slime/bin/tests/sicp.slime

;; (define (abs x)
;;   (cond ((< x 0) (- x))
;;         (else x)))

;; (assert (= (abs 1) 1))
;; (assert (= (abs (- 2)) 2))


(define (abs x)
  (if (< x 0)
      (- x)
    x))

;; (assert (= (abs 12) 12))
;; (assert (= (abs (- 32)) 32))


;; (define (>= x y)
;;   (or (> x y)
;;       (= x y)))

;; (assert (>= 2 2))
;; (assert (>= 3 2))
;; (assert (not (>= 1 2)))
;; (assert (not (>= 12 44)))


;; (define (>= x y)
;;   (not (< x y)))

;; (assert (>= 2 2))
;; (assert (>= 3 2))
;; (assert (not (>= 1 2)))
;; (assert (not (>= 12 44)))


;; (define (a-plus-abs-b a b)
;;   ((if (> b 0) + -) a b))

;; (assert (= (a-plus-abs-b 1  2) 3))
;; (assert (= (a-plus-abs-b 1 -2) 3))

(define (square x) (* x x))
(define (cube x) (* x x x))

;; (assert (= ((lambda (x y z)
;;               (+ x y (square z)))
;;             1 2 3)
;;            12))

;; ;;; --------------------
;; ;;;    newtons method
;; ;;; --------------------

;; (define tolerance 0.001)

;; (define (square x)
;;   (* x x))

(define (average x y)
  (/ (+ x y) 2))

;; (define (improve guess x)
;;   (average guess (/ x guess)))

;; (define (good-enough? guess x)
;;   (< (abs (- (square guess) x)) tolerance))

;; (define (sqrt-iter guess x)
;;   (if (good-enough? guess x)
;;       guess
;;     (sqrt-iter (improve guess x) x)))

;; (define (sqrt x)
;;   (sqrt-iter 1.0 x))

;; (define (sqrt2 x)
;;   (define (good-enough? guess x)
;;     (< (abs (- (square guess) x)) 0.001))

;;   (define (improve guess x)
;;     (average guess (/ x guess)))

;;   (define (sqrt-iter guess x)
;;     (if (good-enough? guess x)
;;         guess
;;       (sqrt-iter (improve guess x) x)))

;;   (sqrt-iter 1.0 x))

;; (define (sqrt3 x)
;;   (define (good-enough? guess)
;;     (< (abs (- (square guess) x)) 0.001))

;;   (define (improve guess)
;;     (average guess (/ x guess)))

;;   (define (sqrt-iter guess)
;;     (if (good-enough? guess)
;;         guess
;;       (sqrt-iter (improve guess))))

;;   (sqrt-iter 1.0))

;; (assert      (< (abs (- 3 (sqrt 9)))  tolerance))
;; (assert      (< (abs (- 4 (sqrt 16))) tolerance))
;; (assert (not (< (abs (- 4 (sqrt 15))) tolerance)))

;; (assert      (< (abs (- 3 (sqrt2 9)))  tolerance))
;; (assert      (< (abs (- 4 (sqrt2 16))) tolerance))
;; (assert (not (< (abs (- 4 (sqrt2 15))) tolerance)))

;; (assert      (< (abs (- 3 (sqrt3 9)))  tolerance))
;; (assert      (< (abs (- 4 (sqrt3 16))) tolerance))
;; (assert (not (< (abs (- 4 (sqrt3 15))) tolerance)))


;; ;;; -----------------
;; ;;;     factorial
;; ;;; -----------------

(define (factorial n)
  (if (= n 1)
      1
    (* n (factorial (- n 1)))))

(define (factorial2 n)
  (fact-iter 1 1 n))

(define (fact-iter product counter max-count)
  (if (> counter max-count)
      product
    (fact-iter (* counter product) (+ counter 1) max-count)))

(define (factorial3 n)
  (define (iter product counter)
    (if (> counter n)
        product
      (iter (* counter product) (+ counter 1))))

  (iter 1 1))

(assert (= (factorial  6) 720))
(assert (= (factorial2 6) 720))
(assert (= (factorial3 6) 720))

;;; ----------------
;;;     ackermann
;;; ----------------

(define (A m n)
    (cond ((= m 0) (+ n 1))
          ((= n 0) (A (- m 1) 1))
          (else (A (- m 1) (A m (- n 1))))))

(assert (= (A 0 0) 1))
(assert (= (A 1 2) 4))
(assert (= (A 3 1) 13))


;; ;;; ---------------
;; ;;;    Fibonacci
;; ;;; ---------------

;; (define (fib n)
;;   (cond ((= n 0) 0)
;;         ((= n 1) 1)
;;         (else (+ (fib (- n 1)) (fib (- n 2))))))

;; (define (fib2 n)
;;   (fib-iter 1 0 n))

;; (define (fib-iter a b count)
;;   (if (= count 0)
;;       b
;;     (fib-iter (+ a b) a (- count 1))))

;; (assert (= (fib 2) 1))
;; (assert (= (fib 3) 2))
;; (assert (= (fib 4) 3))
;; (assert (= (fib 5) 5))
;; (assert (= (fib 6) 8))

;; (assert (= (fib2 2) 1))
;; (assert (= (fib2 3) 2))
;; (assert (= (fib2 4) 3))
;; (assert (= (fib2 5) 5))
;; (assert (= (fib2 6) 8))

;; ;;; ------------------
;; ;;;    count change
;; ;;; ------------------

;; (define (count-change amount)
;;   (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)))))

;;   (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)))

;;   (cc amount 5))

;; (assert (= (count-change 100) 292))

;; ;;; --------------------
;; ;;;    exponentiation
;; ;;; --------------------

;; (define (expt b n)
;;   (if (= n 0)
;;       1
;;     (* b (expt b (- n 1)))))

;; (define (expt2 b n)
;;   (define (expt-iter b counter product)
;;     (if (= counter 0)
;;         product
;;       (expt-iter b (- counter 1) (* b product))))

;;   (expt-iter b n 1))

;; (define (fast-expt b n)
;;   (define (even? n)
;;     (= (% n 2) 0))

;;   (cond ((= n 0) 1)
;;         ((even? n) (square (fast-expt b (/ n 2))))
;;         (else (* b (fast-expt b (- n 1))))))

;; (assert (= (expt 1 2) 1))
;; (assert (= (expt 2 2) 4))
;; (assert (= (expt 2 3) 8))

;; (assert (= (expt2 1 2) 1))
;; (assert (= (expt2 2 2) 4))
;; (assert (= (expt2 2 3) 8))

;; (assert (= (fast-expt 1 2) 1))
;; (assert (= (fast-expt 2 2) 4))
;; (assert (= (fast-expt 2 3) 8))

;; ;;; ----------
;; ;;;    gcd
;; ;;; ----------

;; (define (gcd a b)
;;   (if (= b 0)
;;       a
;;     (gcd b (% a b))))

;; (assert (= (gcd 40 6) 2))
;; (assert (= (gcd 13 4) 1))


;; ;;; ----------
;; ;;;   primes
;; ;;; ----------

;; (define (smallest-divisor n)
;;   (find-divisor n 2))

;; (define (find-divisor n test-divisor)
;;   (cond ((> (square test-divisor) n) n)
;;         ((divides? test-divisor n) test-divisor)
;;         (else (find-divisor n (+ test-divisor 1)))))

;; (define (divides? a b)
;;   (= (% b a) 0))

;; (define (prime? n)
;;   (= n (smallest-divisor n)))

;; (assert (prime? 13))
;; (assert (prime? 11))
;; (assert (not (prime? 12)))


;;; ----------------------
;;;    simple integral
;;; ----------------------

;; (define (sum term a next b)
;;   (if (> a b)
;;       0
;;     (+ (term a) (sum term (next a) next b))))

;; (define (integral f a b dx)
;;   (define (add-dx x) (+ x dx))
;;   (* (sum f (+ a (/ dx 2.0)) add-dx b) dx))

;; (define (pi-sum a b)
;;   (define (pi-term x) (/ 1.0 (* x (+ x 2))))
;;   (define (pi-next x) (+ x 4))
;;   (sum pi-term a pi-next b))

;; (assert (< (abs (- (* 8 (pi-sum 1 100))     3.121595)) 0.0001))
;; (assert (< (abs (- (integral cube 0 1 0.02) 0.249950)) 0.0001))


;; ------------------------------------------------------------
;;       F(x,y) = x(1 + xy)^2 + y(1 − y) + (1 + xy)(1 − y)
;; ------------------------------------------------------------

;; (define (f x y)
;;   (let ((a (+ 1 (* x y)))
;;         (b (- 1 y)))
;;     (+ (* x (square a))
;;        (* y b)
;;        (* a b))))

;; (assert (= (f 0 0) 1))
;; (assert (= (f 1 1) 4))


;; ;;; ---------------
;; ;;;    find zero
;; ;;; ---------------

;; (define (positive? x) (< 0 x))
;; (define (negative? x) (< x 0))

;; (define (search f neg-point pos-point)
;;   (let ((midpoint (average neg-point pos-point)))
;;     (if (close-enough? neg-point pos-point)
;;         midpoint
;;       (let ((test-value (f midpoint)))
;;         (cond ((positive? test-value) (search f neg-point midpoint))
;;               ((negative? test-value) (search f midpoint pos-point))
;;               (else midpoint))))))

;; (define (close-enough? x y) (< (abs (- x y)) 0.001))

;; (assert (close-enough? (search (lambda (x) (- 1 (square x))) -3 3) -1))