sicp第一章部分习题解答

(begin
    (load "util.scm")
    ;ex 1.16 计算b的幂
    (define (_expt product b n maxn)
        (if (= n maxn) product
         (if (<= (* n n) maxn) (_expt (* product product) b (+ n n) maxn)
          (_expt (* product b) b (+ n 1) maxn))))
    (define (fast-expt b n)
        (if (<= n 0) 1
            (_expt b b 1 n)))
    ;ex 1.11
    (define (ex1-f n)
        (cond ((< n 3) n)
            (else
                (+ (ex1-f (- n 1)) (* 2 (ex1-f (- n 2))) (* 3 (ex1-f (- n 3)))))))            
    (define (expmod base exp m)
      (cond ((= exp 0) 1)
            ((even? exp)
             (remainder (square (expmod base (/ exp 2) m))
                        m))
            (else
             (remainder (* base (expmod base (- exp 1) m))
                        m))))        
;    (define (expmod base exp m)
;        (remainder (fast-expt base exp) m))
    (define (fermat-test n)
      (define (try-it a)
        (= (expmod a n n) a))
      (try-it (+ 1 (random (- n 1)))))

    (define (fast-prime? n times)
      (cond ((= times 0) true)
            ((fermat-test n) (fast-prime? n (- times 1)))
            (else false)))
;    (define (sum term a next b)
;      (if (> a b)
;          0
;          (+ (term a)
;             (sum term (next a) next b))))
    ;ex 1.30
    (define (sum term a next b)
        (define (iter a result)
            (if (> a b)
                result
                (iter (next a) (+ (term a) result))))
        (iter a 0))
    ;ex 1.31    
    (define (product term a next b)
        (define (iter a result)
            (if (> a b)
                result
                (iter (next a) (* (term a) result))))
        (iter a 1))
    ;ex 1.32    
    (define (accumulate1 combiner null-value term a next b)
        (define (iter a result)
            (if (> a b)
                result
                (iter (next a) (combiner (term a) result))))
        (iter a null-value))
    ;ex 1.33
    (define (filtered-accumulate filter combiner null-value term a next b)
        (define (iter a result)
            (if (> a b)
                result
                (if (filter a)
                    (iter (next a) (combiner (term a) result))
                    (iter (next a) result))))
        (iter a null-value))        

    (define (inc n) (+ n 1))
    (define (cube x) (* x x x))
    (define (sum-cubes a b)
      (sum cube a inc b))

    (define (identity x) x)
    (define (sum-integers a b)
      (accumulate1 + 0 identity a inc b))
    (define (product-integers a b)
      (accumulate1 * 1 identity a inc b))

    (define (sum-integers-even a b)
      (filtered-accumulate even? + 0 identity a inc b))
    (define (product-integers-even a b)
      (filtered-accumulate even? * 1 identity a inc b))      
;    (define (sum-integers a b)
;      (sum identity a inc b))
;    (define (product-integers a b)
;      (product identity a inc b))      
)