Work transfer
This commit is contained in:
Felix Brendel
+348
-340
@@ -1,340 +1,348 @@
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;; (define (abs x)
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;; (cond ((< x 0) (- x))
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;; (else 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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(else (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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;; (else (+ (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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;; (else (+ (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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;; (else (* 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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;; (else (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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;; (else 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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;; (define (abs x)
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;; (cond ((< x 0) (- x))
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;; (else x)))
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;; (assert (= (abs 1) 1))
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;; (assert (= (abs (- 2)) 2))
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|
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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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|
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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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|
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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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|
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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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|
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;; (define tolerance 0.001)
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|
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;; (define (square x)
|
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;; (* x x))
|
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|
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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)))
|
||||
|
||||
;; (define (good-enough? guess x)
|
||||
;; (< (abs (- (square guess) x)) tolerance))
|
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|
||||
;; (define (sqrt-iter guess x)
|
||||
;; (if (good-enough? guess x)
|
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;; 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))))))
|
||||
|
||||
;; (define (A m n)
|
||||
;; (if (= m 0)
|
||||
;; (+ n 1)
|
||||
;; (if (= n 0)
|
||||
;; (A (- m 1) 1)
|
||||
;; (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))
|
||||
|
||||
Reference in New Issue
Block a user