Add upto 2.39

ex-2-30.rkt

@@ -52,10 +52,71 @@
 
 
 ;; 2.33
-(define (map p sequence)
-  (accumulate (lambda (x y) ⟨??⟩) nil sequence))
-(define (append seq1 seq2)
-  (accumulate cons ⟨??⟩ ⟨??⟩))
-(define (length sequence)
-  (accumulate ⟨??⟩ 0 sequence))
+;; this one kinda tripped me up for a long while, because
+;; I'm used to using `reduce` for this kind of stuff (yeah
+;; I used to do common lisp) and accumulate here is basically
+;; reduce, but kind of wonky.
+;; e.g. (reduce (λ (x y) ...) seq) is (kind of, not really) equivalent to
+;;      (accumulate (λ (x y) ...) (car seq) (cdr seq))
+;; not exactly equivalent, the order in which accumulate traverses
+;; its list argument is also the reverse of reduce... but you get the idea.
+;;
+;; edit after 2.38: apparently racket also has both accumulate and reduce:
+;; they're called foldr and foldl respectively. (though still a little different,
+;; compared to reduce, the differences are mostly trivial)
+(define (my-map p sequence)
+  (accumulate (lambda (x y) (cons (p x) y)) '() sequence))
+(define (my-append seq1 seq2)
+  (accumulate cons seq2 seq1))
+(define (my-length sequence)
+  (accumulate (λ (x y) (+ y 1)) 0 sequence))
+
+;; 2.34
+;; first element of coefficient-sequence is the coefficient of x^0, then x^1 and so on.
+(define (horner-eval x coefficient-sequence)
+  (accumulate (lambda (this-coeff higher-terms)
+                (+ (* higher-terms x) this-coeff))
+              0
+              coefficient-sequence))
+
+;; 2.35
+(define (count-leaves t)
+  (accumulate + 0
+              (map (λ (x) (if (cons? x)
+                              (count-leaves x)
+                              1))
+                   t)))
+
+;; 2.36
+(define (accumulate-n op init seqs)
+  (if (null? (car seqs))
+      '()
+      (cons (accumulate op init (map car seqs))
+            (accumulate-n op init (map cdr seqs)))))
+
+;; 2.37 yeah, I'm not good with matrix stuff.
+(define (dot-product v w)
+  (accumulate + 0 (map * v w)))
+(define (matrix-*-vector m v)
+  (map (λ (x) (dot-product x v)) m))
+(define (transpose mat)
+  (accumulate-n cons '() mat))
+(define (matrix-*-matrix m n)
+  (let ((cols (transpose n)))
+    (map (λ (v) (matrix-*-vector cols v)) m)))
+;; not sure about matrix-*-matrix, I didn't bother to check
+;; if it was correct
+
+
+;; 2.38 (op a b) must strictly equal (op b a)
+;; a.k.a the operation must be commutative.
+
+;; 2.39
+(define (reversel sequence)
+  (foldl (lambda (x y) (cons x y)) '() sequence))
+(define (reverser sequence)
+  (foldr (lambda (x y) (append y (list x))) '() sequence))
+;; reverser is kinda inefficient, has to traverse y for each x
+;; has O(N^2) time complexity as a result and so I hate it.
+;; compare it to reversel which is O(N)