@@ -1,4 +1,11 @@ ; Write a Scheme expression whose evaluation would result in an error -; if and were a procedure but actually will have a value because and -; is a special form. Do the same for or. +; if `and` were a procedure but actually will have a value because and +; is a special form. Do the same for `or`. +(defn and- [a b] (and a b)) +(defn or- [a b] (or a b)) + +(defn loopy [] (loopy)) + +(and false (loopy)) +(or true (loopy)) 1.1.6/m1.3.clj @@ -2,3 +2,13 @@ ; returns 1 if the number is positive, -1 if the number is negative, ; and 0 if the number is 0. +(defn sign [val] + (cond (> val 0) 1 + (< val 0) -1 + :else 0)) + +(= 1 (sign 10)) +(= 1 (sign 1)) +(= 0 (sign 0)) +(= -1 (sign -1)) +(= -1 (sign -10)) 1.1.6/m1.4.clj @@ -10,3 +10,8 @@ ; Write two definitions of true-false - one that uses if and one that ; uses cond. +(defn true-false [val] + (if val 1 0)) + +(= 1 (true-false (> 3 2))) +(= 0 (true-false (and (> 3 2) (< 3 1)))) 1.1.6/m1.5.clj @@ -9,15 +9,18 @@ ; Design a square-root procedure that uses this kind of end test. Does this ; work better for small and large numbers? -(defn abs [x] - (cond (< x 0) (- x) - :else x)) +; Clojure builtin +;(defn abs [x] +; (cond (< x 0) (- x) +; :else x)) -(defn square [x] - (* x x)) +; Clojure builtin +;(defn square [x] +; (* x x)) -(defn average [x y] - (/ (+ x y) 2)) +; Clojure builtin +;(defn average [x y] +; (/ (+ x y) 2)) (defn improve [guess x] (average guess (/ x guess))) 1.1.7/1.7.clj @@ -3,9 +3,58 @@ ; greater than or equal to 0, the roots are both real; otherwise the ; roots are complex with real part -b/2a. Define a procedure ; smallest-real-part that takes the coefficients a, b and c as arguments -; and returns either the real part of the roots (if theyare complex), +; and returns either the real part of the roots (if they are complex), ; or else the real root having the smaller absolute value. Be sure ; that your procedure continues to work if some of the coefficients ; or the discriminant are zero (but you may assume that a is always ; nonzero). +(defn improve [guess x] + (average guess (/ x guess))) +(defn good-enough? [guess x] + (or (= guess x) + (< (abs (- (square guess) x)) (* x 0.0000001)))) +(defn sqrt-iter [guess x] + (if (good-enough? guess x) + guess + (recur (improve guess x) + x))) +(defn sqrt [x] + (sqrt-iter 1.0 x)) + + +(defn discriminant [a b c] + (- (* b b) (* 4 a c))) + +(defn real-root? [a b c] + (<= 0 (discriminant a b c))) + +(= true (real-root 1 0 0)) +(= true (real-root 1 0 -1)) +(= false (real-root 1 0 1)) + +(defn real-part [a b c] + (/ (- b) (* 2 a))) + +(defn root [sign a b c] + ; -b +- sqrt(bb - 4ac) + ; -------------------- + ; 2a + (/ (sign (- b) + (sqrt (discriminant a b c))) + (* 2 a))) + +(defn root-one [a b c] + (root + a b c)) +(defn root-two [a b c] + (root - a b c)) + +(defn smallest-real-part [a b c] + (if (real-root? a b c) + (min (abs (root-one a b c)) (abs (root-two a b c))) + (real-part a b c))) + +; todo: some concrete examples with known answers to test with? +(smallest-real-part 1 0 0) +(smallest-real-part 1 0 -1) +(smallest-real-part 1 3 1) 1.1.7/m1.6.clj f33227bc70149ef041473d44a2441f0614741827 Jamie Macey jamie.git@tracefunc.com http://github.com/jamie/sicp/commit/d0074a212f3074cc2c6c1595fb0149fab6fc65a7 d0074a212f3074cc2c6c1595fb0149fab6fc65a7 2009-01-22T11:11:14-08:00 2009-01-22T11:11:14-08:00 implement remaining sec 1.1 instructors exercises b16eb42b2de6c0f1e47de0a0a220b4353ef57a58 Jamie Macey jamie.git@tracefunc.com