[add] 1.9, 1.10 resolved

1 Building Abstractions with Procedures/kazu04r.scm

@@ -0,0 +1,199 @@
+;;------------------
+;; 1.9
+;;------------------
+
+(define inc
+  (lambda (x)
+    (+ x 1)))
+
+(define dec
+  (lambda (x)
+    (- x 1)))
+
+(define (+ a b)
+  (if (= a 0)
+      b
+      (inc (+ (dec a) b))))
+
+;;(+ 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)
+;;(+ 3 6)
+;;(+ 2 7)
+;;(+ 1 8)
+;;(+ 0 9)
+;;9
+
+;;------------------
+;; 1.10
+;;------------------
+
+(define (A x y)
+  (cond ((= y 0) 0)
+        ((= x 0) (* 2 y))
+        ((= y 1) 2)
+        (else (A (- x 1)
+                 (A x (- y 1))))))
+
+(define (f n) (A 0 n)) -> 2n
+
+(define (g n) (A 1 n)) -> (A 0 (A 1 (- n 1))) -> (* 2 (A 1 (- n 1))) -> (* 2 (A 0 (A 1 (- (- n 1) 1)))) -> (* 2 (* 2 (A 1 (- (- n 1) 1)))) -> 2^n
+
+(define (h n) (A 2 n)) -> (A 1 (A 2 (- n 1))) -> (^ 2 (A 2 (- n 1))) -> (^ 2 (A 1 (A 2 (- (- n 1) 1)))) -> (^ 2 (^ 2 (A 2 (- (- n 1) 1)))) -> 2^n^n == (A 1 (* n n))
+
+(define (k n) (* 5 n n))
+
+;;------------------
+;; 1.11
+;;------------------
+
+(define fun11recur
+  (lambda (n)
+    (cond
+     ((<= n 3) n)
+     (else (+ (fun11recur (- n 1)) (* 2 (fun11recur (- n 2))) (* 3 (fun11recur (- n 3))))))))
+
+(define fun11iter
+  (lambda (n)
+    (let loop ((n n) (a 3) (b 2) (c 1))
+v      (cond
+       ((<= n 3) a)
+       (else
+	(loop (- n 1) (+ a (* 2 b) (* 3 c)) a b))))))
+
+;;------------------
+;; 1.12
+;;------------------
+;;TODO
+
+;; n = 1 1
+;; n = 2 1 1
+;; n = 3 1 2 1
+;; n = 4 1 3 3 1
+;; n = 5 1 4 6 4 1
+;; ...
+;; n = n 1 f(n-1,1)+f(n-1,2) f(n-1,2)+f(n-1,3) ... 1
+
+;;------------------
+;; 1.13
+;;------------------
+;;TODO
+
+;;------------------
+;; 1.14
+;;------------------
+;;TODO
+
+(define (count-change amount)
+  (cc amount 5))
+
+(define (cc amount kinds-of-coins)
+  (cond ((= amount 0) 1)
+        ((or (< amount 0) (= kinds-of-coins 0)) 0)
+        (else (+ (cc amount
+                     (- kinds-of-coins 1))
+                 (cc (- amount
+                        (first-denomination kinds-of-coins))
+                     kinds-of-coins)))))
+
+(define (first-denomination kinds-of-coins)
+  (cond ((= kinds-of-coins 1) 1)
+        ((= kinds-of-coins 2) 5)
+        ((= kinds-of-coins 3) 10)
+        ((= kinds-of-coins 4) 25)
+        ((= kinds-of-coins 5) 50)))
+
+;;------------------
+;; 1.15
+;;------------------
+(define p-count 1)
+
+(define (cube x) (* x x x))
+
+(define (p x) (print p-count)(set! p-count (+ p-count 1)) (- (* 3 x) (* 4 (cube x))))
+
+(define (sine angle)
+   (if (not (> (abs angle) 0.1))
+       angle
+       (p (sine (/ angle 3.0)))))
+
+;; gosh> (sine 12.15)
+;; 1
+;; 2
+;; 3
+;; 4
+;; 5
+;; -0.39980345741334
+
+;; (sine 12.15) -> (p (sine (/ 12.15 3))) -> (p (p (sine (/ (/ 12.15 3))))) ->
+;; (sine a) -> (p (sine (/ a 3))) -> (p (p (sine (/ a/3 3)))) -> (p (p (p (sine (/ a/9 3)))))
+
+;; ステップ Θ(n) ?
+;; スペース Θ(n) ?
+
+;;------------------
+;; 1.16
+;;------------------
+
+(define (expt b n)
+  (expt-iter b n 1))
+
+(define (expt-iter b counter product)
+  (if (= counter 0)
+      product
+      (expt-iter b
+                (- counter 1)
+                (* b product))))
+
+(define (even? n)
+  (= (remainder n 2) 0))
+
+(define expt-fast
+  (lambda (b n)
+    (expt-iter-fast b n 1)))
+
+(define expt-iter-fast
+  (lambda (b n res)
+    (if (= n 0)
+	res
+	(if (even? n)
+	    (expt-iter-fast b (/ n 2) (* res res))
+	    (expt-iter-fast b (- n 1) (* res (* b b)))))))
+
+;;------------------
+;; 1.17
+;;------------------
+
+(define my-double (lambda (x) (+ x x)))
+
+(define my-halve (lambda (x) (/ x 2)))
+
+(define (my-* a b)
+  (if (= b 0)
+      0
+      (+ a (my-* a (- b 1)))))
+
+;;iter
+(define my-*2
+  (lambda (a b)
+    (let loop ((a a) (b b) (res 0))
+      (if (= b 0)
+	  res
+	  (loop a (- b 1) (+ res a))))))
+
+