Add some initial scheme code

lib.scm

@@ -0,0 +1,76 @@
+(define (sqrt x)
+  (define (average x y) (/ (+ x y) 2))
+  (define (square x) (* x x))
+  (define (good-enough? guess)
+    (< (abs (- (square guess) x)) 0.00001))
+  (define (improve guess)
+    (average guess (/ x guess)))
+  (define (sqrt-iter guess)
+    (if (good-enough? guess)
+        guess
+        (sqrt-iter (improve guess))))
+  (sqrt-iter 1.0))
+
+;(define (factorial n)
+;  (if (= n 1) 1 (* n (factorial (- n 1)))))
+
+(define (factorial n)
+  (define (fact-iter product counter max-count)
+    (if (> counter max-count)
+        product
+        (fact-iter (* counter product)
+                   (+ counter 1)
+                   max-count)))
+
+  (fact-iter 1 1 n))
+
+
+(define (A x y)
+  (cond ((= y 0) 0)
+        ((= x 0) (* 2 y))
+        ((= y 1) 2)
+        (else (A (- x 1)
+                 (A x (- y 1))))))
+
+;(define (fib n)
+;  (cond ((= n 0) 0)
+;        ((= n 1) 1)
+;        (else (+ (fib(- n 1))
+;                 (fib(- n 2))))))
+
+(define (fib n)
+  (define (fib-iter a b count)
+    (if (= count 0)
+        b
+        (fib-iter (+ a b) a (- count 1))))
+  
+  (fib-iter 1 0 n))
+
+
+(define (count-change amount)
+  (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)))
+
+  (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)))))
+  
+  (cc amount 5))
+
+
+(define (ptri n)
+  (if (< n 3) n
+      (+
+       (ptri (- n 1))
+       (+ (* (ptri (- n 2)) 2)
+          (* (ptri (- n 3)) 3)))))