solution to 3.27

diff --git a/src/sicp/ex3_27.rkt b/src/sicp/ex3_27.rkt
new file mode 100644 (file)
index 0000000..51862b9
--- /dev/null
+++ b/src/sicp/ex3_27.rkt
@@ -0,0 +1,40 @@
+#lang r5rs
+
+(define (fib n)
+  (cond
+    ((= n 0) 0)
+    ((= n 1) 1)
+    (else (+ (fib (- n 1))
+             (fib (- n 2))))))
+
+(define memo-fib
+  (memoize (lambda (n)
+             (cond 
+               ((= n 0) 0)
+               ((= n 1) 1)
+               (else (+ (memo-fib (- n 1))
+                        (memo-fib (- n 2))))))))
+
+(define (memoize f)
+  (let ((previous-output (make-table)))
+    (lambda (x)
+      (let ((lookup-result (lookup x previous-output)))
+        (if lookup-result
+            lookup-result
+            (let ((result (f x)))
+              (insert! x result previous-output)
+              result))))))
+          
+#|
+
+If we define memo-fib as
+
+(define memo-fib
+  (memoize fib))
+
+and say, call (memo-fib 10), then, we cache the result of calling fib with n=10.
+But (fib n) calls (fib (- n 1)) and (fib (- n 2)) and this way of calling memo-fib won't cache those intermediate values.
+
+On the other hand, if we define memo-fib the way it is defined above, all intermediate calls to memo-fib also goes through memoize call and hence will get cached in the results table. Hence this is much more efficient.
+
+|#