SICP第二章40~42题解答

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;2.40;flatmap中的proc应该是给定元素x，能做出多个含x的序对序列的过程(define (flatmap proc seq) (accumulate append '() (map proc seq)))(define (enumerate-interval low high) (if (> low high) '() (cons low (enumerate-interval (+ low 1) high))));(enumerate-interval 1 10)(define (unique-pairs n) (flatmap (lambda (i) (map (lambda (j) (list i j)) (enumerate-interval 1 (- i 1)))) (enumerate-interval 2 n)));(unique-pairs 6)(define (prime-sum? pair) (prime? (+ (car pair) (cadr pair))))(define (make-pair-sum pair) (list (car pair) (cadr pair) (+ (car pair) (cadr pair))))(define (prime-sum-pairs n) (map make-pair-sum (filter prime-sum? (unique-pairs n))));(prime-sum-pairs 10);2.41(define (is-elem-of e set) (cond ((null? set) false) ((= e (car set)) true) (else (is-elem-of e (cdr set)))));(is-elem-of 5 (list 2 6 6))(define (diff seqa seqb) (accumulate (lambda (a res-list) (if (is-elem-of a seqb) res-list (cons a res-list))) '() seqa));(diff (list 1 2 3 4) '(1 3))(define (expand-seq iter n seqs) (define (ex-seq seq) (map (lambda (t) (append seq (list t))) (diff (enumerate-interval 1 n) seq))) (let ((xseqs (flatmap ex-seq seqs))) (if (<= iter 0) seqs (expand-seq (- iter 1) n xseqs))));(expand-seq 3 10 (list '()));;2.42;采用一维表示法来表示八皇后的解，例如 (3 7 2 8 5 1 4 6)代表一个解，其中的数字是row number，列是隐藏的按顺序排列的。(define (safe? k positions) ;直接看positions第k项（其实就是最后一项）与前面的几个皇后是否冲突 (define (get-kthelem k positions) (if (> k 1) (get-kthelem (- k 1) (cdr positions)) (car positions)) ) (if (< k 2) true (let ( (kelem (get-kthelem k positions)) (elem (car positions))) ;检查elem和第k项在直线上是否有冲突，检查在两条对角线上是否有冲突，发现冲突直接返回false (if (or (= elem kelem) (= (- elem (- k 1)) kelem) (= (+ elem (- k 1)) kelem)) false (safe? (- k 1) (cdr positions))))));(safe? 4 (list 3 7 2 8));在第row行col列放置一个皇后(define (adjoin-position row col positions) ;col是隐藏的 (append positions (list row)));(adjoin-position 5 6 (list 3 6 7 8 2))(define (queens board-size) (define (queen-cols k) ;queen-cols返回前k列所有合法的格局 (if (= k 0) (list '()) (filter (lambda (positions) (safe? k positions)) (flatmap (lambda (rest-of-queens) (map (lambda (new-row) (adjoin-position new-row k rest-of-queens)) (enumerate-interval 1 board-size))) (queen-cols (- k 1)))))) (queen-cols board-size))(queens 8)