (length xs)
             (length ys))
         (apply #'+ (mapcar #'* xs ys))
         nil))
   
   (dot '(1 2 3) '(2 3 4))