CS61A_fa02_mt2

# CS61A_fa02_mt2 - CS 61A Fall 2002 Midterm#2 L Rowe 1(10...

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CS 61A, Fall, 2002, Midterm #2, L. Rowe 1. (10 points, 1 point each part) Consider the following five box-and-arrow diagrams. For each of the following Scheme expressions, indicate which diagram is produced when the expression is evaluated. It may be that some diagrams above are not used in any answer below, and the diagrams for some answers may appear above. Enter the answer “none” if the result of evaluating the expression does not match a diagram above. (i) (list (cons 1 2) (cons ‘() 3)) (ii) (list (append 1 2 ‘(3))) (iii) ‘((1 2 (3))) (iv) (accumulate cons nil (filter number? ‘(a 1 b 3 c d 3))) (v) (list 1 2 ‘(3)) (vi) (let ((x ‘(1))) (set-cdr! x (cons 2 3))) 1 2 3 a) d) 1 2 3 b) 1 2 3 3 1 2 e) c) 1 2 3

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(vii) (append (list ‘(1 2)) ‘(3)) (viii) (let ((x (list 1 2 3))) (set-car! (cddr x) (cons (caddr x) nil)) (list x)) (ix) ‘((1 2) 3) (x) ‘(1 (2) 3) 2. (10 points) The textbook suggests that we can view lists that contain lists as trees. For example, the list ‘(1 (2 3) 4) can be thought of as a tree that looks like. As you can see, a branch of a tree connects two nodes. A node with no branches is called a leaf node . This tree has six nodes and five branches. Four nodes are leaves, one node is the root, and the remaining node has two leaves (i.e., 2 and 3) below it. (i) (4 points) Draw a box-and-arrow diagram for the example list ‘(1 (2 3) 4). Remember to add the arrow that points at the list. (ii) (2 points) Eva Lu Ator makes an interesting observation. She tells Louis Reasoner: “Hey Louis, observe that the number of branches in any tree is always one less than the number of nodes in the tree.” Louis is not convinced that Eva is correct, so he writes the following procedures, each of which takes a tree as an argument (i.e., a list), to verify her claim: (define (is-eva-right? t) (= (- (count-nodes t) 1) (count-branches t))) (define (count-nodes t) (cond ((null? t) 1) ((not (pair? t)) 1) 1 4 2 3
(else (+ (count-nodes (car t)) (count-nodes (cdr t)))))) (define (count-branches t) (cond ((null? t) 0) ((not (pair? t)) 0) (else (+ (count-branches (car t)) (count-branches (cdr t)))))) Eva remarks, “Louis, your count-nodes procedure always returns the number of leaves, not the number of nodes.” Is she right? Circle your answer.

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