Write a recursive function in lisp to calculate the factorial of a given positive number num

Week_04

1. 
   Write a recursive function in LISP to calculate the factorial of a given positive number num:
   

(defun fact ( num )

;; base case if num=0 return 1
;; otherwise – accumulate the product recursively

)
(defun fact ( num )

2. 
   Consider the following Lisp expression (function definition):
   

(defun pow(bas ex)

(if (= bas 0) 1

(* bas (pow bas (1- ex)))))

1. 
   What this function is supposed to do?
   

2. 
   Copy/paste it in clisp interpreter.
   

3. 
   Run it:
   

4. 
   Correct the function definition to produce a correct result:
   

(delete 1 '( 2 1 4 1 3 1 1 4 5 6 2 ))

3. 
   Using LISP function delete, create a LISP function uniq that will take one argument of type list and will return a list with the unique elements:
   

(uniq '(1 2 4 5 7 3 2 7 6 5 7 7 7))

(1 2 4 5 7 3 6)
Copy your solution here:

(defun uniq (list)
(cond

((null list) '())

((t (cons (car list) (uniq (delete (car list) list)))))
)

4. 
   Create a recursive LISP function named insert1 that will insert a number num into a sorted in increasing order list of numbers nums
   

(defun insert1 (num nums)

;; num is a number

;; nums is a list of numbers (sorted in increasing order)

;; if nums is empty or if num is <= than the first element

;; in nums

;; then the function returns a list constructed by num and

;; the list nums which constructor will you use?

;; if it is not the base case - make a recursion

;; construct a list with the first element from nums and

;; the result of

;; calling the insert1 function with num and the rest of

;;nums (cdr nums)

)

5. 
   Use the insert1 function created on the previous step to create a LISP function
   insert-sort that will recursively sort a list of numbers nums
   

(defun insert-sort (nums)

;; define here the base case to stop the recursion:

;; if nums is empty, return an empty list

6. 
   Test your functions (use (trace insert1 insert-sort) to see how the recursion works):
   

insert1:

(insert-sort '(5 3 7 5 9 2 10 4 5 6 7))