cleanup and sicp file, but crashes
This commit is contained in:
FelixBrendel
@@ -0,0 +1,340 @@
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(define (abs x)
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(cond ((< x 0) (- x))
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(t x)))
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(assert (= (abs 1) 1))
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(assert (= (abs (- 2)) 2))
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(define (abs x)
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(if (< x 0)
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(- x)
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x))
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(assert (= (abs 12) 12))
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(assert (= (abs (- 32)) 32))
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(define (>= x y)
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(or (> x y)
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(= x y)))
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(assert (>= 2 2))
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(assert (>= 3 2))
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(assert (not (>= 1 2)))
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(assert (not (>= 12 44)))
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(define (>= x y)
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(not (< x y)))
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(assert (>= 2 2))
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(assert (>= 3 2))
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(assert (not (>= 1 2)))
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(assert (not (>= 12 44)))
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(define (a-plus-abs-b a b)
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((if (> b 0) + -) a b))
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(assert (= (a-plus-abs-b 1 2) 3))
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(assert (= (a-plus-abs-b 1 -2) 3))
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(define (square x) (* x x))
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(define (cube x) (* x x x))
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(assert (= ((lambda (x y z)
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(+ x y (square z)))
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1 2 3)
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12))
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;;; --------------------
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;;; newtons method
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;;; --------------------
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(define tolerance 0.001)
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(define (square x)
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(* x x))
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(define (average x y)
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(/ (+ x y) 2))
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(define (improve guess x)
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(average guess (/ x guess)))
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(define (good-enough? guess x)
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(< (abs (- (square guess) x)) tolerance))
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(define (sqrt-iter guess x)
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(if (good-enough? guess x)
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guess
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(sqrt-iter (improve guess x) x)))
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(define (sqrt x)
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(sqrt-iter 1.0 x))
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(define (sqrt2 x)
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(define (good-enough? guess x)
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(< (abs (- (square guess) x)) 0.001))
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(define (improve guess x)
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(average guess (/ x guess)))
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(define (sqrt-iter guess x)
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(if (good-enough? guess x)
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guess
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(sqrt-iter (improve guess x) x)))
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(sqrt-iter 1.0 x))
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(define (sqrt3 x)
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(define (good-enough? guess)
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(< (abs (- (square guess) x)) 0.001))
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(define (improve guess)
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(average guess (/ x guess)))
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(define (sqrt-iter guess)
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(if (good-enough? guess)
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guess
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(sqrt-iter (improve guess))))
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(sqrt-iter 1.0))
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(assert (< (abs (- 3 (sqrt 9))) tolerance))
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(assert (< (abs (- 4 (sqrt 16))) tolerance))
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(assert (not (< (abs (- 4 (sqrt 15))) tolerance)))
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(assert (< (abs (- 3 (sqrt2 9))) tolerance))
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(assert (< (abs (- 4 (sqrt2 16))) tolerance))
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(assert (not (< (abs (- 4 (sqrt2 15))) tolerance)))
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(assert (< (abs (- 3 (sqrt3 9))) tolerance))
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(assert (< (abs (- 4 (sqrt3 16))) tolerance))
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(assert (not (< (abs (- 4 (sqrt3 15))) tolerance)))
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;;; -----------------
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;;; factorial
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;;; -----------------
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(define (factorial n)
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(if (= n 1)
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1
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(* n (factorial (- n 1)))))
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(define (factorial2 n)
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(fact-iter 1 1 n))
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(define (fact-iter product counter max-count)
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(if (> counter max-count)
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product
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(fact-iter (* counter product) (+ counter 1) max-count)))
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(define (factorial3 n)
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(define (iter product counter)
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(if (> counter n)
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product
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(iter (* counter product) (+ counter 1))))
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(iter 1 1))
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(assert (= (factorial 6) 720))
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(assert (= (factorial2 6) 720))
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(assert (= (factorial3 6) 720))
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;;; ----------------
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;;; ackermann
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;;; ----------------
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(define (A m n)
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(cond ((= m 0) (+ n 1))
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((= n 0) (A (- m 1) 1))
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(t (A (- m 1) (A m (- n 1))))))
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(assert (= (A 0 0) 1))
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(assert (= (A 1 2) 4))
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(assert (= (A 3 1) 13))
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;;; ---------------
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;;; Fibonacci
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;;; ---------------
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(define (fib n)
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(cond ((= n 0) 0)
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((= n 1) 1)
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(t (+ (fib (- n 1)) (fib (- n 2))))))
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(define (fib2 n)
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(fib-iter 1 0 n))
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(define (fib-iter a b count)
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(if (= count 0)
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b
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(fib-iter (+ a b) a (- count 1))))
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(assert (= (fib 2) 1))
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(assert (= (fib 3) 2))
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(assert (= (fib 4) 3))
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(assert (= (fib 5) 5))
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(assert (= (fib 6) 8))
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(assert (= (fib2 2) 1))
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(assert (= (fib2 3) 2))
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(assert (= (fib2 4) 3))
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(assert (= (fib2 5) 5))
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(assert (= (fib2 6) 8))
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;;; ------------------
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;;; count change
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;;; ------------------
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;; (define (count-change amount)
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;; (define (cc amount kinds-of-coins)
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;; (cond ((= amount 0) 1)
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;; ((or (< amount 0) (= kinds-of-coins 0)) 0)
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;; (t (+ (cc amount (- kinds-of-coins 1))
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;; (cc (- amount (first-denomination kinds-of-coins)) kinds-of-coins)))))
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;; (define (first-denomination kinds-of-coins)
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;; (cond ((= kinds-of-coins 1) 1)
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;; ((= kinds-of-coins 2) 5)
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;; ((= kinds-of-coins 3) 10)
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;; ((= kinds-of-coins 4) 25)
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;; ((= kinds-of-coins 5) 50)))
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;; (cc amount 5))
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;; (assert (= (count-change 100) 292))
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;;; --------------------
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;;; exponentiation
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;;; --------------------
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(define (expt b n)
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(if (= n 0)
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1
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(* b (expt b (- n 1)))))
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(define (expt2 b n)
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(define (expt-iter b counter product)
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(if (= counter 0)
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product
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(expt-iter b (- counter 1) (* b product))))
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(expt-iter b n 1))
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(define (fast-expt b n)
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(define (even? n)
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(= (% n 2) 0))
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(cond ((= n 0) 1)
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((even? n) (square (fast-expt b (/ n 2))))
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(t (* b (fast-expt b (- n 1))))))
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(assert (= (expt 1 2) 1))
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(assert (= (expt 2 2) 4))
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(assert (= (expt 2 3) 8))
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(assert (= (expt2 1 2) 1))
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(assert (= (expt2 2 2) 4))
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(assert (= (expt2 2 3) 8))
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(assert (= (fast-expt 1 2) 1))
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(assert (= (fast-expt 2 2) 4))
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(assert (= (fast-expt 2 3) 8))
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;;; ----------
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;;; gcd
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;;; ----------
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(define (gcd a b)
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(if (= b 0)
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a
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(gcd b (% a b))))
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(assert (= (gcd 40 6) 2))
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(assert (= (gcd 13 4) 1))
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;;; ----------
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;;; primes
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;;; ----------
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(define (smallest-divisor n)
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(find-divisor n 2))
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(define (find-divisor n test-divisor)
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(cond ((> (square test-divisor) n) n)
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((divides? test-divisor n) test-divisor)
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(t (find-divisor n (+ test-divisor 1)))))
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(define (divides? a b)
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(= (% b a) 0))
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(define (prime? n)
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(= n (smallest-divisor n)))
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(assert (prime? 13))
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(assert (prime? 11))
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(assert (not (prime? 12)))
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;;; ----------------------
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;;; simple integral
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;;; ----------------------
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(define (sum term a next b)
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(if (> a b)
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0
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(+ (term a) (sum term (next a) next b))))
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(define (integral f a b dx)
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(define (add-dx x) (+ x dx))
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(* (sum f (+ a (/ dx 2.0)) add-dx b) dx))
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(define (pi-sum a b)
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(define (pi-term x) (/ 1.0 (* x (+ x 2))))
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(define (pi-next x) (+ x 4))
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(sum pi-term a pi-next b))
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(assert (< (abs (- (* 8 (pi-sum 1 100)) 3.121595)) 0.0001))
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(assert (< (abs (- (integral cube 0 1 0.02) 0.249950)) 0.0001))
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;; ------------------------------------------------------------
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;; F(x,y) = x(1 + xy)^2 + y(1 − y) + (1 + xy)(1 − y)
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;; ------------------------------------------------------------
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(define (f x y)
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(let ((a (+ 1 (* x y)))
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(b (- 1 y)))
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(+ (* x (square a))
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(* y b)
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(* a b))))
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(assert (= (f 0 0) 1))
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(assert (= (f 1 1) 4))
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;;; ---------------
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;;; find zero
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;;; ---------------
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(define (positive? x) (< 0 x))
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(define (negative? x) (< x 0))
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(define (search f neg-point pos-point)
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(let ((midpoint (average neg-point pos-point)))
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(if (close-enough? neg-point pos-point)
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midpoint
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(let ((test-value (f midpoint)))
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(cond ((positive? test-value) (search f neg-point midpoint))
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((negative? test-value) (search f midpoint pos-point))
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(t midpoint))))))
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(define (close-enough? x y) (< (abs (- x y)) 0.001))
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(assert (close-enough? (search (lambda (x) (- 1 (square x))) -3 3) -1))
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