Exercise 1.14

src/sicp/chapter_1/ex_1_13.clj

@@ -1,3 +1,8 @@
 (ns sicp.chapter-1.ex-1-13)
 
+; Exercise 1.13
+; Prove that Fib(n) is the closest integer to φn/5⎯√, where φ=(1+5⎯√)/2.
+; Hint: Let ψ=(1−5⎯√)/2.
+; Use induction and the definition of the Fibonacci numbers (see 1.2.2) to prove that Fib(n)=(φn−ψn)/5⎯√
+
 ; Skipped. I'm too young for higher math.

src/sicp/chapter_1/ex_1_14.clj

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+(ns sicp.chapter-1.ex-1-14)
+
+; Exercise 1.14
+; Draw the tree illustrating the process generated by the count-change procedure of 1.2.2 in making change for 11 cents.
+; What are the orders of growth of the space and number of steps used by this process as the amount to be changed increases?
+
+(defn first-denomination
+  [type-of-coins]
+  (cond (= type-of-coins 1) 1
+        (= type-of-coins 2) 5
+        (= type-of-coins 3) 10
+        (= type-of-coins 4) 25
+        (= type-of-coins 5) 50))
+
+(defn change
+  [amount type-of-coins]
+  (cond (= amount 0) 1
+        (or (< amount 0) (= type-of-coins 0)) 0
+        :else (+ (change amount (- type-of-coins 1))
+                 (change (- amount (first-denomination type-of-coins)) type-of-coins))))
+
+(defn money-change
+  [amount]
+  (change amount 5))

test/sicp/chapter_1/ex_1_14_test.clj

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+(ns sicp.chapter-1.ex-1-14-test
+  (:require [clojure.test :refer :all]
+            [sicp.chapter-1.ex-1-14 :refer [money-change]]))
+
+(deftest count-change-test
+  (is (= 1 (money-change 1)))
+  (is (= 4 (money-change 10)))
+  (is (= 292 (money-change 100))))