首页 > 代码库 > SICP_3.27
SICP_3.27
1 (define false #f) 2 (define true #t) 3 4 (define (make-table) 5 (let ((local-table (list ‘*table*))) 6 7 (define (assoc key records) 8 (cond ((null? records) false) 9 ((equal? (caar records) key) (car records)) 10 (else (assoc key (cdr records))))) 11 12 (define (lookup keys) 13 (define (lookup-helper keys table) 14 (let ((subtable (assoc (car keys) (cdr table)))) 15 (if subtable 16 (if (null? (cdr keys)) 17 (cdr subtable) 18 (lookup-helper (cdr keys) subtable)) 19 false))) 20 (lookup-helper keys local-table)) 21 22 (define (insert! keys value) 23 (define (insert-helper! keys table) 24 (if (null? table) 25 (if (null? (cdr keys)) 26 (cons (car keys) value) 27 (list (car keys) (insert-helper! (cdr keys) ‘()))) 28 (let ((sub (assoc (car keys) (cdr table)))) 29 (if sub 30 (if (null? (cdr keys)) 31 (set-cdr! sub value) 32 (insert-helper! (cdr keys) sub)) 33 (if (null? (cdr keys)) 34 (set-cdr! table (cons (cons (car keys) value) (cdr table))) 35 (set-cdr! table (cons 36 (list (car keys)(insert-helper! (cdr keys) ‘())) 37 ;;可以直接用(insert-helper! keys ‘()) 38 (cdr table)))))))) 39 (insert-helper! keys local-table) 40 ‘ok) 41 42 (define (dispatch m) 43 (cond ((eq? m ‘lookup-proc) lookup) 44 ((eq? m ‘insert-proc) insert!) 45 (else (error "Unknow operation --TABLE" m)))) 46 47 dispatch)) 48 49 (define (lookup x table) 50 (let ((keys (list x))) 51 ((table ‘lookup-proc) keys))) 52 53 (define (insert! x result table) 54 (let ((keys (list x))) 55 ((table ‘insert-proc) keys result))) 56 57 ;;;;;;;;;;;;;;;;;;;;;;;;;;;; 58 59 (define (memoize f) 60 (let ((table (make-table))) 61 (lambda (x) 62 (let ((previously-computed-result (lookup x table))) 63 (or previously-computed-result 64 (let ((result (f x))) 65 (insert! x result table) 66 result)))))) 67 68 69 (define memo-fib 70 (memoize (lambda (n) 71 (cond ((= n 0) 0) 72 ((= n 1) 1) 73 (else (+ (memo-fib (- n 1)) 74 (memo-fib (- n 2)))))))) 75 76 77 (memo-fib 0)
简单的定义为
(memoize fib)
能工作,但这样并没有意义,因为这样定义在处理 fib(n-2)和fib(n-1)时就是普通fib函数了
步数:
在计算fib(n)时 需要fib(n-1)和fib(n-2)而fib(n-1)的值需要fib(n-2)的值,如使用记忆法,则fib(n-2),fib(n-3)已事先存在表中。所以事先
要计算fib(n-2),一直到达n=0 和 n=1时整个表都被填满,总的来看就是求一遍fib(2)到fib(n-1)所以需要O(n)步来计算fib(n)。
SICP_3.27
声明:以上内容来自用户投稿及互联网公开渠道收集整理发布,本网站不拥有所有权,未作人工编辑处理,也不承担相关法律责任,若内容有误或涉及侵权可进行投诉: 投诉/举报 工作人员会在5个工作日内联系你,一经查实,本站将立刻删除涉嫌侵权内容。