|CSC 153||Grinnell College||Spring, 2005|
|Computer Science Fundamentals|
This laboratory exercise provides practice in defining and using the insertion sort as a mechanism to order numbers on a list.
Consider the following code that inserts an item into an ordered list, ensuring that the new list remains ordered:
;;; procedure to insert an item into a list, where elements are in ;;; ascending order (define insert-item (lambda (item ls) (if (or (null? ls) (<= item (car ls))) (cons item ls) (cons (car ls) (insert-item item (cdr ls))) ) ) )
insert-itemworks correctly in inserting the numbers 1, 9, 11 and 30 into the list
(2 3 5 7 9 10 13 18 24).
insert-item, so that the body contains a named-let expression that performs the above work using tail recursion.
insert-itemis not already ordered? For example, what happens if 6 is inserted into the list
(9 7 5 3 1)?
delete-itemwhich removes one copy of a designated item from an ordered list. If the item is not present on the list, return an error. In your code, use the ordering of the list to minimize the amount of searching through the list.
The following procedure uses the insert-item to successively build up an ordered list of values.
(define insertion-sort (lambda (ls) (if (null? ls) ls (insert-item (car ls) (insertion-sort (cdr ls))) ) ) )
(insertion-sort '(3 1 4 1 5 9 2 6 5 3 5)) (insertion-sort '(2 3 5 7 9 10 13 18 24)) (insertion-sort '(24 18 13 10 9 7 5 3 2))
insertion-sortby changing the
The following procedure combines the procedures,
insertion-sort, witin a single procedure:
(define sort-ascending (lambda (ls) (letrec ((insert-item (lambda (item ls) (if (or (null? ls) (<= item (car ls))) (cons item ls) (cons (car ls) (insert-item item (cdr ls))))))) (if (null? ls) ls (insert-item (car ls) (sort-ascending (cdr ls))) ) ) ) )
sort-ascending, so that the list is sorted in descending order rather than ascending order.
This document is available on the World Wide Web as
created March 8, 1998
last revised February 3, 2005
|For more information, please contact Henry M. Walker at firstname.lastname@example.org.|