Homework 4

Language: Beginning Student with List Abbreviations

1 Binary search trees

Do exercises 14.2.3, 14.2.5, and 14.2.6 from HtDP.

2 Sorted lists

; A sorted-list is either

; - empty

; - (cons number[n] sorted-list[l])

; INVARIANT: each number in ‘l’ is larger than ‘n’

Write the following function:

; in? : sorted-list number -> boolean

; determines if ‘n’ is in ‘l’

(define (in? l n) ---)

You must exploit the sorted-list invariant.

3 Heap

; A heap is either

; - false

; - (make-node number[n] heap[l] heap[r])

; INVARIANT: each number in ‘l’ is larger than ‘n’

; INVARIANT: each number in ‘r’ is larger than ‘n’

Write the following functions:

; in-heap? : heap number -> boolean

; determines if ‘n’ is in ‘h’

(define (in-heap? h n) ---)

; insert-in-heap : heap number -> heap

; constructs a new heap that contains

; all of the numbers in ‘h’, plus ‘n’

(define (insert-in-heap h n) ---)

You must exploit/maintain the heap invariant in each function (as appropriate).