SICP_2.33-2.39

  1 #lang racket
  2 
  3 ;;;;;;;;;;;;;;;;;;;;;;;;;;;2.33
  4 (define (accumulate op initial sequence)
  5   (if (null? sequence)
  6       initial
  7       (op (car sequence)
  8           (accumulate op initial (cdr sequence)))))
  9 
 10 (define (my-map p sequence)
 11   (accumulate (lambda (x y)
 12                 (cons (p x) y)) '() sequence))
 13 
 14 (define (my-append seq1 seq2)
 15   (accumulate cons seq2 seq1))
 16 
 17 (define (my-length sequence)
 18   (accumulate (lambda (x y) (+ 1 y)) 0 sequence))
 19 
 20 ;;;;;;;;;;;;test
 21 (my-map (lambda (x) (* x x)) (list 1 2 3))
 22 
 23 (my-append (list 1 2 3) (list 4 5 6))
 24 
 25 (my-length (list 1 2 3 4 5))
 26 
 27 ;;;;;;;;;;;;;;;;;;;;;;;;;2.34
 28 (define (horner-eval x coefficient-sequence)
 29   (accumulate (lambda (this-coeff higher-terms)
 30                 (+ this-coeff (* x higher-terms)))
 31               0
 32               coefficient-sequence))
 33 
 34 ;;;;;;;;;;test
 35 (horner-eval 2 (list 1 3 0 5 0 1))
 36 
 37 ;;;;;;;;;;;;;;;;;;;;;;;;2.35
 38 (define (count-leaves tree)
 39   (accumulate + 0 (map (lambda (node)
 40                          (if (pair? node)
 41                              (count-leaves node)
 42                              1))
 43                        tree)))
 44 
 45 ;;;;;;;;;;;;test
 46 (count-leaves (list '(1 2 3) '(2 3 4) 4 5))
 47 
 48 ;;;;;;;;;;;;;;;;;;;;2.36
 49 (define (accumulate-n op init seqs)
 50   (if (null? (car seqs))
 51       '()
 52       (cons (accumulate op init (map car seqs))
 53             (accumulate-n op init (map cdr seqs)))))
 54 
 55 ;;;;;;;;;;;;test
 56 (define seqs (list '(1 2 3) '(4 5 6) '(7 8 9) '(10 11 12)))
 57 (accumulate-n + 0 seqs)
 58 
 59 ;;;;;;;;;;;;;;;;;;;;2.37
 60 (define (dot-product v1 v2)
 61   (accumulate + 0 (map * v1 v2)))
 62 
 63 (define (matrix-*-vector m v)
 64   (map (lambda (x) (dot-product x v)) m))
 65 
 66 (define (matrix-*-matrix m n)
 67   (let ((n-cols (transpose n)))
 68     (map (lambda (m-row)
 69            (map (lambda (n-col)
 70                   (dot-product m-row n-col))
 71                 n-cols))
 72          m)))
 73 
 74 (define (transpose mat)
 75   (accumulate-n cons '() mat))
 76 
 77 (define matrix1 (list '(1 2 3) '(1 9 3) '(1 3 4)))
 78 (define matrix2 (list '(1 3 4) '(3 4 5) '(6 2 4)))
 79 ;;;;;;;;;;;;test
 80 (dot-product (list 1 1 1) (list 1 2 3))
 81 (matrix-*-vector (list '(1 2 3) '(1 2 3) '(1 3 3)) '(2 3 4))
 82 (matrix-*-matrix matrix1 matrix2)
 83 
 84 ;;;;;;;;;;;;;;;;;;;2.38
 85 
 86 (define (fold-left op initial sequence)
 87   (define (iter result rest)
 88     (if (null? rest)
 89         result
 90         (iter (op result (car rest))
 91               (cdr rest))))
 92   (iter initial sequence))
 93 
 94 (define (fold-right op initial sequence)
 95   (accumulate op initial sequence))
 96 
 97 ;;;;;;;;;;;;;;;test
 98 (fold-right / 1 (list 1 2 3))
 99 (fold-left / 1 (list 1 2 3))
100 (fold-right list '() (list 1 2 3))
101 (fold-left list '() (list 1 2 3))
102 ;;;;;;;;;;;用cons或list这些将产生不同结果
103 ;;;;;;;;;;;要使用那些在操作数互换位置后意义相同的。
104 
105 ;;;;;;;;;;;;;;;;;;2.39
106 
107 (define (reverse1 sequence)
108   (fold-right (lambda (x y)
109                 (append y (list x))) '() sequence))
110 
111 (define (reverse2 sequence)
112   (fold-left (lambda (x y)
113                (append (list y) x)) '() sequence))
114 
115 ;;;;;;;;;;;;test
116 (reverse1 (list 1 2 3 4 6 8 9))
117 (reverse2 (list 1 2 3 4 7 8 5))

终于会一点了

 

需要复习线性代数了，感觉白学了！

转载于:https://www.cnblogs.com/tclan126/p/6411812.html