Scheme (6)

By freeuniverser

It is very convenient to use Scheme to write a numerical computation program. Functional language is an excellent tool for playing mathematical computation. It can solve many mathematical problems by definition. This is very flexible for coder.

For example, define a function.F (n), when n <3, f (n) = n; when n> = 3, f (n) = f (n-1) + 2f (n-2) + 3f (n-3). Therefore:

UseRecursionMethod:

1 (define (f n)2 3   (cond ((< n 3) n)4 5            ((>= n 3)6 7            (+ (f (- n 1)) (* 2 (f (- n 2)))8 9                (* 3 (f (- n 3)))))))

UseIterationMethod:

 1 (define (f n) 2  3    (define (f0 a b c count) 4  5       (if (= count 0) 6  7          c 8  9          (f0 (+ a (* 2 b) (* 3 c)) a b (- count 1))))10 11     (f0 2 1 0 n))

In this example, we can see thatRecursionRelatively clear, but its efficiency is not the latterIterationThe two ideas complement each other.

Next, let's take a look at the interesting classic questions:Fibonacci numbers

1 ;fibonacci numbers by recursion2 3 (define (fib n)4 5    (cond ((= n 0) 0)6 7             ((= n 1) 1)8 9             (else (+ (fib (- n 1)) (fib (- n 2))))))

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 1 ;fibonacci numbers by iteration 2  3 (define (fib n) 4  5    (define (fib-iter a b count) 6  7       (if (= count 0) 8  9             b10 11             (fib-iter (+ a b) a (- count 1))))12 13   (fib-iter 1 0 n))

The following method is used to calculate ononacci In the logarithm step:

 1 (define (fib n) 2   (define (square n) (* n n)) 3   (define (fib-iter a b p q count) 4     (cond ((= count 0) b) 5           ((even? count) 6            (fib-iter a 7                      b 8                      (+ (square p) (square q)) 9                      (+ (* 2 p q) (square q))10                      (/ count 2)))11            (else (fib-iter (+ (* b q) (* a q) (* a p))12                            (+ (* b p) (* a q))13                            p14                            q15                            (- count 1)))))16     (fib-iter 1 0 0 1 n))

ComputingFactorialIt is also convenient to use Scheme:

1 ;factorial by recursion2 3 (define (factorial n)4 5     (if (= n 1)6 7         18 9         (* n (factorial (- n 1)))))

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 1 ;factorial by iteration 2  3 (define (factorial n) 4  5      (define (iter product counter) 6  7         (if (> counter n) 8  9               product10 11               (iter (* product counter)12 13                       (+ counter 1))))14 15     (iter 1 1))

NextPascal triangle:

1 (define (pascal-triangle a b)2 3      (cond ((= a b) 1)4 5               ((= b 0) 1)6 7               (else (+ (pascal-triangle (- a 1) (- b 1))8 9                           (pascal-triangle (- a 1) b)))))

The computing power of Scheme is not small. Its syntax is clear and elegant ~