Problem Set 4

Language: Beginning Student with List Abbreviations
Due: 11:59 PM Thursday, Feb 2.

1 Sorted lists

; A sorted-list is either

; - empty

; - (cons number[n] sorted-list[l])

; INVARIANT: each number in `l' is greater than `n'

Design the following function.

; in? : sorted-list number -> boolean

; determines if `n' is in `l'

(define (in? n l)

---)

You must exploit the sorted-list invariant.

2 Binary search trees

; a person is

; (make-person number symbol)

(define-struct person (ssn name))

; A database is either

; - empty

; - (make-db-node person[p] database[l] database[r])

(define-struct db-node (person left right))

; INVARIANT:

; every person in `l' has a smaller SSN than `p', and

; every person in `r' has a larger SSN than `p'

Design the function inorder. It consumes a database and produces a list of all the SSNs in the database. The list contains the SSNs in ascending order.

You must exploit the database invariant.

Design the function create-database. It consumes a database d and a person p. It produces a database that is just like d but contains the following db-node structure in place of the appropriate empty database:

(make-db-node p empty empty)

Design the function create-database-from-list. It consumes a list of persons; it produces a database by repeatedly applying create-database.

3 Linear combinations

Complete exercise 17.6.4 from HTDP/1e.