yao2030

(define (last-pair list1)
  (if (= (length list1) 1)
      (car list1)
      (last-pair (cdr list1))))
(define (but-last list1)
  (if (= (length list1) 1)
      '()
      (cons (car list1) (but-last (cdr list1)))))
(define (reverse x)
  (if (null? x)

yao2030

(define (same-parity a . b)
  (let ((test (if (even? a)
		  even?
		  odd?)))
    (cons a (parity a test b))))
(define (parity a test  b)
  (cond ((and (not (null? b))(test (car b))) (cons (car b) (parity a test  (cdr b) )))
	((null? b) '())
	(else (parity a test (cdr b) ))))

yao2030

(define (pascal row col)
	(cond ((= col 0) 1)
	      ((= col row) 1)
	      ((< row col) 0)
	      (else (+ (pascal (- row 1) (- col 1))
	         (pascal  (- row 1) col)))))

yao2030

;; Exercise 1.39
;; sicp
(define (tan-cf x k)
  (define (n i)
    (if (= i 1)
	x
	(square x)))
  (define (d i)
    (- (* 2 i) 1))
  (define (cont-frac n d k)

yao2030

(define (d x)
	(if (= (remainder x 3) 2)
	    (* 2 (+ (quotient x 3) 1))
	    1))
;; exercise 1.38, sicp

yao2030

(define (cont-frac n d k)
  (define (cont-help i result)
    (if (= i 0)
	 result
	(cont-help (- i 1) (/ (n i) (+ (d i) result)))))
  (cont-help k 0.0))

(cont-frac (lambda (i) 1.0) (lambda (i) 1.0) 100)
;; A so-called k-term finite continued fraction
;; gives the value of the gold ratio

yao2030

(define (cont-frac n d k)
  (define (cont-help i result)
    (if (= i k)
	(/ 1.0 result)
	(cont-help (+ i 1) (/ (n i) (+ (d i) result)))))
  (cont-help 1 0.0))

(cont-frac (lambda (i) 1.0) (lambda (i) 1.0) 100)
;; A so-called k-term finite continued fraction
;; gives the value of the gold ratio

yao2030

(define (filtered-accumulate combiner null-value term a next b predicate)
  (if (> a b)
      null-value
      (combiner (if (predicate (term a))
		    (term a)
		    null-value)
		(filtered-accumulate combiner null-value term (next a) next b predicate))))
		    

yao2030

(define (pi n)
	(define (p-term x)
	  (if (even? x)
	      (/ x (- x 1))
	      (/ (- x 1) x)))
	(define (p-next x)
	      (+ x 1))
	(* 4.0 (product p-term 3 p-next n)))

yao2030

(define (integral f a b n)
	(define h (/ (- b a) n))
	(define (i-next x) (+ x 1))
	(define (i-term x)
	(cond ((or (= x 0) (= x n)) (f (+ a (* x h))))
	      ((even? x) (* 2 (f (+ a (* x h)))))
	      (else (* 4 (f (+ a (* x h)))))))
	(* (/ h 3) (sum i-term 0 i-next n)))