Implement till 2.76

ex-2_24-32.scm

@@ -0,0 +1,206 @@
+(load "util.scm")
+
+(display "\nex-2.24\n")
+
+(define x (cons (list 1 2) (list 3 4)))
+
+(define (display-spaces n)
+  (cond ((= n 0) ()) (else (display " ") (display-spaces (- n 1)))))
+
+; Procedure to print a tree (in an ugly way)
+(define (display-tree tree level)
+  (cond
+    ((null? tree) ())
+    ((not (pair? tree)) (display-spaces level) (display tree) (newline))
+    (else
+      (display-spaces level) (display tree) (newline)
+      (map (lambda (tree) (display-tree tree (+ level 1))) tree))))
+
+
+(define x (list 1 (list 2 (list 3 4))))
+(display-tree x 0)
+
+; (1 (2 (3 4))) ; result interpreter
+; [. .]->[. /]
+;  |      |
+;  1     [. .]->[. /]
+;         |      |
+;         2     [. .]->[. /]
+;                |      |
+;                3      4
+;   /\
+;  1  \
+;     /\
+;    2  \
+;        \
+;        /\
+;       3  4
+
+(display "\nex-2.25\n")
+
+(define x (list 1 3 (list 5 7) 9))
+(display x) (newline)
+; (1 3 (5 7) 9)
+(display (car (cdr (car (cdr (cdr x)))))) (newline)
+
+(define x (list (list 7)))
+(display x) (newline)
+; ((7))
+(display (car (car x))) (newline)
+
+(define x (list 1 (list 2 (list 3 (list 4 (list 5 (list 6 7)))))))
+(display x) (newline)
+; (1 (2 (3 (4 (5 (6 7))))))
+(display (car (cdr (car (cdr (car (cdr (car (cdr (car (cdr (car (cdr x))))))))))))) (newline)
+(display (cadr (cadr (cadr (cadr (cadr (cadr x)))))))
+(newline)
+
+(display "\nex-2.26\n")
+
+(define x (list 1 2 3))
+(define y (list 4 5 6))
+
+(display (append x y)) (newline)
+; (1 2 3 4 5 6)
+(display (cons x y)) (newline)
+; ((1 2 3) 4 5 6)
+(display (list x y)) (newline)
+; ((1 2 3) (4 5 6))
+
+(display "\nex-2.27 - deep reverse\n")
+
+(define x (list (list 1 2) (list 3 4)))
+
+; I didn't implement in this elegantly when I first did this exercise. I am
+; learning and growing!
+(define (deep-reverse xs)
+  (if (pair? xs)
+    (reverse (map deep-reverse xs))
+    xs))
+
+(display x) (newline)
+(display (reverse x)) (newline)
+(display (deep-reverse x)) (newline)
+
+(display "\nex-2.28 - fringe aka flatten\n")
+
+(define (fringe xs)
+  (cond
+    ((null? xs) xs)
+    ((pair? xs) (append (fringe (car xs)) (fringe (cdr xs))))
+    (else (list xs))))
+
+(display (fringe x)) (newline)
+(display (fringe (list x x))) (newline)
+
+(display "\nex-2.29 - mobile balancing\n")
+
+(define (make-mobile left right)
+  (list left right))
+
+(define (make-branch length structure)
+  (list length structure))
+
+(define m1
+  (make-mobile
+    (make-branch 10 20)
+    (make-branch 5 41)))
+
+(define m2
+  (make-mobile
+    (make-branch 1 70)
+    (make-branch 2
+                 (make-mobile
+                   (make-branch 3 20)
+                   (make-branch 4 15)))))
+
+; 2.29 a)
+(define left-branch car)
+(define right-branch cadr)
+(define branch-length car)
+(define branch-structure cadr)
+(display (branch-length (right-branch m1))) (newline)
+
+; 2.29 b)
+(define (total-weight m)
+  (if (pair? m)
+    (+ (total-weight (branch-structure (left-branch m)))
+       (total-weight (branch-structure (right-branch m))))
+    m))
+
+(display (total-weight m1)) (newline)
+(display (total-weight m2)) (newline)
+
+; 2.29 c)
+(define (balanced? m)
+  (define (torque b)
+    (* (branch-length b) (total-weight (branch-structure b))))
+  (if (pair? m)
+    (let ((l (left-branch m))
+          (r (right-branch m)))
+      (and
+        (balanced? (branch-structure l))
+        (balanced? (branch-structure r))
+        (= (torque l) (torque r))))
+    #t)))
+
+(display (balanced? m1)) (newline)
+(display (balanced? m2)) (newline)
+
+; 2.29 d)
+; Only the selectors must be changed if we change the constructors.
+(define (make-mobile left right)
+  (cons left right))
+(define (make-branch length structure)
+  (cons length structure))
+
+(display "\nex-2.30 - tree square\n")
+
+; using tail recursion
+(define (square-tree t)
+  (cond
+    ((null? t) nil)
+    ((not (pair? t)) (square t))
+    (else (cons (square-tree (car t)) (square-tree (cdr t))))))
+
+(display x) (newline)
+(display (square-tree x)) (newline)
+
+; using map
+(define (square-tree t)
+  (cond
+    ((null? t) nil)
+    ((not (pair? t)) (square t))
+    (else (map square-tree t))))
+
+(display (square-tree x)) (newline)
+
+(display "\nex-2.31\n")
+
+(define (tree-map proc tree)
+  (cond
+    ((null? tree) tree)
+    ((not (pair? tree)) (proc tree))
+    (else (map (lambda (t) tree-map proc t) tree))))
+
+(define (square-tree tree) (tree-map square tree))
+(display (square-tree x)) (newline)
+
+(display "\nex-2.32\n")
+
+(define (subsets s)
+  (if (null? s)
+      (list nil)
+      (let ((rest (subsets (cdr s))))
+        (append rest (map (lambda (r) (cons (car s) r)) rest)))))
+
+; Assuming we have an oracle procedure subsets and we get a new list that we
+; split into car and cdr). If we use the oracle to compute the subsets for cdr
+; then we get a new list rest. To compute the new subsets from that list we
+; have to a) keep the rest as it is and b) add the current element (car) to all
+; the subsets (rest). The only other tricky part (that was already given) is
+; that when we get an empty list we want to return a list including that empty
+; list.
+
+(display (subsets (list 1 2 3)))
+