Racket 基本的数学运算
纯函数式编程语言不能用循环，一切这种结构都要改作递归实现
1.平方根（牛顿切线法）
Racket
x
13
13
1
#lang racket2
(define (sqrt x)3
(define (good-enough? a b) (< (abs (- (* a a) b)) 0.00001))4
(define (improve a b) (average a (/ b a)))5
(define (average a b) ( / (+ a b) 2))6
(define (_sqrt guess x)7
(if (good-enough? guess x)8
guess9
(_sqrt (improve guess x) x)10
))11
(_sqrt 1.0 x)12
)13
2. 判断质数
Racket
1
17
17
1
#lang racket2
(define (isPrime x)3
(define (_isPrime idx x)4
(define (<= a b) (or (< a b) (= a b)))5
(define (inRange? j i) (<= (* j j) i))6
(if (inRange? idx x)7
(if (= (remainder x idx) 0)8
#f9
(_isPrime (+ idx 1) x)10
)11
#t12
)13
)14
(if (< x 2)15
#f16
(_isPrime 2 x))17
)3. 求平方根（二分法）
Racket
1
22
22
1
#lang racket2
(define (sqrt x)3
(define (good-enough? lwbd upbd)4
(let ((epsilon 0.00001))5
(< (abs (- upbd lwbd)) epsilon)6
)7
)8
(define (f x) (* x x))9
(define (_sqrt lwbd upbd x)10
(let ((m (/ (+ lwbd upbd) 2)))11
(if (good-enough? upbd lwbd)12
m13
(if (> (* (- (f lwbd) x) (- (f m) x) ) 0)14
(_sqrt m upbd x)15
(_sqrt lwbd m x)16
)17
)18
)19
)20
(_sqrt 0.0 x x)21
)22
4.分数的四则运算
Racket
1
52
52
1
#lang racket2
(define (make-rat a b)3
(let ((_a (abs a))4
(_b (abs b))5
)6
(let ((_g (gcd _a _b)))7
(if (< (* a b) 0)8
(cons (- (/ _a _g)) (/ _b _g))9
(cons (/ _a _g) (/ _b _g))))10
)11
)12
(define (numer f) (car f))13
(define (denom f) (cdr f))14
(define (output-rat s)15
(display (numer s))16
(display "/")17
(display (denom s))18
)19
(define (gcd x y)20
(if (= (remainder x y) 0)21
y22
(gcd y (remainder x y))))23
(define (add-rat a b)24
(let ((_n (+ (* (numer a) (denom b)) (* (numer b) (denom a))))25
(_d (* (denom a) (denom b)) ))26
(make-rat _n _d))27
)28
(define (sub-rat a b)29
(define (neg x) (make-rat (- (numer x)) (denom x)))30
(add-rat a (neg b))31
)32
(define (mul-rat a b)33
(let ((_n (* (numer a) (numer b)))34
(_d (* (denom a) (denom b)))35
)36
(make-rat _n _d)37
)38
)39
(define (div-rat a b)40
(define (reci x)41
(make-rat (denom x) (numer x)))42
(mul-rat a (reci b))43
)44
(output-rat (add-rat (make-rat 3 5) (make-rat 1 2)))45
(newline)46
(output-rat (sub-rat (make-rat 4 5) (make-rat 1 7)))47
(newline)48
(output-rat (mul-rat (make-rat 2 5) (make-rat 1 2)))49
(newline)50
(output-rat (div-rat (make-rat 1 7) (make-rat 1 3)))51
(newline)52
5.对list的map和变长参数的imap
Scheme
1
8
1
(define (map f h)2
(if (null? h)3
null4
(cons (f (car h)) (map f (cdr h)))5
))6
(define (imap f . h)7
(map f h)8
)