trianglesHEADmaster

1 files changed, 42 insertions, 2 deletions

diff --git a/coding-exercises/3/3.5.2/53.rkt b/coding-exercises/3/3.5.2/53.rkt
index 776e619..275a990 100644
--- a/coding-exercises/3/3.5.2/53.rkt
+++ b/coding-exercises/3/3.5.2/53.rkt
@@ -13,7 +13,7 @@
 (define (partial-sums s)
     (define me (stream-cons 0 (add-streams s me)))
     me)
-(stream-ref (partial-sums integers) 4)
+(display-stream-until (partial-sums integers) 4)
 
 (newline) (print "56") (newline)
 (define (merge s1 s2)
@@ -40,4 +40,44 @@
                                        (add-streams-counted (stream-cdr fibs)
                                                             fibs))))
 (stream-ref fibs 20)
-(println additions) (newline) (println "Streams in racket are forced when car is called.")
+(println additions) (newline)
+(println "Without memoization the number of additions is proportional to the additions of the previous steps since each time all additions of previous steps are recalculated, which is a characteristic of exponential functions.")
+(println "To show it is you could do a proof by counting additions at each step. Or use the fact that fibonacci has the phi^2 relation.")
+
+(newline) (print "58") (newline)
+(define (expand num den radix)
+    (stream-cons
+     (quotient (* num radix) den)
+     (expand (remainder (* num radix) den) den radix)))
+(stream-ref (expand 1 7 10) 3)
+(stream-ref (expand 3 8 10) 2)
+
+(newline) (print "59") (newline)
+(define (integrate-series s) (mul-streams s (stream-map / ones integers)))
+(define exp-series (stream-cons 1 (integrate-series exp-series)))
+(define cosine-series
+    (stream-cons 1 (integrate-series (scale-stream sine-series -1))))
+(define sine-series
+    (stream-cons 0 (integrate-series cosine-series)))
+
+(newline) (print "60") (newline)
+;; This was my solution after doodling how to traverse the coefficients.
+(define (mul-series s1 s2)
+    (stream-cons
+     (* (stream-car s1) (stream-car s2))
+     (add-streams
+      (scale-stream (stream-cdr s2) (stream-car s1))
+      (mul-series (stream-cdr s1) s2))))
+(display-stream-until (add-streams (mul-series sine-series sine-series)
+                                   (mul-series cosine-series cosine-series)) 8)
+
+;; This one is also interesting: http://community.schemewiki.org/?sicp-ex-3.60
+;; Instead of diagonal traversals in one direction, this one makes triangles.
+(define (psum-mul-series s1 s2)
+  (stream-cons
+    (* (stream-car s1) (stream-car s2))
+    (add-streams (add-streams (scale-stream (stream-cdr s1) (stream-car s2))
+                              (scale-stream (stream-cdr s2) (stream-car s1)))
+                 (stream-cons 0 (psum-mul-series (stream-cdr s1) (stream-cdr s2))))))
+(display-stream-until (add-streams (psum-mul-series sine-series sine-series)
+                                   (psum-mul-series cosine-series cosine-series)) 8)