fixup

12 files changed, 270 insertions, 3 deletions

diff --git a/coding-exercises/1/27.rkt b/coding-exercises/1/27.rkt
index 8762d6c..5a7a8d7 100644
--- a/coding-exercises/1/27.rkt
+++ b/coding-exercises/1/27.rkt
@@ -5,7 +5,7 @@
   (* x x))
 
 (define (expmod base e m)
-  (cond 
+  (cond
     ((= e 0) 1)
     ((even? e)
      (remainder (square (expmod base (/ e 2) m)) m))
diff --git a/coding-exercises/1/28.rkt b/coding-exercises/1/28.rkt
index 39a10d9..4e984fb 100644
--- a/coding-exercises/1/28.rkt
+++ b/coding-exercises/1/28.rkt
@@ -12,7 +12,7 @@
     (else x))) ;; no root found
 
 (define (expmod base e m)
-  (cond 
+  (cond
     ((= e 0) 1)
     ((even? e)
      (signal base e m (remainder (square (expmod base (/ e 2) m)) m)))
@@ -30,4 +30,4 @@
         (else false)))
   (f n n))
 
-(all-mr 1)
+(all-mr 5)
diff --git a/coding-exercises/1/30.rkt b/coding-exercises/1/30.rkt
index c9bf57d..09b354e 100644
--- a/coding-exercises/1/30.rkt
+++ b/coding-exercises/1/30.rkt
@@ -1,4 +1,14 @@
 #lang racket
 (require sicp)
 
+(define (sum term a next b)
+  (define (iter a result)
+    (if (> a b)
+      result
+      (iter (next a) (+ result (term a)))))
+  (iter a 0))
 
+
+(define (id x) x)
+
+(sum id 0 (lambda (x) (+ x 1)) 2)
diff --git a/coding-exercises/1/31.rkt b/coding-exercises/1/31.rkt
new file mode 100644
index 0000000..10f52c5
--- /dev/null
+++ b/coding-exercises/1/31.rkt
@@ -0,0 +1,31 @@
+#lang racket
+(require sicp)
+
+(define (id x) x)
+
+(define (factorial n)
+  (product id 1 inc n))
+
+(define (product term a next b)
+  (define (iter result a)
+    (if (> a b)
+      result
+      (iter (* (term a) result) (next a))))
+  (iter 1 a))
+
+(define (even? x)
+  (= (remainder x 2) 0))
+
+(define (pi-product n)
+  (/ (product (lambda (x) 
+                (if (even? x) 
+                  x 
+                  (+ x 1))) 
+              2 inc n)
+     (product (lambda (x)
+                (if (even? x)
+                  (+ x 1)
+                  x))
+              2 inc n)))
+
+(* 1.0 (pi-product 1000))
diff --git a/coding-exercises/1/32.rkt b/coding-exercises/1/32.rkt
new file mode 100644
index 0000000..21a557c
--- /dev/null
+++ b/coding-exercises/1/32.rkt
@@ -0,0 +1,38 @@
+#lang racket
+
+(define (accumulate combiner null-value term a next b)
+  (define (iter a result)
+    (if (> a b)
+      result
+      (iter 
+        (next a)
+        (combiner
+          (term a)
+          result))))
+  (iter null-value a))
+
+(define (accumulate combiner null-value term a next b)
+  (if (> a b)
+    null-value
+    (combiner 
+      (term a)
+      (accumulate 
+        combiner 
+        null-value 
+        term (next a) next b)))) 
+
+
+(define (sum term a next b)
+  (accumulate
+    (lambda (x y) (+ x y))
+    0
+    term a next b))
+
+(define (product term a next b)
+  (accumulate
+    (lambda (x y) (* x y))
+    1
+    term a next b))
+
+(sum id 0 inc 8)
+(product id 1 inc 3)
diff --git a/coding-exercises/1/33.rkt b/coding-exercises/1/33.rkt
new file mode 100644
index 0000000..ff82408
--- /dev/null
+++ b/coding-exercises/1/33.rkt
@@ -0,0 +1,45 @@
+#lang racket
+;; import miller raban prime test
+(load "coding-exercises/1/28.rkt")
+
+;; sum of squares of the prime numbers in the interval a to b
+(define (prime? x)
+ (all-mr x))
+
+(define (filtered-accumulate pred combiner null-value term a next b)
+  (define (iter a result)
+    (cond
+      ((> a b) result)
+      ((pred a) (iter
+                   (next a)
+                   (combiner
+                     (term a)
+                     result)))
+      (else (iter (next a) result))))
+  (iter a null-value))
+
+(define (square-prime-sum a b)
+  (filtered-accumulate
+    prime?
+    (lambda (x y) (+ x y))
+    0
+    (lambda (x) (* x x))
+    a inc b))
+
+(square-prime-sum 2 5)
+
+(define (coprime-product n)
+  (define (coprime? a)
+     (if (= 1 (gcd a n))
+       ((lambda ()
+          (println a)
+          true))
+       false))
+  (filtered-accumulate
+    coprime?
+    (lambda (x y) (* x y))
+    1
+    (lambda (x) x)
+    1 inc (- n 1)))
+
+(coprime-product 10)
diff --git a/coding-exercises/1/34.rkt b/coding-exercises/1/34.rkt
new file mode 100644
index 0000000..e003817
--- /dev/null
+++ b/coding-exercises/1/34.rkt
@@ -0,0 +1,8 @@
+#lang racket
+
+(define (f g)
+  (g 2))
+
+(f f)
+
+
diff --git a/coding-exercises/1/35.rkt b/coding-exercises/1/35.rkt
new file mode 100644
index 0000000..2f597c7
--- /dev/null
+++ b/coding-exercises/1/35.rkt
@@ -0,0 +1,20 @@
+#lang racket
+(require sicp)
+
+(define (fixed-point f first-guess)
+  (define (close-enough? v1 v2)
+    (< (abs (- v1 v2)) 0.0001))
+  (define (try guess)
+    (let ((next (f guess)))
+      (if (close-enough? guess next)
+          next
+          (try next))))
+  (try first-guess))
+
+(define (golden-ratio)
+  (fixed-point 
+    (lambda (x) (+ 1 (/ 1 x)))
+    1.0))
+
+(golden-ratio)
+(/ (log 10) (log 2))
diff --git a/coding-exercises/1/36.rkt b/coding-exercises/1/36.rkt
new file mode 100644
index 0000000..a785d8a
--- /dev/null
+++ b/coding-exercises/1/36.rkt
@@ -0,0 +1,39 @@
+#lang racket
+(require sicp)
+
+(define (fixed-point damper f first-guess)
+  (define (close-enough? v1 v2)
+    (< (abs (- v1 v2)) 0.0001))
+  (define (try guess)
+    (let ((next (damper guess (f guess))))
+      (newline)
+      (display next)
+      (if (close-enough? guess next)
+          next
+          (try next))))
+  (try first-guess))
+
+(define (golden-ratio)
+  (fixed-point 
+    (lambda (x) (+ 1 (/ 1 x)))
+    1.0))
+
+(define (log1000)
+  (fixed-point
+    (lambda (guess next)
+      next)
+    (lambda (x) (/ (log 1000) (log x)))
+    2.0))
+
+(define (log1000-average-damped)
+  (define (average a b)
+    (/ (+ a b) 2))
+  (fixed-point
+    (lambda (guess next)
+      (average guess next))
+    (lambda (x) (/ (log 1000) (log x)))
+    2.0))
+
+(log1000)
+(println " *** second time")
+(log1000-average-damped)
diff --git a/coding-exercises/1/37.rkt b/coding-exercises/1/37.rkt
new file mode 100644
index 0000000..6ab3150
--- /dev/null
+++ b/coding-exercises/1/37.rkt
@@ -0,0 +1,26 @@
+#lang racket
+(require sicp)
+
+;; recurse down
+(define (cont-frac n d k)
+  (define (recurse i)
+   (if (> i k)
+     0
+     (/ (n i) (+ (d i) (recurse (inc i))))))
+ (recurse 1))
+
+;; iter up
+(define (cont-frac n d k)
+  (define (iter result i)
+   (if (= i 0)
+     result
+     (iter
+      (/ (n i) (+ (d i) result))
+      (dec i))))
+  (iter 0 k))
+
+;; test
+(cont-frac
+  (lambda (i) 1.0)
+  (lambda (i) 1.0)
+  11.0)
diff --git a/coding-exercises/1/38.rkt b/coding-exercises/1/38.rkt
new file mode 100644
index 0000000..5e78719
--- /dev/null
+++ b/coding-exercises/1/38.rkt
@@ -0,0 +1,22 @@
+#lang racket
+(require sicp)
+
+;; recurse down
+(define (cont-frac n d k)
+  (define (recurse i)
+   (if (> i k)
+     0
+     (/ (n i) (+ (d i) (recurse (inc i))))))
+ (recurse 1))
+
+(define (euler-d i)
+  (let ((next3 (+ i 1)))
+   (if (= 0 (remainder next3 3))
+      (* 2 (/ next3 3))
+      1)))
+
+;; test
+(+ 2 (cont-frac
+       (lambda (i) 1.0)
+       euler-d
+       16.0))
diff --git a/coding-exercises/1/39.rkt b/coding-exercises/1/39.rkt
new file mode 100644
index 0000000..90f9908
--- /dev/null
+++ b/coding-exercises/1/39.rkt
@@ -0,0 +1,28 @@
+#lang racket
+(require sicp)
+
+(define (odd? i)
+  (= 1 (remainder i 2)))
+
+;; iter up
+(define (cont-frac n d k)
+  (define (iter result i)
+   (if (= i 0)
+     result
+     (iter
+      (/ (n i) (+ (d i) result))
+      (dec i))))
+  (iter 0 k))
+
+;; test
+(define (tan-cf x k)
+    (cont-frac
+      (lambda (i) 
+        (cond
+          ((= i 1) x)
+          ((> i 1) (* -1 (* x x)))
+          (else (error "invalid argument to cont-frac"))))
+      (lambda (i) (- (* 2 i) 1))
+      k))
+
+(tan-cf 2.0 10)