more exercises done

sicp-exercises/exercise1-10.scm

@@ -0,0 +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))))))
+
+(print (A 0 10))
+(print (A 1 10))
+(print (A 2 4))
+(print (A 15 1))

sicp-exercises/exercise1-11.scm

@@ -0,0 +1,17 @@
+(define (fn-recursive n)
+  (cond ((< n 3) n)
+		(else (+ (fn-recursive (- n 1)) (* 2 (fn-recursive (- n 2))) (* 3 (fn-recursive (- n 3)))))))
+
+
+(define (fn-wrapper n)
+	(define (fn-iterative n1 n2 n3 count)
+	  (cond ((= count 0) n1)
+			(else (fn-iterative (+ n1 (* 2 n2) (* 3 n3)) n1 n2 (- count 1) ))))
+  
+	(if (< n 3)
+	  n
+	  (fn-iterative 2 1 0 (- n 2)))
+)
+
+(print (fn-recursive 10))
+(print (fn-wrapper 10))

sicp-exercises/exercise1-12.scm

@@ -0,0 +1,11 @@
+(define (pascal-x-y column row)
+	(cond ((= column 0) 1)
+		  ((= column row) 1)
+		  ((= row 0) 1)
+		  ((> column row) 0) 
+	(else (+ (pascal-x-y (- column 1) (- row 1)) (pascal-x-y column (- row 1)))))
+)
+
+(print (pascal-x-y 0 0))
+(print (pascal-x-y 0 4))
+(print (pascal-x-y 3 4))

sicp-exercises/exercise1-6.scm

@@ -0,0 +1,28 @@
+;this program does not work, it will cause an infinite loop
+
+(define (sqrt_iter new_guess last_guess x)
+	(new-if (good_enough? new_guess last_guess)
+	  new_guess
+	  (sqrt_iter (improve new_guess x) new_guess x)
+	)
+)
+
+(define (new-if predicate then-clause else-clause)
+	(cond (predicate then-clause)
+		  (else else-clause)))
+
+(define (improve guess x)
+	(/ (+ guess (/ x guess)) 2))
+
+
+(define (good_enough? guess last_guess) 
+  (< (absolute (- guess last_guess)) 0.000000000000001))
+
+(define (absolute x)
+	(if (< x 0)
+	  (- 0 x)
+	  x))
+
+(define (sqrt x) (sqrt_iter (/ x 2.0) x x))
+
+(print (sqrt 10))

sicp-exercises/exercise1-7.scm

@@ -0,0 +1,22 @@
+(define (sqrt_iter new_guess last_guess x)
+	(if (good_enough? new_guess last_guess)
+	  new_guess
+	  (sqrt_iter (improve new_guess x) new_guess x)
+	)
+)
+
+(define (improve guess x)
+	(/ (+ guess (/ x guess)) 2))
+
+
+(define (good_enough? guess last_guess) 
+  (< (absolute (- guess last_guess)) 0.000000000000001))
+
+(define (absolute x)
+	(if (< x 0)
+	  (- 0 x)
+	  x))
+
+(define (sqrt x) (sqrt_iter (/ x 2.0) x x))
+
+(print (sqrt 10))

sicp-exercises/exercise1-8.scm

@@ -0,0 +1,22 @@
+(define (cuberoot_iter new_guess last_guess x)
+	(if (good_enough? new_guess last_guess)
+	  new_guess
+	  (cuberoot_iter (improve new_guess x) new_guess x)
+	)
+)
+
+(define (improve guess x)
+	(/ (+ (/ x (* guess guess)) (* 2 guess)) 3))
+
+
+(define (good_enough? guess last_guess) 
+  (< (absolute (- guess last_guess)) 0.000000000000001))
+
+(define (absolute x)
+	(if (< x 0)
+	  (- 0 x)
+	  x))
+
+(define (cbrt x) (cuberoot_iter (/ x 2.0) x x))
+
+(print (cbrt 27))