Nekaj vaj, TODO

zapiski/g1smo/1_3_zapiski_vaje.org

@@ -101,23 +101,152 @@ Iterativne procedure:
       (if (> a b)
          result
          (iter (next a) (* result (term a)))))
-    (iter a 0))
+    (iter a 1))
 
   (define (piblizek n)
-    (define (stevec n)
+    (define (stevec m)
-      (+ n 2))
+      (+ m 2))
-    (* 4 (/ (prod-iter (lambda (n) (* (- n 1) (+ n 1)))
+    (* 4 (/ (prod-iter (lambda (a) (* (- a 1) (+ a 1)))
                        3
                        stevec
                        n)
-            (prod-iter (lambda (n) (* n n))
+            (prod-iter (lambda (b) (* b b))
                        3
                        stevec
                        n))))
 
-  (piblizek 10)
+  (+ (piblizek 10000) 0.0)
+#+end_src
+
+#+RESULTS:
+: 3.1417497371492673
+
+** 1.32 Akumulator (reduce funkcija)
+
+#+begin_src scheme :exports both
+  (define (accumulate combiner null-value term a next b)
+    (if (> a b)
+        null-value
+        (combiner (term a) (accumulate combiner null-value term (next a) next b))))
+
+  (define (sum term a next b)
+    (accumulate + 0 term a next b))
+
+  (define (cube n) (* n n n))
+
+  (define (sum-cubes a b) (sum cube a (lambda (n) (+ n 1)) b))
+
+  (define (prod term a next b)
+    (accumulate * 1 term a next b))
+
+  (define (piblizek n)
+    (define (stevec m)
+      (+ m 2))
+    (* 4 (/ (prod (lambda (a) (* (- a 1) (+ a 1)))
+                  3
+                  stevec
+                  n)
+            (prod (lambda (b) (* b b))
+                  3
+                  stevec
+                  n))))
+
+  (list (sum-cubes 1 10) (+ (piblizek 10000) 0.0))
+#+end_src
+
+#+RESULTS:
+| 3025 | 3.1417497371492673 |
+
+** 1.32b Akumulator iterativno (reduce funkcija)
+
+#+begin_src scheme :exports both
+  (define (accumulate-iter combiner null-value term a next b)
+    (define (combine a combination)
+      (if (> a b)
+          combination
+          (combine (next a) (combiner combination (term a)))))
+    (combine a null-value))
+
+  (define (sum term a next b)
+    (accumulate-iter + 0 term a next b))
+
+  (define (cube n) (* n n n))
+
+  (define (sum-cubes a b) (sum cube a (lambda (n) (+ n 1)) b))
+
+  (define (prod term a next b)
+    (accumulate-iter * 1 term a next b))
+
+  (define (piblizek n)
+    (define (stevec m)
+      (+ m 2))
+    (* 4 (/ (prod (lambda (a) (* (- a 1) (+ a 1)))
+                  3
+                  stevec
+                  n)
+            (prod (lambda (b) (* b b))
+                  3
+                  stevec
+                  n))))
+
+  (list (sum-cubes 1 10) (+ (piblizek 10000) 0.0))
+#+end_src
+
+#+RESULTS:
+| 3025 | 3.1417497371492673 |
+
+** 1.33 filtriran akumulator
+
+*** a) vsota kvadratov praštevil med a in b
+#+begin_src scheme
+  (define (accumulate-filter combiner null-value term a next b predikat?)
+    (if (> a b)
+        null-value
+        (if (predikat? a)
+            (combiner (term a) (accumulate-filter combiner null-value term (next a) next b predikat?))
+            (accumulate-filter combiner null-value term (next a) next b predikat?))))
+
+  (define (je-prastevilo? a)
+    (define (preveri-prastevilo? x a)
+      (if (> x (/ a 2))
+          #t
+          (and (not (integer? (/ a x)))
+               (preveri-prastevilo? (+ x 1) a))))
+    (preveri-prastevilo? 2 a))
+
+  ;; (vsota kvadratov praštevil med 1 in 12 je 209)
+  (= (accumulate-filter + 0 (lambda (n) (* n n)) 1 (lambda (n) (+ n 1)) 12 je-prastevilo?)
+     209)
+#+end_src
+
+#+RESULTS:
+: #t
+
+*** a) produkt vseh naravnih števil manjših od n ki so "relativno pra-n"  (torej si z n ne delijo skupnega delitelja razen n)
+
+#+begin_src scheme
+  (define (accumulate-filter combiner null-value term a next b predikat?)
+    (if (> a b)
+        null-value
+        (if (predikat? a)
+            (combiner (term a) (accumulate-filter combiner null-value term (next a) next b predikat?))
+            (accumulate-filter combiner null-value term (next a) next b predikat?))))
+
+  (define (id a) a)
+  (define (inc a) (+ a 1))
+  (define (IN a b) (and a b))
+
+  (define (relativni-prastevili? a b)
+    (accumulate-filter IN #t (lambda (x) (and (not (integer? (/ a x)))
+                                              (not (integer? (/ b x)))))
+                       2 inc a id))
+
+  (define (produkt-relativnih-prastevil n)
+    (accumulate-filter * 1 id 1 inc n (lambda (x) (relativni-prastevili? x n))))
+
+  (produkt-relativnih-prastevil 9)
 #+end_src
 
 #+RESULTS:
 
-TODO popravi!
+TODO popravi!! ^