2.41

练习 2.41 请写出一个过程，它能产生出所有小于等于给定整数n的正的相异整数i、j和k的有序三元组，使每个三元组的三个元之和等于给定的整数s。

首先，定义 accumulate

(define (accumulate op initial sequence)
    (if (null? sequence)
        initial
        (op (car sequence)
            (accumulate op initial (cdr sequence))) 
    )
)

然后，定义 flatmap

(define (flatmap proc seq)
    (accumulate append '()  (map proc seq)))

(define (enumerate-interval low high)
    (if (> low high)
        '()
        (cons low (enumerate-interval (+ low 1) high))))


(define (pairs n)
    (define interval (enumerate-interval 1 n))
    (flatmap  
        (lambda (x) 
            (filter 
                (lambda (lst) (< (car lst) (cadr lst)))
                (map 
                    (lambda (y) (list x y)) 
                    (remove x interval))))
        interval))



(pairs 10)

(define (make-pair-sum pair)
    (list (car pair) (cadr pair) (+ (car pair) (cadr pair))))

(define (s-sum-pairs n s)
    (map 
        make-pair-sum 
        (filter 
            (lambda (pair) (= (+ (car pair) (cadr pair)) s))
            (pairs n)))
)

(s-sum-pairs 10 11)