Exercise 1.23 (#21)

src/sicp/chapter_1/part_2/ex_1_22.clj

@@ -31,11 +31,11 @@
 ; to the number of steps required for the computation?
 
 (defn find-primes
-  [from to]
+  [from to print-log]
   (cond (>= from to) (do
-                       ; (println "finish")
+                       (when print-log (println "finish"))
                        from)
-        (even? from) (find-primes (+ from 1) to)            ; Just skip to the next odd
+        (even? from) (find-primes (+ from 1) to print-log)  ; Just skip to the next odd
         :else (do
-                ; (println from)
-                (find-primes (+ from 2) to))))              ; Takes only odds
+                (when print-log (println from))
+                (find-primes (+ from 2) to print-log))))    ; Takes only odds

src/sicp/chapter_1/part_2/ex_1_23.clj

@@ -0,0 +1,43 @@
+(ns sicp.chapter-1.part_2.ex-1-23)
+
+; Exercise 1.23
+; The smallest-divisor procedure shown at the start of this section does lots of needless testing:
+; After it checks to see if the number is divisible by 2 there is no point in checking to see
+; if it is divisible by any larger even numbers.
+;
+; This suggests that the values used for test-divisor should not be 2, 3, 4, 5, 6, …, but rather 2, 3, 5, 7, 9, ….
+;
+; To implement this change, define a procedure next that returns 3 if its input is equal to 2
+; and otherwise returns its input plus 2.
+;
+; Modify the smallest-divisor procedure to use (next test-divisor) instead of (+ test-divisor 1).
+;
+; With timed-prime-test incorporating this modified version of smallest-divisor,
+; run the test for each of the 12 primes found in Exercise 1.22.
+;
+; Since this modification halves the number of test steps, you should expect it to run about twice as fast.
+;
+; Is this expectation confirmed? If not, what is the observed ratio of the speeds of the two algorithms,
+; and how do you explain the fact that it is different from 2?
+
+(defn next-odd
+  [x]
+  (if (= x 2) 3 (+ x 2)))
+
+(defn divides?
+  [a b]
+  (= (mod b a) 0))
+
+(defn find-divisor
+  [num test-divisor]
+  (cond (> (* test-divisor test-divisor) num) num
+        (divides? test-divisor num) test-divisor
+        :else (find-divisor num (next-odd test-divisor))))
+
+(defn smallest-divisor
+  [num]
+  (find-divisor num 2))
+
+(defn prime?
+  [n]
+  (= n (smallest-divisor n)))

test/sicp/chapter_1/part_2/ex_1_22_test.clj

@@ -3,4 +3,4 @@
             [sicp.chapter-1.part_2.ex-1-22 :refer [find-primes]]))
 
 (deftest find-primes-test
-  (is (= 5 (find-primes 1 5))))                             ; Change arguments and see the output
+  (is (= 5 (find-primes 1 5 false))))                       ; Change arguments and see the output

test/sicp/chapter_1/part_2/ex_1_23_test.clj

@@ -0,0 +1,40 @@
+(ns sicp.chapter-1.part_2.ex-1-23-test
+  (:require [clojure.test :refer [deftest is]]
+            [sicp.chapter-1.part_2.ex-1-23 :refer [find-divisor next-odd prime? smallest-divisor]]))
+
+(deftest next-odd-test
+  (is (= 3 (next-odd 1)))
+  (is (= 3 (next-odd 2)))
+  (is (= 5 (next-odd 3)))
+  (is (= 6 (next-odd 4)))
+  (is (= 7 (next-odd 5))))
+
+(deftest smallest-divisor-test
+  (is (= 2 (smallest-divisor 2)))
+  (is (= 3 (smallest-divisor 3)))
+  (is (= 2 (smallest-divisor 6)))
+  (is (= 2 (smallest-divisor 30)))
+  (is (= 11 (smallest-divisor 11)))
+  (is (= 31 (smallest-divisor 31))))
+
+(deftest find-divisor-test
+  (is (= 2 (find-divisor 2 4)))
+  (is (= 5 (find-divisor 5 35)))
+  (is (= 7 (find-divisor 7 35)))
+  (is (= 100 (find-divisor 100 100)))
+  (is (= 10 (find-divisor 10 100))))
+
+(deftest prime?-test
+  ; Prime
+  (is (= true (prime? 1)))
+  (is (= true (prime? 2)))
+  (is (= true (prime? 3)))
+  (is (= true (prime? 5)))
+  (is (= true (prime? 7)))
+  (is (= true (prime? 11)))
+  (is (= true (prime? 23)))
+  ; Not prime
+  (is (= false (prime? 4)))
+  (is (= false (prime? 6)))
+  (is (= false (prime? 8)))
+  (is (= false (prime? 20))))