1.9 to 1.11

Author: kleungkw

kenric/ex.1.10.rkt

@@ -0,0 +1,29 @@
+#lang racket
+
+(define (A x y)
+  (cond ((= y 0) 0)
+        ((= x 0) (* 2 y))
+        ((= y 1) 2)
+        (else (A (- x 1) (A x (- y 1))))))
+
+; (A 1 10) 1024
+; (A 2 4) 65536
+; (A 3 3) 65536
+
+(A 2 n)
+(A 1 (A 2 (- n 1)))
+(A 1 (A 1 (A 2 (- (- n 1) 1))))
+(A 0 (A 1 (A 2 (- n 2)) (A 1 (A 2 (- n 2)))))
+
+#|
+                         | 0  if n = 0
+(define (f n) (A 0 n)) = | 2  if n = 1
+                         | 2n if n > 1
+
+                         | 0 if n = 0
+(define (g n) (A 1 n)) = | 2^n if n > 0
+
+                         | 0 if n = 0
+(define (h n) (A 2 n)) = | 2 if n = 1
+                         | Knuth's up arrow notation  if n > 1
+|#

kenric/ex.1.11.rkt

@@ -0,0 +1,20 @@
+#lang racket
+
+;; recursive
+(define (f n)
+  (if (< n 3)
+      n
+      (+ (f (- n 1))
+         (* 2 (f (- n 2)))
+         (* 3 (f (- n 3))))))
+
+;; iterative
+(define (fn n)
+  (if (< n 3)
+      n
+      (helper 2 1 0 n)))
+
+(define (helper a b c n)
+  (if (< n 3)
+      a
+      (helper (+ a (* 2 b) (* 3 c)) a b (- n 1))))

kenric/ex.1.9.rkt

@@ -0,0 +1,33 @@
+#lang racket
+
+; (+ 4 5)
+
+(define (+ a b)
+  (if (= a 0) b (inc (+ (dec a) b))))
+
+#|
+(+ 4 5)
+(if (= 4 0) 5 (inc (+ (dec 4) 5)))
+(inc (+ 3 5))
+(inc (inc (+ 2 5)))
+(inc (inc (inc (+ 1 5))))
+(inc (inc (inc (inc (+ 0 5)))))
+(inc (inc (inc (inc 5))))
+(inc (inc (inc 6)))
+(inc (inc 7))
+(inc 8)
+9
+|#
+
+(define (+ a b)
+  (if (= a 0) b (+ (dec a) (inc b))))
+
+#|
+(+ 4 5)
+(if (= 4 0) 5 (+ (dec 4) (inc 5)))
+(+ 3 6)
+(+ 2 7)
+(+ 1 8)
+(+ 0 9)
+9
+|#