add book code

Author: knothhe

SICP/Book-Code/ex-2.64.rkt

@@ -0,0 +1,29 @@
+#lang sicp
+
+(define (entry tree) (car tree))
+(define (left-branch tree) (cadr tree))
+(define (right-branch tree) (caddr tree))
+(define (make-tree entry left right)
+  (list entry left right))
+
+(define (list->tree elements)
+  (car (partial-tree elements (length elements))))
+
+(define (partial-tree elts n)
+  (if (= n 0)
+      (cons '() elts)
+      (let ((left-size (quotient (- n 1) 2)))
+        (let ((left-result (partial-tree elts left-size)))
+          (let ((left-tree (car left-result))
+                (non-left-elts (cdr left-result))
+                (right-size (- n (+ left-size 1))))
+            (let ((this-entry (car non-left-elts))
+                  (right-result (partial-tree (cdr non-left-elts)
+                                              right-size)))
+              (let ((right-tree (car right-result))
+                    (remaining-elts (cdr right-result)))
+                (cons (make-tree this-entry left-tree right-tree)
+                      remaining-elts))))))))
+
+(display (list->tree (list 1 3 5 7 9 11)))
+

SICP/Book-Code/sc-1.1.7.rkt

@@ -0,0 +1,24 @@
+#lang sicp
+
+(define (sqrt-iter guess x)
+  (if (good-enough? guess x)
+      guess
+      (sqrt-iter (improve guess x)
+                 x)))
+
+(define (improve guess x)
+  (average guess (/ x guess)))
+
+(define (average x y)
+  (/ (+ x y) 2))
+
+(define (good-enough? guess x)
+  (< (abs (- (square guess) x)) 0.001))
+
+(define (square x) (* x x))
+
+(define (sqrt x)
+  (sqrt-iter 1.0 x))
+
+; test case
+(sqrt 0.0001)

SICP/Book-Code/sc-1.1.8.rkt

@@ -0,0 +1,21 @@
+#lang sicp
+
+(define (sqrt x)
+  (define (good-enough? guess)
+    (< (abs (- (improve guess) guess))
+       (* guess 0.001)))
+  (define (improve guess)
+    (average guess (/ x guess)))
+  (define (average a b)
+    (/ (+ a b) 2))
+  (define (sqrt-iter guess)
+    (if (good-enough? guess)
+        guess
+        (sqrt-iter (improve guess))))
+  (sqrt-iter 1.0))
+
+; test case
+(sqrt 4)
+(sqrt 16)
+(sqrt 10000)
+(sqrt 0.01)

SICP/Book-Code/sc-1.2.1.rkt

@@ -0,0 +1,30 @@
+#lang sicp
+
+(define (factorial n)
+  (fact-iter 1 1 n))
+
+(define (fact-iter product counter max-counter)
+  (if (> counter max-counter)
+      product
+      (fact-iter (* product counter) (+ counter 1) max-counter)))
+
+(define (factorial2 n)
+  (define (fact-iter product counter)
+    (if (> counter n)
+        product
+        (fact-iter (* product counter)
+                   (+ counter 1))))
+  (fact-iter 1 1))
+
+; test case
+(factorial 2)
+(factorial 3)
+(factorial 4)
+(factorial 5)
+(factorial 6)
+
+(factorial2 2)
+(factorial2 3)
+(factorial2 4)
+(factorial2 5)
+(factorial2 6)

SICP/Book-Code/sc-1.2.2.rkt

@@ -0,0 +1,46 @@
+#lang sicp
+
+(define (fib n)
+  (cond ((= n 0) 0)
+        ((= n 1) 1)
+        (else (+ (fib (- n 1))
+                 (fib (- n 2))))))
+
+(define (fib2 n)
+  (define (fib-iter a b count)
+    (if (= 0 count)
+        b
+        (fib-iter (+ a b) a (- count 1))))
+  (fib-iter 1 0 n))
+
+(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)))
+
+; test cases
+; (fib 2)
+; (fib 3)
+; (fib 4)
+; (fib 5)
+; 
+; (fib2 2)
+; (fib2 3)
+; (fib2 4)
+; (fib2 5)
+
+(count-change 100)

SICP/Book-Code/sc-1.2.4.rkt

@@ -0,0 +1,31 @@
+#lang sicp
+
+; b^n = b*b^{n-1}
+; b^0 = 1
+(define (expt-recursive b n)
+  (if (= n 0)
+      1
+      (* b (expt-recursive b (- n 1)))))
+
+(define (expt b n)
+  (expt-iter b n 1))
+
+(define (expt-iter b counter product)
+  (if (= counter 0)
+      b
+      (expt-iter b
+                 (- counter 1)
+                 (* product b))))
+
+; b^n = (b^{n/2})^2, n is even
+; b^n = b*b^{n-1}, n is odd
+; b^0 = 1
+(define (fast-expt b n)
+  (cond ((= n 0) 1)
+        ((even? n) (square (fast-expt b (/ n 2))))
+        (else (* b (fast-expt (- n 1))))))
+
+(define (square x) (* x x))
+
+(define (even? n)
+  (= (remainder n 2) 0))

SICP/Book-Code/sc-1.2.5.rkt

@@ -0,0 +1,6 @@
+#lang sicp
+
+(define (gcd a b)
+  (if (= b 0)
+      a
+      (gcd b (remainder a b))))

SICP/Book-Code/sc-1.2.6.rkt

@@ -0,0 +1,42 @@
+#lang sicp
+
+(define (square n) (* n n))
+(define (even? n)
+  (= (remainder n 2) 0))
+
+(define (smallest-divisor n)
+  (find-divisor n 2))
+
+(define (find-divisor n test-divisor)
+  (cond ((> (square test-divisor) n) n)
+        ((divides? test-divisor n) test-divisor)
+        (else (find-divisor n (+ test-divisor 1)))))
+
+(define (divides? a b)
+  (= (remainder b a) 0))
+
+(define (prime? n)
+  (= n (smallest-divisor n)))
+
+(prime? 10)
+
+(define (expmod base exp m)
+  (cond ((= exp 0) 1)
+        ((even? exp)
+         (remainder (square (expmod base (/ exp 2) m))
+                     m))
+        (else
+         (remainder (* base (expmod base (- exp 1) m))
+                    m))))
+
+(define (fermat-test n)
+  (define (try-it a)
+    (= (expmod a n n) a))
+  (try-it (+ (random (- n 1)) 1)))
+
+(define (fast-prime? n times)
+  (cond ((= times 0) true)
+        ((fermat-test n) (fast-prime? n (- times 1)))
+        (else false)))
+
+(fast-prime? 10 (log 10))

SICP/Book-Code/sc-1.3.1.rkt

@@ -0,0 +1,55 @@
+#lang sicp
+
+(define (cube n)
+  (* n n n))
+
+;; (define (sum-integers a b)
+;;   (if (> a b)
+;;       0
+;;       (+ a (sum-integers (+ a 1) b))))
+
+;; (define (sum-cubes a b)
+;;   (if (> a b)
+;;       0
+;;       (+ (cube a) (sum-cubes (+ a 1) b))))
+
+;; (define (pi-sum a b)
+;;   (if (> a b)
+;;       0
+;;       (+ (/ 1.0 (* a (+ a 2))) (pi-sum (+ a 4) b))))
+
+
+(define (sum term a next b)
+  (if (> a b)
+      0
+      (+ (term a)
+         (sum term (next a) next b))))
+
+(define (inc n) (+ n 1))
+(define (sum-cubes a b)
+  (sum cube a inc b))
+
+(sum-cubes 1 10)
+
+(define (identity x) x)
+(define (sum-integers a b)
+  (sum identity a inc b))
+
+(sum-integers 1 10)
+
+(define (pi-sum a b)
+  (define (pi-term x)
+    (/ 1.0 (* x (+ x 2))))
+  (define (pi-next x)
+    (+ x 4))
+  (sum pi-term a pi-next  b))
+
+(* 8 (pi-sum 1 1000))
+
+(define (integral f a b dx)
+  (define (add-dx x) (+ x dx))
+  (* (sum f (+ a (/ dx 2.0)) add-dx b)
+     dx))
+
+(integral cube 0 1 0.01)
+(integral cube 0 1 0.001)

SICP/Book-Code/sc-1.3.2.rkt

@@ -0,0 +1,23 @@
+#lang sicp
+
+(define (sum term a next b)
+  (if (> a b)
+      0
+      (+ (term a)
+         (sum term (next a) next b))))
+
+(define (pi-sum a b)
+  (sum (lambda (x) (/ 1.0 (* x (+ x 2))))
+       a
+       (lambda (x) (+ x 4))
+       b))
+
+(define (integral f a b dx)
+  (* (sum f
+          (+ a (/ dx 2.0))
+          (lambda (x) (+ x dx))
+          b)
+     dx))
+
+(define plus4
+  (lambda (x) (+ x 4)))