Exercise 1.11

src/sicp/chapter_1/ex_1_11.clj

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+(ns sicp.chapter-1.ex-1-11)
+
+; Exercise 1.11
+; A function f is defined by the rule that f(n)=n
+; if n<3 and f(n)=f(n−1)+2f(n−2)+3f(n−3)
+; if n≥3.
+
+; Write a procedure that computes f by means of a recursive process.
+; Write a procedure that computes f by means of an iterative process.
+
+(defn f [n]                                                 ; Recursive process
+  (cond (< n 3) n
+        :else (+ (f (- n 1))
+                 (* 2 (f (- n 2)))
+                 (* 3 (f (- n 3))))))
+
+(defn f-v2-iter [a b c count]
+  (if (= count 0)
+    c
+    (f-v2-iter b
+               c
+               (+ c (* 2 b) (* 3 a))
+               (- count 1))))
+
+(defn f-v2 [n]                                              ; Iterative process
+  (cond (< n 3) n
+        :else (f-v2-iter 0 1 2 (- n 2))))

test/sicp/chapter_1/ex_1_11_test.clj

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+(ns sicp.chapter-1.ex-1-11-test
+  (:require [clojure.test :refer :all]
+            [sicp.chapter-1.ex-1-11 :refer [f f-v2]]))
+
+(deftest f-test
+  ; ~ O(3^n)
+  (time (is (= (f 1) 1)))                                   ; "Elapsed time: 3.541558 msecs"
+  (time (is (= (f 2) 2)))                                   ; "Elapsed time: 2.143086 msecs"
+  (time (is (= (f 3) 4)))                                   ; "Elapsed time: 1.413709 msecs"
+  (time (is (= (f 4) 11)))                                  ; "Elapsed time: 1.343298 msecs"
+  (time (is (= (f 5) 25)))                                  ; "Elapsed time: 1.148649 msecs"
+  (time (is (= (f 6) 59)))                                  ; "Elapsed time: 1.667051 msecs"
+  (time (is (= (f 7) 142)))                                 ; "Elapsed time: 1.326258 msecs"
+  (time (is (= (f 8) 335)))                                 ; "Elapsed time: 1.483437 msecs"
+  (time (is (= (f 9) 796)))                                 ; "Elapsed time: 3.40105 msecs"
+  (time (is (= (f 10) 1892)))                               ; "Elapsed time: 2.025039 msecs"
+  (time (is (= (f 20) 10771211)))                           ; "Elapsed time: 32.969995 msecs
+  (time (is (= (f 25) 812934961)))                          ; "Elapsed time: 77.825729 msecs
+  (time (is (= (f 30) 61354575194)))                        ; "Elapsed time: 470.359975 msecs"
+)
+
+(deftest f-v2-test
+  ; ~ O(n)
+  (time (is (= (f-v2 1) 1)))                                ; "Elapsed time: 3.209596 msecs"
+  (time (is (= (f-v2 2) 2)))                                ; "Elapsed time: 1.38101 msecs"
+  (time (is (= (f-v2 3) 4)))                                ; "Elapsed time: 2.122814 msecs"
+  (time (is (= (f-v2 4) 11)))                               ; "Elapsed time: 1.531897 msecs"
+  (time (is (= (f-v2 5) 25)))                               ; "Elapsed time: 1.403303 msecs"
+  (time (is (= (f-v2 6) 59)))                               ; "Elapsed time: 1.383425 msecs"
+  (time (is (= (f-v2 7) 142)))                              ; "Elapsed time: 1.335105 msecs"
+  (time (is (= (f-v2 8) 335)))                              ; "Elapsed time: 1.88524 msecs"
+  (time (is (= (f-v2 9) 796)))                              ; "Elapsed time: 2.091203 msecs"
+  (time (is (= (f-v2 10) 1892)))                            ; "Elapsed time: 3.245716 msecs"
+  (time (is (= (f-v2 20) 10771211)))                        ; "Elapsed time: 3.275056 msecs"
+  (time (is (= (f-v2 25) 812934961)))                       ; "Elapsed time: 1.989168 msecs"
+  (time (is (= (f-v2 30) 61354575194)))                     ; "Elapsed time: 2.462203 msecs"
+)