kouddy

> (f 1)
1
> (f 2)
2
> (f 3)
4
> (f 4)
11
> (f 5)
25

kouddy

(define (f-iter n)
  (f-iter-aux 2 1 0 n))

(define (f-iter-aux a b c n)
  (if (= 0 n)
      c
      (f-iter-aux (+ a (* 2 b) (* 3 c))
                  a
                  b
                  (- n 1))))

kouddy

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

kouddy

;;;(sine 12.15)
(sine 12.15)
(p (sine 4.05))
(p (p (sine 1.35)))
(p (p (p (sine 0.45))))
(p (p (p (p (sine 0.15)))))
(p (p (p (p (p (sine 0.05))))))
(p (p (p (p (p 0.05)))))

kouddy

(define (square x) (* x x))

(define (even? n)
  (= (remainder n 2) 0))

(define (fast-expt b n)
  (fast-expt-iter 1 b n))

(define (fast-expt-iter a b n)
  (cond ((= n 0) a)

kouddy

(define (double a) (* a 2))

(define (halve a) (/ a 2))

(define (even? n) (= (remainder n 2) 0))

(define (fast-mult a b )
  (fast-mult-iter 0 a b))

(define (fast-mult-iter a b n)

kouddy

;;; (fast-mult 3 15)
(fast-mult-iter 0 3 15)
(fast-mult-iter 3 3 14)
(fast-mult-iter 3 6 7)
(fast-mult-iter 9 6 6)
(fast-mult-iter 9 12 3)
(fast-mult-iter 21 12 2)
(fast-mult-iter 21 24 1)
(fast-mult-iter 45 24 0)
45

kouddy

;;;(fast-expt 2 7)
(* 2 (fast-expt 2 6))
(* 2 (square (fast-expt 2 3)))
(* 2 (square (* 2 (fast-expt 2 2))))
(* 2 (square (* 2 (square (fast-expt 2 1)))))
(* 2 (square (* 2 (square (* 2 (fast-expt 2 0))))))
(* 2 (square (* 2 (square (* 2 1))))
(* 2 (square (* 2 (square 2))))
(* 2 (square (* 2 4)))
(* 2 (square 8))

kouddy

;;;(fast-mult 2 7)
(+ 2 (fast-mult 2 6))
(+ 2 (* 2 (fast-mult 2 3)))
(+ 2 (* 2 (+ 2 (fast-mult 2 2))))
(+ 2 (* 2 (+ 2 (* 2 (fast-mult 2 1)))))
(+ 2 (* 2 (+ 2 (* 2 (+ 2 (fast-mult 2 0))))))
(+ 2 (* 2 (+ 2 (* 2 (+ 2 0)))))
(+ 2 (* 2 (+ 2 (* 2 2))))
(+ 2 (* 2 (+ 2 4)))
(+ 2 (* 2 6))

kouddy

(define (double n) (* n 2))
(define (halve n) (/ n 2))
(define (even? n) (= (remainder n 2) 0))

(define (fast-mult a b)
  (cond ((= b 0) 0)
        ((even? b) (double (fast-mult a (halve b))))
        (else (+ a (fast-mult a (- b 1))))))