Insert1 that will insert a number num into a sorted in increasing order list of numbers nums

COS 470 – Artificial Intelligence and AI Programming

Week_05

LISP Practice

1. 
   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?
(cons (car nums) (insert1 num (rest nums)))

)
;; 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)

)

2. 
   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

;; otherwise call insert1 appropriately

)

3. 
   Test your functions (use (trace insert1 insert-sort) to see how the recursion works):
   

(insert1 5 '(1 2 2 4 6 7))

insert-sort:

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

(2 3 4 5 5 5 6 7 7 9 10)

4. 
   Write a function, ``remove,'' which takes a list and an element, and returns the original list with the first occurrence of the element removed.
   

(remove '(a 1 c 2 c 7) 'c) result (A 1 2 C 7)

5. 
   Write a function, ``search,'' which takes a nested list and an atom, and it returns 't if it finds the atom within the nested list and returns nil otherwise.
   

(search '(a (1 c) 2 7) 'c) result: T

6. 
   Write a function, ``sum-of-list,'' which takes a list of numbers and returns their sum. Write a similar function, ``product-of-list,'' which takes a list of numbers and returns their product.
   

7. 
   Write a function called ``remainder,'' which takes two positive non-zero numbers, n and m, and returns the remainder when n is divided by m.