From: Ramakrishnan Muthukrishnan <vu3rdd@gmail.com>
Date: Tue, 4 May 2010 09:54:06 +0000 (+0530)
Subject: namespace confusions resolved.
X-Git-Url: https://git.rkrishnan.org/?a=commitdiff_plain;h=72cc7c9ba92d6f5668e95f00b47acd08952f371c;p=sicp.git

namespace confusions resolved.
---

diff --git a/src/sicp/ch1_3.clj b/src/sicp/ch1_3.clj
new file mode 100644
index 0000000..0cf7b28
--- /dev/null
+++ b/src/sicp/ch1_3.clj
@@ -0,0 +1,43 @@
+
+(ns sicp.ch1-3
+  (:use [sicp utils]
+	[clojure.contrib test-is]))
+
+;; 1.3.1: Procedures as arguments
+(defn sum-integers [a b]
+  (if (> a b)
+    0
+    (+ a (sum-integers (+ a 1) b))))
+
+(defn sum-cubes [a b]
+  (if (> a b)
+    0
+    (+ (cube a) (sum-cubes (+ a 1) b))))
+
+(defn pi-sum [a b]
+  (if (> a b)
+    0
+    (+ (/ 1.0 (* a (+ a 2))) (pi-sum (+ a 1) b))))
+
+(defn sum [term a next b]
+  (if (> a b)
+    0
+    (+ (term a)
+       (sum term (next a) next b))))
+
+(def sum-cubes-new (fn[a b] (sum cube a inc b)))
+
+(deftest test-sum-of-first-10-integers
+  (is (sum #(identity %) 1 inc 10) 55))
+
+;; (* (sum #(/ 1.0 (* % (+ % 2))) 1 #(+ % 4) 1000) 8)
+;;=> 3.139592655589783  (approaches PI)
+
+(defn integral [f a b dx]
+  (* (sum f (+ a (/ dx 2)) #(+ % dx) b)
+     dx))
+
+(integral cube 0 1 0.001)
+;;=>0.249999875000001
+(integral cube 0 1 0.005)
+;;=>0.24999687500000028
\ No newline at end of file
diff --git a/src/sicp/ex1_1.clj b/src/sicp/ex1_1.clj
new file mode 100644
index 0000000..ad9b8de
--- /dev/null
+++ b/src/sicp/ex1_1.clj
@@ -0,0 +1,27 @@
+(ns sicp.ex1_1
+  (:use [sicp utils]
+	[clojure.contrib trace test-is]))
+
+;; exercise 1.1: What is the result printed by the interpreter in response
+;;               to each expression (in order) ?
+
+(def a 3)
+(def b (+ a 1))
+
+(+ a b (* a b))  ; 19
+(= a b) ; false
+
+(if (and (> b a) (< b (* a b)))
+    b
+    a)   ; 4
+
+(cond (= a 4) 6
+      (= b 4) (+ 6 7 a)
+      :else 25)  ; 16
+
+(+ 2 (if (> b a) b a)) ; 6
+
+(* (cond (> a b) a
+	 (< a b) b
+	 :else -1)
+   (+ a 1))      ; 16
diff --git a/src/sicp/ex1_10.clj b/src/sicp/ex1_10.clj
new file mode 100644
index 0000000..413e30c
--- /dev/null
+++ b/src/sicp/ex1_10.clj
@@ -0,0 +1,36 @@
+(ns sicp.ex1_10
+  (:use [sicp utils]
+	[clojure.contrib trace test-is]))
+
+;; exercise 1.10
+;; ackerman functions
+(defn A [x y]
+  (cond (= y 0) 0
+	(= x 0) (* 2 y)
+	(= y 1) 2
+	:else (A (- x 1)
+		 (A x (- y 1)))))
+
+;; (comment
+;; user> (A 1 10)
+;; 1024
+;; user> (A 2 4)
+;; 65536
+;; user> (A 3 3)
+;; 65536
+;; )
+
+(defn f [n] (A 0 n)) ; f(n) = 2n
+(defn g [n] (A 1 n)) ; g(n) = 2^n
+;; (comment
+;;   g (n) = A (1,n)
+;;         = A (0, A (1, n-1)) = f (A(1,n-1))
+;; 	  = f (f (1,n-2)) 
+;; 	    .....
+;; 	    = f (f (f ... f (1,(n- (n-1)))))
+;; 	      = f (f (f ... 2))
+;; 		= 2 * (2^(n-1))
+;; 		  = 2^n
+;; )
+
+(defn h [n] (A 2 n)) ; h(n) = 2^(n^2)
diff --git a/src/sicp/ex1_11.clj b/src/sicp/ex1_11.clj
new file mode 100644
index 0000000..d76c807
--- /dev/null
+++ b/src/sicp/ex1_11.clj
@@ -0,0 +1,48 @@
+(ns sicp.ex1_11
+  (:use [sicp utils]
+	[clojure.contrib trace test-is]))
+
+;; exercise 1.11: A function f is defined by the rule that f(n) = n if n < 3
+;;                and f(n) = f(n - 1) + 2f(n  - 2) + 3f(n - 3) if n> 3.
+;;                Write a procedure that computes f by means of a recursive
+;;                process. Write a procedure that computes f by means of an
+;;                iterative process. 
+(defn f [n]
+  (if (< n 3)
+    n
+    (+ (f (- n 1))
+       (* 2 (f (- n 2)))
+       (* 3 (f (- n 3))))))
+
+;; (comment
+;; user> (map f (range 10))
+;; (0 1 2 4 11 25 59 142 335 796)  
+;; )
+
+;; ex 1.11: iterative version
+(defn f-iter [count prev0 prev1 prev2]
+  (if (= count 3)
+    (+ prev0
+       (* 2 prev1)
+       (* 3 prev2))
+    (f-iter (dec count)
+	    (+ prev0
+	       (* 2 prev1)
+	       (* 3 prev2))
+	    prev0
+	    prev1)))
+
+(defn f [n]
+  (if (< n 3)
+    n
+    (f-iter n 2 1 0)))
+
+;; ex 1.11: iterative version with let
+(defn f-iter [count prev0 prev1 prev2]
+  (let [res (+ prev0 (* 2 prev1) (* 3 prev2))]
+    (if (= count 3)
+      res
+      (f-iter (dec count)
+	      res
+	      prev0
+	      prev1))))
diff --git a/src/sicp/ex1_12.clj b/src/sicp/ex1_12.clj
new file mode 100644
index 0000000..ff3e39a
--- /dev/null
+++ b/src/sicp/ex1_12.clj
@@ -0,0 +1,22 @@
+(ns sicp.ex1_12
+  (:use [sicp utils]
+	[clojure.contrib trace test-is]))
+
+;; exercise 1.12.  The following pattern of numbers is called Pascal's triangle.
+;;          1
+;;        1   1
+;;      1   2   1
+;;    1   3   3   1
+;;  1   4   6   4   1
+;; ...................
+;;
+;;                 The numbers at the edge of the triangle are all 1, and each
+;;                 number inside the triangle is the sum of the two numbers above
+;;                 it. Write a procedure that computes elements of Pascal's triangle
+;;                 by means of a recursive process. 
+(defn pascal [row col]
+  (when (<= col row)
+    (if (or (= col 0) (= row col))
+      1
+      (+ (pascal (dec row) col)
+	 (pascal (dec row) (dec col))))))
diff --git a/src/sicp/ex1_13.clj b/src/sicp/ex1_13.clj
new file mode 100644
index 0000000..e9b1fd7
--- /dev/null
+++ b/src/sicp/ex1_13.clj
@@ -0,0 +1,18 @@
+(ns sicp.ex1_13
+  (:use [sicp utils]
+	[clojure.contrib trace test-is]))
+
+;; exercise 1.13:
+(comment
+See the pdfs in the directory for the answers.
+)
+
+;; ex 1.13 (contd)
+(defn fib-approx [n]
+  (let [phi (/ (+ 1 (sqrt 5)) 2)]
+    (/ (expt phi n) (sqrt 5))))
+
+;; (comment
+;; user> (map fib-approx (range 10))
+;; (0.4472135954999579 0.7236067977499789 1.1708203932499368 1.8944271909999157 3.065247584249853 4.959674775249769 8.024922359499623 12.984597134749393 21.009519494249016 33.99411662899841)
+;; )
diff --git a/src/sicp/ex1_14.clj b/src/sicp/ex1_14.clj
new file mode 100644
index 0000000..a3df2aa
--- /dev/null
+++ b/src/sicp/ex1_14.clj
@@ -0,0 +1,133 @@
+(ns sicp.ex1_14
+  (:use [sicp utils]
+	[clojure.contrib trace test-is]))
+
+;; exercise 1.14: tree of (count-changes 11)
+(comment
+  See the notebook (sorry, don't have the time to scan it and put it on the web)
+  for the tree representation.
+)
+
+;; order of size and computation
+;; see PDF, but below is the trace tree.
+;; (comment
+;; user> (use 'clojure.contrib.trace)
+;; nil
+;; user> (dotrace [count-change cc] (count-change 11))
+;; TRACE t2609: (count-change 11)
+;; TRACE t2610: |    (cc 11 5)
+;; TRACE t2611: |    |    (cc 11 4)
+;; TRACE t2612: |    |    |    (cc 11 3)
+;; TRACE t2613: |    |    |    |    (cc 11 2)
+;; TRACE t2614: |    |    |    |    |    (cc 11 1)
+;; TRACE t2615: |    |    |    |    |    |    (cc 11 0)
+;; TRACE t2615: |    |    |    |    |    |    => 0
+;; TRACE t2616: |    |    |    |    |    |    (cc 10 1)
+;; TRACE t2617: |    |    |    |    |    |    |    (cc 10 0)
+;; TRACE t2617: |    |    |    |    |    |    |    => 0
+;; TRACE t2618: |    |    |    |    |    |    |    (cc 9 1)
+;; TRACE t2619: |    |    |    |    |    |    |    |    (cc 9 0)
+;; TRACE t2619: |    |    |    |    |    |    |    |    => 0
+;; TRACE t2620: |    |    |    |    |    |    |    |    (cc 8 1)
+;; TRACE t2621: |    |    |    |    |    |    |    |    |    (cc 8 0)
+;; TRACE t2621: |    |    |    |    |    |    |    |    |    => 0
+;; TRACE t2622: |    |    |    |    |    |    |    |    |    (cc 7 1)
+;; TRACE t2623: |    |    |    |    |    |    |    |    |    |    (cc 7 0)
+;; TRACE t2623: |    |    |    |    |    |    |    |    |    |    => 0
+;; TRACE t2624: |    |    |    |    |    |    |    |    |    |    (cc 6 1)
+;; TRACE t2625: |    |    |    |    |    |    |    |    |    |    |    (cc 6 0)
+;; TRACE t2625: |    |    |    |    |    |    |    |    |    |    |    => 0
+;; TRACE t2626: |    |    |    |    |    |    |    |    |    |    |    (cc 5 1)
+;; TRACE t2627: |    |    |    |    |    |    |    |    |    |    |    |    (cc 5 0)
+;; TRACE t2627: |    |    |    |    |    |    |    |    |    |    |    |    => 0
+;; TRACE t2628: |    |    |    |    |    |    |    |    |    |    |    |    (cc 4 1)
+;; TRACE t2629: |    |    |    |    |    |    |    |    |    |    |    |    |    (cc 4 0)
+;; TRACE t2629: |    |    |    |    |    |    |    |    |    |    |    |    |    => 0
+;; TRACE t2630: |    |    |    |    |    |    |    |    |    |    |    |    |    (cc 3 1)
+;; TRACE t2631: |    |    |    |    |    |    |    |    |    |    |    |    |    |    (cc 3 0)
+;; TRACE t2631: |    |    |    |    |    |    |    |    |    |    |    |    |    |    => 0
+;; TRACE t2632: |    |    |    |    |    |    |    |    |    |    |    |    |    |    (cc 2 1)
+;; TRACE t2633: |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    (cc 2 0)
+;; TRACE t2633: |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    => 0
+;; TRACE t2634: |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    (cc 1 1)
+;; TRACE t2635: |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    (cc 1 0)
+;; TRACE t2635: |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    => 0
+;; TRACE t2636: |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    (cc 0 1)
+;; TRACE t2636: |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    => 1
+;; TRACE t2634: |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    => 1
+;; TRACE t2632: |    |    |    |    |    |    |    |    |    |    |    |    |    |    => 1
+;; TRACE t2630: |    |    |    |    |    |    |    |    |    |    |    |    |    => 1
+;; TRACE t2628: |    |    |    |    |    |    |    |    |    |    |    |    => 1
+;; TRACE t2626: |    |    |    |    |    |    |    |    |    |    |    => 1
+;; TRACE t2624: |    |    |    |    |    |    |    |    |    |    => 1
+;; TRACE t2622: |    |    |    |    |    |    |    |    |    => 1
+;; TRACE t2620: |    |    |    |    |    |    |    |    => 1
+;; TRACE t2618: |    |    |    |    |    |    |    => 1
+;; TRACE t2616: |    |    |    |    |    |    => 1
+;; TRACE t2614: |    |    |    |    |    => 1
+;; TRACE t2637: |    |    |    |    |    (cc 6 2)
+;; TRACE t2638: |    |    |    |    |    |    (cc 6 1)
+;; TRACE t2639: |    |    |    |    |    |    |    (cc 6 0)
+;; TRACE t2639: |    |    |    |    |    |    |    => 0
+;; TRACE t2640: |    |    |    |    |    |    |    (cc 5 1)
+;; TRACE t2641: |    |    |    |    |    |    |    |    (cc 5 0)
+;; TRACE t2641: |    |    |    |    |    |    |    |    => 0
+;; TRACE t2642: |    |    |    |    |    |    |    |    (cc 4 1)
+;; TRACE t2643: |    |    |    |    |    |    |    |    |    (cc 4 0)
+;; TRACE t2643: |    |    |    |    |    |    |    |    |    => 0
+;; TRACE t2644: |    |    |    |    |    |    |    |    |    (cc 3 1)
+;; TRACE t2645: |    |    |    |    |    |    |    |    |    |    (cc 3 0)
+;; TRACE t2645: |    |    |    |    |    |    |    |    |    |    => 0
+;; TRACE t2646: |    |    |    |    |    |    |    |    |    |    (cc 2 1)
+;; TRACE t2647: |    |    |    |    |    |    |    |    |    |    |    (cc 2 0)
+;; TRACE t2647: |    |    |    |    |    |    |    |    |    |    |    => 0
+;; TRACE t2648: |    |    |    |    |    |    |    |    |    |    |    (cc 1 1)
+;; TRACE t2649: |    |    |    |    |    |    |    |    |    |    |    |    (cc 1 0)
+;; TRACE t2649: |    |    |    |    |    |    |    |    |    |    |    |    => 0
+;; TRACE t2650: |    |    |    |    |    |    |    |    |    |    |    |    (cc 0 1)
+;; TRACE t2650: |    |    |    |    |    |    |    |    |    |    |    |    => 1
+;; TRACE t2648: |    |    |    |    |    |    |    |    |    |    |    => 1
+;; TRACE t2646: |    |    |    |    |    |    |    |    |    |    => 1
+;; TRACE t2644: |    |    |    |    |    |    |    |    |    => 1
+;; TRACE t2642: |    |    |    |    |    |    |    |    => 1
+;; TRACE t2640: |    |    |    |    |    |    |    => 1
+;; TRACE t2638: |    |    |    |    |    |    => 1
+;; TRACE t2651: |    |    |    |    |    |    (cc 1 2)
+;; TRACE t2652: |    |    |    |    |    |    |    (cc 1 1)
+;; TRACE t2653: |    |    |    |    |    |    |    |    (cc 1 0)
+;; TRACE t2653: |    |    |    |    |    |    |    |    => 0
+;; TRACE t2654: |    |    |    |    |    |    |    |    (cc 0 1)
+;; TRACE t2654: |    |    |    |    |    |    |    |    => 1
+;; TRACE t2652: |    |    |    |    |    |    |    => 1
+;; TRACE t2655: |    |    |    |    |    |    |    (cc -4 2)
+;; TRACE t2655: |    |    |    |    |    |    |    => 0
+;; TRACE t2651: |    |    |    |    |    |    => 1
+;; TRACE t2637: |    |    |    |    |    => 2
+;; TRACE t2613: |    |    |    |    => 3
+;; TRACE t2656: |    |    |    |    (cc 1 3)
+;; TRACE t2657: |    |    |    |    |    (cc 1 2)
+;; TRACE t2658: |    |    |    |    |    |    (cc 1 1)
+;; TRACE t2659: |    |    |    |    |    |    |    (cc 1 0)
+;; TRACE t2659: |    |    |    |    |    |    |    => 0
+;; TRACE t2660: |    |    |    |    |    |    |    (cc 0 1)
+;; TRACE t2660: |    |    |    |    |    |    |    => 1
+;; TRACE t2658: |    |    |    |    |    |    => 1
+;; TRACE t2661: |    |    |    |    |    |    (cc -4 2)
+;; TRACE t2661: |    |    |    |    |    |    => 0
+;; TRACE t2657: |    |    |    |    |    => 1
+;; TRACE t2662: |    |    |    |    |    (cc -9 3)
+;; TRACE t2662: |    |    |    |    |    => 0
+;; TRACE t2656: |    |    |    |    => 1
+;; TRACE t2612: |    |    |    => 4
+;; TRACE t2663: |    |    |    (cc -14 4)
+;; TRACE t2663: |    |    |    => 0
+;; TRACE t2611: |    |    => 4
+;; TRACE t2664: |    |    (cc -39 5)
+;; TRACE t2664: |    |    => 0
+;; TRACE t2610: |    => 4
+;; TRACE t2609: => 4
+;; 4  
+;; )
+
+
+;; TODO: orders of growth in space and number of steps.
diff --git a/src/sicp/ex1_15.clj b/src/sicp/ex1_15.clj
new file mode 100644
index 0000000..11249f5
--- /dev/null
+++ b/src/sicp/ex1_15.clj
@@ -0,0 +1,43 @@
+(ns sicp.ex1_15
+  (:use [sicp utils]
+	[clojure.contrib trace test-is]))
+
+;; exercise 1.15: sin (x) calculation
+;;    a.  How many times is the procedure p applied when (sine 12.15)
+;;        is evaluated?
+;;    b.  What is the order of growth in space and number of steps (as
+;;        a function of a) used by the process generated by the sine
+;;        procedure when (sine a) is evaluated?
+(defn p [x] (- (* 3 x) (* 4 (cube x))))
+
+(defn sine [angle]
+  (if (not (> (myabs angle) 0.1))
+    angle
+    (p (sine (/ angle 3.0)))))
+
+;; solution to (a) => 5
+;; (comment
+;; user> (dotrace [p] (sine 12.15))
+;; TRACE t2490: (p 0.049999999999999996)
+;; TRACE t2490: => 0.1495
+;; TRACE t2491: (p 0.1495)
+;; TRACE t2491: => 0.4351345505
+;; TRACE t2492: (p 0.4351345505)
+;; TRACE t2492: => 0.9758465331678772
+;; TRACE t2493: (p 0.9758465331678772)
+;; TRACE t2493: => -0.7895631144708228
+;; TRACE t2494: (p -0.7895631144708228)
+;; TRACE t2494: => -0.39980345741334
+;; -0.39980345741334
+;; )
+
+;; solution to b
+;; both space and number of steps grows as log3(a) -> log a to the base 3.
+;;
+;; proof:
+;;   a * (1/3)^n <= 0.1
+;;   => take log to the base 3 on both the sides.
+
+;; Note: Finding the order of space in a recursive process is sort of, equiv
+;;       to finding the number of deferred operations. Which is in-turn the
+;;       same as the depth of the evaluation tree.
diff --git a/src/sicp/ex1_16.clj b/src/sicp/ex1_16.clj
new file mode 100644
index 0000000..9bc774a
--- /dev/null
+++ b/src/sicp/ex1_16.clj
@@ -0,0 +1,12 @@
+(ns sicp.ex1_16
+  (:use [sicp utils]
+	[clojure.contrib trace test-is]))
+
+;; exercise 1.16:
+(defn myexpt [b n]
+  (expt-iter b n 1))
+
+(defn expt-iter [b n a]
+  (cond (= n 0) a
+	(even? n) (expt-iter (square b) (/ n 2) a)
+	:else (expt-iter b (- n 1) (* a b))))
diff --git a/src/sicp/ex1_17.clj b/src/sicp/ex1_17.clj
new file mode 100644
index 0000000..ac057e0
--- /dev/null
+++ b/src/sicp/ex1_17.clj
@@ -0,0 +1,18 @@
+(ns sicp.ex1_17
+  (:use [sicp utils]
+	[clojure.contrib trace test-is]))
+
+;; exercise 1.17:
+(defn mult [a b]
+  (if (= b 0)
+    0
+    (+ a (mult a (- b 1)))))
+
+;; double
+;; product = 2 * (a * (b/2)) for even b
+;;         = a    + (a * (b - 1)) for odd b
+(defn fast-mult [a b]
+  (cond (= b 0) 0
+	(= b 1) a
+	(even? b) (twice (fast-mult a (half b)))
+	:else (+ a (fast-mult a (- b 1)))))
diff --git a/src/sicp/ex1_18.clj b/src/sicp/ex1_18.clj
new file mode 100644
index 0000000..7e45dd1
--- /dev/null
+++ b/src/sicp/ex1_18.clj
@@ -0,0 +1,28 @@
+(ns sicp.ex1_18
+  (:use [sicp utils]
+	[clojure.contrib trace test-is]))
+
+;; exercise 1.18: iterative multiply thru addition
+;; the idea is to keep a state variable.
+(defn fast-mult-iter [a b k]
+  (cond (= b 0) k
+	(even? b) (fast-mult-iter (twice a) (half b) k)
+	:else (fast-mult-iter a (- b 1) (+ k a))))
+
+(defn fast-mult-new [a b]
+  (fast-mult-iter a b 0))
+
+;; (comment
+;; user> (dotrace [fast-mult-new fast-mult-iter] (fast-mult-new 2 3))
+;; TRACE t2915: (fast-mult-new 2 3)
+;; TRACE t2916: |    (fast-mult-iter 2 3 0)
+;; TRACE t2917: |    |    (fast-mult-iter 2 2 2)
+;; TRACE t2918: |    |    |    (fast-mult-iter 4 1 2)
+;; TRACE t2919: |    |    |    |    (fast-mult-iter 4 0 6)
+;; TRACE t2919: |    |    |    |    => 6
+;; TRACE t2918: |    |    |    => 6
+;; TRACE t2917: |    |    => 6
+;; TRACE t2916: |    => 6
+;; TRACE t2915: => 6
+;; 6
+;; )
diff --git a/src/sicp/ex1_19.clj b/src/sicp/ex1_19.clj
new file mode 100644
index 0000000..06ab367
--- /dev/null
+++ b/src/sicp/ex1_19.clj
@@ -0,0 +1,22 @@
+(ns sicp.ex1_19
+  (:use [sicp utils]
+	[clojure.contrib trace test-is]))
+
+;; exercise 1.19: fast fibonacci
+;; see the pdf of the notebook scan for the derivation of p' and q'
+(defn ffib-iter [a b p q count]
+  (cond (= count 0) b
+	(even? count)
+	(ffib-iter a
+		   b
+		   (+ (* p p) (* q q))
+		   (+ (* 2 p q) (* q q))
+		   (/ count 2))
+	:else (ffib-iter (+ (* b q) (* a q) (* a p))
+			 (+ (* b p) (* a q))
+			 p
+			 q
+			 (- count 1))))
+
+(defn ffib [n]
+  (ffib-iter 1 0 0 1 n))
diff --git a/src/sicp/ex1_2.clj b/src/sicp/ex1_2.clj
new file mode 100644
index 0000000..2fae959
--- /dev/null
+++ b/src/sicp/ex1_2.clj
@@ -0,0 +1,7 @@
+(ns sicp.ex1_2
+  (:use [sicp utils]
+	[clojure.contrib trace test-is]))
+
+;; exercise 1.2: Translate the given expression into prefix form
+(/ (+ 5 4 (- 2 (- 3 (+ 6 (/ 1 5)))))
+   (* 3 (- 6 2) (- 2 7)))  ; -71/300
diff --git a/src/sicp/ex1_20.clj b/src/sicp/ex1_20.clj
new file mode 100644
index 0000000..a7d0a62
--- /dev/null
+++ b/src/sicp/ex1_20.clj
@@ -0,0 +1,10 @@
+(ns sicp.ex1_20
+  (:use [sicp utils]
+	[clojure.contrib trace test-is]))
+
+;;; exercise 1.20.
+;;
+;;  normal order - 18, applicative order - 4.
+;;
+;;   too lazy to scan things from the notebook. May be I should instead
+;;   use a wiki.
diff --git a/src/sicp/ex1_21.clj b/src/sicp/ex1_21.clj
new file mode 100644
index 0000000..af6d91b
--- /dev/null
+++ b/src/sicp/ex1_21.clj
@@ -0,0 +1,13 @@
+(ns sicp.ex1_21
+  (:use [sicp utils]
+	[clojure.contrib trace test-is]))
+
+;; exercise 1.21
+(comment
+user> (smallest-divisor 199)
+199
+user> (smallest-divisor 1999)
+1999
+user> (smallest-divisor 19999)
+7
+)
diff --git a/src/sicp/ex1_22.clj b/src/sicp/ex1_22.clj
new file mode 100644
index 0000000..daf7815
--- /dev/null
+++ b/src/sicp/ex1_22.clj
@@ -0,0 +1,112 @@
+(ns sicp.ex1_22
+  (:use [sicp utils]
+	[clojure.contrib trace test-is]))
+
+;; exercise 1.22
+(defn timed-prime-test [n]
+  (prn)
+  (print n)
+  (start-prime-test n (System/nanoTime)))
+
+(defn start-prime-test [n start-time]
+  (if (prime? n)
+    (report-prime (- (System/nanoTime) start-time))))
+
+(defn report-prime [elapsed-time]
+  (print " *** ")
+  (print elapsed-time))
+
+(defn search-for-primes [a b]
+  (cond (>= a b) nil
+	(even? a) (search-for-primes (+ 1 a) b)
+	(timed-prime-test a) (search-for-primes (+ 2 a) b)
+	:else (search-for-primes (+ 2 a) b)))
+
+;;; three smallest primes greater than 1000
+;;; 1009, 1013, 1019
+(take 3 (filter #(prime? %) (iterate inc 1000)))
+;=> (1009 1013 1019)
+
+;=> 0.9642028750000001
+
+;;; > 10,000: 10007, 10009, 10037
+(take 3 (filter #(prime? %) (iterate inc 10000)))
+;=> (10007 10009 10037)
+
+;=> 1.5897884999999998
+
+;;; > 100,000: 100003, 100019, 100043
+(take 3 (filter #(prime? %) (iterate inc 100000)))
+;=> (100003 100019 100043)
+
+;=> 1.8525091250000003
+
+;;; > 1,000,000: 1000003, 1000033, 1000037
+(take 3 (filter #(prime? %) (iterate inc 1000000)))
+;=> (1000003 1000033 1000037)
+
+;=> 1.908832125
+
+;; time taken seem to increase as the range increases.
+;; but they are totally random on the jvm, so I can't find
+;; the exact relation.
+
+(comment
+user> (microbench 10 (take 3 (filter #(prime? %) (iterate inc 1000))))
+Warming up!
+Benchmarking...
+(1009 1013 1019)
+(1009 1013 1019)
+(1009 1013 1019)
+(1009 1013 1019)
+(1009 1013 1019)
+(1009 1013 1019)
+(1009 1013 1019)
+(1009 1013 1019)
+(1009 1013 1019)
+(1009 1013 1019)
+Total runtime:  0.28404500000000005
+Highest time :  0.083949
+Lowest time  :  0.019416
+Average      :  0.022585000000000008
+(0.083949 0.019416 0.023257 0.020394 0.024165 0.024514 0.024374 0.020813 0.021721 0.021442)
+user> (microbench 10 (take 3 (filter #(prime? %) (iterate inc 10000))))
+Warming up!
+Benchmarking...
+(10007 10009 10037)
+(10007 10009 10037)
+(10007 10009 10037)
+(10007 10009 10037)
+(10007 10009 10037)
+(10007 10009 10037)
+(10007 10009 10037)
+(10007 10009 10037)
+(10007 10009 10037)
+(10007 10009 10037)
+Total runtime:  0.26462800000000003
+Highest time :  0.067118
+Lowest time  :  0.020533
+Average      :  0.022122125000000006
+(0.067118 0.022698 0.024095 0.023537 0.020533 0.020882 0.020603 0.021372 0.020603 0.023187)
+user> (microbench 10 (take 3 (filter #(prime? %) (iterate inc 100000))))
+Warming up!
+Benchmarking...
+(100003 100019 100043)
+(100003 100019 100043)
+(100003 100019 100043)
+(100003 100019 100043)
+(100003 100019 100043)
+(100003 100019 100043)
+(100003 100019 100043)
+(100003 100019 100043)
+(100003 100019 100043)
+(100003 100019 100043)
+Total runtime:  0.265118
+Highest time :  0.073263
+Lowest time  :  0.020254
+Average      :  0.021450125000000004
+(0.073263 0.023048 0.023467 0.021022 0.020394 0.020254 0.021302 0.020812 0.020743 0.020813)  
+)
+
+;;; can't make out any sqrt(10) relation between the numbers. may be because
+;;; jvm compilation is doing some behind the scene tricks.
diff --git a/src/sicp/ex1_23.clj b/src/sicp/ex1_23.clj
new file mode 100644
index 0000000..8200ecf
--- /dev/null
+++ b/src/sicp/ex1_23.clj
@@ -0,0 +1,19 @@
+(ns sicp.ex1_23
+  (:use [sicp utils]
+	[clojure.contrib trace test-is]))
+
+;;; exercise 1.23
+(defn next-divisor [n]
+  (if (= n 2)
+    3
+    (+ n 2)))
+
+
+(defn find-divisor [n test-divisor]
+  (cond (> (square test-divisor)  n) n
+	(divides? test-divisor n) test-divisor
+	:else (find-divisor n (next-divisor test-divisor))))
+
+(comment
+  I can't see any noticable difference in the speed.
+)
diff --git a/src/sicp/ex1_24.clj b/src/sicp/ex1_24.clj
new file mode 100644
index 0000000..ddffc11
--- /dev/null
+++ b/src/sicp/ex1_24.clj
@@ -0,0 +1,10 @@
+(ns sicp.ex1_24
+  (:use [sicp utils]
+	[clojure.contrib trace test-is]))
+
+;;; exercise 1.24
+(comment
+  (microbench 10 (take 3 (filter #(fast-prime? %) (iterate inc 1000))))
+  ...
+  "I did not observe any difference".
+)
diff --git a/src/sicp/ex1_25.clj b/src/sicp/ex1_25.clj
new file mode 100644
index 0000000..8dfd0fc
--- /dev/null
+++ b/src/sicp/ex1_25.clj
@@ -0,0 +1,17 @@
+(ns sicp.ex1_25
+  (:use [sicp utils]
+	[clojure.contrib trace test-is]))
+
+;; exercise 1.25
+(defn expmod [base exp m]
+  (rem (fast-expt base exp) m))
+
+(comment
+  In the case of the original expmod implementation, square and remainder
+  calls are interspersed, so square always deals with a small number, whereas
+  with the above way, we do a series of squaring and then in the end take
+  remainder. Squaring of big numbers are very inefficient as the CPU has to
+  do multi-byte arithmetic which consumes many cycles.
+
+  So the new version is several times slower than the original.
+)
diff --git a/src/sicp/ex1_26.clj b/src/sicp/ex1_26.clj
new file mode 100644
index 0000000..cd1ba73
--- /dev/null
+++ b/src/sicp/ex1_26.clj
@@ -0,0 +1,12 @@
+(ns sicp.ex1_26
+  (:use [sicp utils]
+	[clojure.contrib trace test-is]))
+
+;;; exercise 1.26
+(comment
+  "Instead of calling (square x), Louis now makes does (* x x). In the former,
+   case, x is evaluated only once, where as in the second, x gets evaluated
+   2x, 4x, 8x, 16x and so on (for any x which is recursive). So, if the original
+   computation is considered T(log_n), then the new process T(n). This can also
+   be illustrated with the call tree."
+)
diff --git a/src/sicp/ex1_27.clj b/src/sicp/ex1_27.clj
new file mode 100644
index 0000000..e0c02e1
--- /dev/null
+++ b/src/sicp/ex1_27.clj
@@ -0,0 +1,34 @@
+(ns sicp.ex1_27
+  (:use [sicp utils]
+	[clojure.contrib trace test-is]))
+
+;; exercise 1.27
+(comment
+  "Some notes on Carmichael numbers: Carmichael numbers are those that fail
+   Fermat little test. That is, for any n in the Carmichael set,
+   (prime? n)      => false
+   (fermat-test n) => true."
+  )
+(defn brute-force-fermat-test [n]
+  (try-all 2 n))
+
+(defn try-all [a n]
+  (cond (= a n) true
+	(try-it a n) (try-all (inc a) n)
+	:else false))
+(comment
+  "all the given numbers pass the above test, i.e. for every a < n,
+   a^n mod n === a mod n"
+  user> (brute-force-fermat-test 561)
+  true
+  user> (brute-force-fermat-test 1105)
+  true
+  user> (brute-force-fermat-test 1729)
+  true
+  user> (brute-force-fermat-test 2465)
+  true
+  user> (brute-force-fermat-test 2821)
+  true
+  user> (brute-force-fermat-test 6601)
+  true
+  )
diff --git a/src/sicp/ex1_28.clj b/src/sicp/ex1_28.clj
new file mode 100644
index 0000000..0a8e1f1
--- /dev/null
+++ b/src/sicp/ex1_28.clj
@@ -0,0 +1,30 @@
+(ns sicp.ex1_28
+  (:use [sicp utils]
+	[clojure.contrib trace test-is]))
+
+
+;;; exercise 1.28
+(defn expmod2 [base exp m]
+  (cond (= exp 0) 1
+	(even? exp) (square-test (expmod2 base (/ exp 2) m) m)
+	:else (rem (* base (expmod2 base (dec exp) m))
+		   m)))
+
+(defn square-test [x m]
+  (if (and (not (or (= x 1) (= x (- m 1))))
+	   (= (rem (square x) m) 1))
+    0
+    (rem (square x) m)))
+
+(defn miller-rabin-test [n]
+  (try-it (+ 2 (rand-int (- n 2)))
+	  n))
+
+(defn try-it [a n]
+  (= (expmod2 a (- n 1) n) 1))
+
+(comment
+  "If the random number generated (a) is 1, then this returns false
+   positives. So generate random numbers between 2 and n-1. (is this
+   assumption correct?) "
+)
\ No newline at end of file
diff --git a/src/sicp/ex1_29.clj b/src/sicp/ex1_29.clj
new file mode 100644
index 0000000..33a3458
--- /dev/null
+++ b/src/sicp/ex1_29.clj
@@ -0,0 +1,28 @@
+(ns sicp.ex1_29
+  (:use [sicp utils]
+	[clojure.contrib trace test-is]))
+
+;; simpson's rule of integration
+(defn sum [term a next b]
+  (if (> a b)
+    0
+    (+ (term a)
+       (sum term (next a) next b))))
+
+(defn make-fac [k n]
+  (cond (= k 0) 1
+	(= k n) 1
+	(even? k) 2
+	:else 4))
+
+(defn simpson-sum [term a next-fn b n k]
+  (let [fac (make-fac k n)]
+    (if (> k n)
+      0
+      (+ (* fac (term a))
+	 (simpson-sum term (next-fn a) next-fn b n (+ k 1))))))
+
+(defn simpson-rule [f a b n]
+  (let [h (/ (- b a) n)]
+    (* (simpson-sum f a #(+ h %) b n 0)
+       (/ h 3.0))))
diff --git a/src/sicp/ex1_3.clj b/src/sicp/ex1_3.clj
new file mode 100644
index 0000000..b7e70b2
--- /dev/null
+++ b/src/sicp/ex1_3.clj
@@ -0,0 +1,25 @@
+(ns sicp.ex1_3
+  (:use [sicp utils]
+	[clojure.contrib trace test-is]))
+
+;; exercise 1.3:  Define a procedure that takes three numbers as
+;;                arguments and returns the sum of the squares of
+;;                the two larger numbers.
+(defn sort3 [a b c]
+  (cond (> b a) (sort3 b a c)
+	(< b c) (sort3 a c b)
+	:else [a b c]))
+
+(defn sum-of-sq-of-two-largest [a b c]
+  (apply sum-of-squares (take 2 (sort3 a b c))))
+
+;; well, I cheated above. Let me use only the constructs introduced
+;; so far in the book. (follows after the sicp meetup #2 on 28/mar/2010.
+(defn sum-of-square-of-two-largest [a b c]
+  (if (> a b)
+    (if (> b c)
+      (sum-of-squares a b) ; a > b > c
+      (sum-of-squares a c))
+    (if (> a c)
+      (sum-of-squares b a)
+      (sum-of-squares b c))))
diff --git a/src/sicp/ex1_4.clj b/src/sicp/ex1_4.clj
new file mode 100644
index 0000000..2d8e0bd
--- /dev/null
+++ b/src/sicp/ex1_4.clj
@@ -0,0 +1,15 @@
+(ns sicp.ex1_4
+  (:use [sicp utils]
+	[clojure.contrib trace test-is]))
+
+;; exercise 1.4: Observe that our model of evaluation allows for
+;;               combinations whose operators are compound
+;;               expressions. Use this observation to describe the
+;;               behavior of the following procedure:
+;; (defn a-plus-abs-b [a b]
+;;   ((if (> b 0) + -) a b))
+(comment
+  If b is positive, we do (+ a b) and if it is negative, we do (- a b).
+  This makes use of the fact that the first element in a list is an
+  operand. Here, the operand is chosen based on other operators.
+  )
diff --git a/src/sicp/ex1_5.clj b/src/sicp/ex1_5.clj
new file mode 100644
index 0000000..9638b3b
--- /dev/null
+++ b/src/sicp/ex1_5.clj
@@ -0,0 +1,30 @@
+(ns sicp.ex1_5
+  (:use [sicp utils]
+	[clojure.contrib trace test-is]))
+
+;; exercise 1.5:  Ben Bitdiddle has invented a test to determine
+;;                whether the interpreter he is faced with is
+;;                using applicative-order evaluation or normal-order
+;;                evaluation. He defines the following two procedures:
+;; (defn p [] (p))
+;; (defn test [x y]
+;;   (if (= x 0)
+;;    0
+;;    y))
+;;
+;; Then he evaluates the expression
+;;
+;; (test 0 (p))
+;;
+;; What behavior will Ben observe with an interpreter that uses
+;; applicative-order evaluation?
+(comment
+  In the case of applicative order evaluation, the test gets into
+  and infinite loop (eventually using all the stack), as the parameters
+  are evaluated before they are actualy used in the function.
+  )
+;; What behavior will he observe with an interpreter that uses
+;; normal-order evaluation? Explain your answer.
+(comment
+  It will print 0, as (p) is not evaluated in this case.
+  )
diff --git a/src/sicp/ex1_6.clj b/src/sicp/ex1_6.clj
new file mode 100644
index 0000000..5144f1b
--- /dev/null
+++ b/src/sicp/ex1_6.clj
@@ -0,0 +1,29 @@
+(ns sicp.ex1_6
+  (:use [sicp utils]
+	[clojure.contrib trace test-is]))
+
+;; exercise 1.6
+;; Alyssa P. Hacker doesn't see why if needs to be provided as a special form.
+;; ``Why can't I just define it as an ordinary procedure in terms of cond?''
+(defn new-if [predicate then-clause else-clause]
+  (cond predicate then-clause
+	:else else-clause))
+
+(new-if (= 3 2) 0 5)  ; 5
+(new-if (= 1 1) 0 5)  ; 0
+
+;; Delighted, Alyssa uses new-if to rewrite the square-root program:
+
+(defn sqrt-iter [guess x]
+  (new-if (good-enough? guess x)
+	  guess
+	  (sqrt-iter (improve guess x)
+		     x)))
+
+;; what happens when Alyssa attempts to use this to compute square roots? Explain.
+(comment
+  Since `new-if' is a function, when it is called from sqrt-iter, the parameters
+  are evaluated before it gets called. good-enough? will return a false unless
+  the guess and x are almost the same. guess evaluated to the initial value of
+  guess. sqrt-iter gets evaluated, but gets into an infinite loop. The predicate
+  will have no effect.)
diff --git a/src/sicp/ex1_7.clj b/src/sicp/ex1_7.clj
new file mode 100644
index 0000000..f79dae6
--- /dev/null
+++ b/src/sicp/ex1_7.clj
@@ -0,0 +1,54 @@
+(ns sicp.ex1_7
+  (:use [sicp utils]
+	[clojure.contrib trace test-is]))
+
+;; Exercise 1.7: The good-enough? test used in computing square roots will not
+;; be very effective for finding the square roots of very small numbers. Also,
+;; in real computers, arithmetic operations are almost always performed with
+;; limited precision. This makes our test inadequate for very large numbers.
+;; Explain these statements, with examples showing how the test fails for small
+;; and large numbers.
+(comment
+ user> (sqrt (square 0.001))
+ 0.031260655525445276
+ user> (sqrt (square 0.2))
+ 0.20060990407779591
+ user> (sqrt (square 0.01))
+ 0.03230844833048122
+ user> (sqrt (square 0.02))
+ 0.0354008825558513
+ user> (sqrt (square 10))
+ 10.000000000139897
+ user> (sqrt (square 100))
+ 100.00000025490743
+ user> (sqrt (square 200))
+ 200.000000510076
+ user> (sqrt (square 2))
+ 2.0000000929222947
+ user> (sqrt (square 0.1))
+ 0.10032578510960607
+ user> (sqrt (square 0.01))
+ 0.03230844833048122
+ user> (sqrt (square 10000))
+ 10000.0
+ user> (sqrt (square 20000))
+ 20000.0
+ user> (sqrt (square 200000))
+ 200000.0
+ user> (sqrt (square 20000000))
+ 2.0E7
+ user> (sqrt (square 20000000000))
+ 2.0E10
+ user> (sqrt (square 200000.012))
+ 200000.012
+ user> (sqrt (square 2000000.123))
+ 2000000.123
+ user> (sqrt (square 200000000.123))
+ 2.00000000123E8
+ user> (sqrt (square 2000000000.123))
+ 2.000000000123E9
+ user> (sqrt (square 20000000000.123))
+ 2.0000000000123E10
+ user> (sqrt (square 2000000000000.123))
+ 2.000000000000123E12
+ )
\ No newline at end of file
diff --git a/src/sicp/ex1_8.clj b/src/sicp/ex1_8.clj
new file mode 100644
index 0000000..bdf2e05
--- /dev/null
+++ b/src/sicp/ex1_8.clj
@@ -0,0 +1,30 @@
+(ns sicp.ex1_8
+  (:use [sicp utils]
+	[clojure.contrib trace test-is]))
+
+;; exercise 1.8: cube root
+(defn improve [guess x]
+  (/ (+ (/ x (square guess)) (* 2 guess)) 3))
+
+(defn cubert-iter [old-guess new-guess x]
+  (if (good-enough? old-guess new-guess x)
+    new-guess
+    (cubert-iter new-guess (improve new-guess x)
+		 x)))
+
+(defn cuberoot [x]
+  (cubert-iter x 1.0 x))
+
+(comment
+user> (cuberoot (cube 2))
+2.000000000012062
+user> (cuberoot (cube 10))
+10.000000000000002
+user> (cuberoot (cube 9))
+9.000000000053902
+user> (cuberoot (cube 0.001))
+0.001000000000000962
+user> (cuberoot (cube 0.0001))
+1.000000000000001E-4
+user>
+)
diff --git a/src/sicp/ex1_9.clj b/src/sicp/ex1_9.clj
new file mode 100644
index 0000000..4029985
--- /dev/null
+++ b/src/sicp/ex1_9.clj
@@ -0,0 +1,48 @@
+(ns sicp.ex1_9
+  (:use [sicp utils]
+	[clojure.contrib trace test-is]))
+
+;; exercise 1.9
+(defn ++ [a b]
+  (if (= a 0)
+    b
+    (inc (++ (dec a) b))))
+
+;; (comment
+;;   This version is a recursive process, where the previous call increments
+;;   the sum by 1 and each call decrement the first operand by 1.
+  
+;; user> (dotrace [++] (++ 4 5))
+;; TRACE t3745: (++ 4 5)
+;; TRACE t3746: |    (++ 3 5)
+;; TRACE t3747: |    |    (++ 2 5)
+;; TRACE t3748: |    |    |    (++ 1 5)
+;; TRACE t3749: |    |    |    |    (++ 0 5)
+;; TRACE t3749: |    |    |    |    => 5
+;; TRACE t3748: |    |    |    => 6
+;; TRACE t3747: |    |    => 7
+;; TRACE t3746: |    => 8
+;; TRACE t3745: => 9
+;; 9
+;; )
+
+(defn ++ [a b]
+  (if (= a 0)
+    b
+    (++ (dec a) (inc b))))
+
+;; (comment
+  
+;; user> (dotrace [++] (++ 4 5))
+;; TRACE t3766: (++ 4 5)
+;; TRACE t3767: |    (++ 3 6)
+;; TRACE t3768: |    |    (++ 2 7)
+;; TRACE t3769: |    |    |    (++ 1 8)
+;; TRACE t3770: |    |    |    |    (++ 0 9)
+;; TRACE t3770: |    |    |    |    => 9
+;; TRACE t3769: |    |    |    => 9
+;; TRACE t3768: |    |    => 9
+;; TRACE t3767: |    => 9
+;; TRACE t3766: => 9
+;; 9
+;; )