Scheme中的笛卡尔积 [英] Cartesian product in Scheme

问题描述

我一直在尝试做一个返回 n 个集合的笛卡尔积的函数，在 Scheme 博士中，这些集合以列表的形式给出，我一整天都被困在这个问题上，我想要一些从哪里开始的指南.

I've been trying to do a function that returns the Cartesian Product of n sets,in Dr Scheme,the sets are given as a list of lists,I've been stuck at this all day,I would like a few guidelines as where to start.

----后期编辑-----

----LATER EDIT -----

这是我想出的解决方案，我确信它不是迄今为止最有效或最简洁的，但我只学习了 3 周的 Scheme，所以请对我放轻松.

Here is the solution I came up with,I'm sure that it's not by far the most efficent or neat but I'm only studing Scheme for 3 weeks so be easy on me.

推荐答案

  ;returs a list wich looks like ((nr l[0]) (nr l[1])......)
  (define cart-1(λ(l nr)
      (if (null? l) 
             l 
             (append (list (list nr (car l))) (cart-1 (cdr l) nr)))))

;Cartesian product for 2 lists
(define cart-2(λ(l1 l2)
                (if(null? l2) 
             '() 
             (append (cart-1 l1 (car l2)) (cart-2 l1 (cdr l2))))))

 ;flattens a list containg sublists
(define flatten
(λ(from)
 (cond [(null? from) from]
      [(list? (car from)) (append (flatten (car from)) (flatten (cdr from)))]
      [else (cons (car from) (flatten (cdr from)))])}) 

;applys flatten to every element of l
(define flat
(λ(l)
(if(null? l)
l
(cons (flatten (car l)) (flat (cdr l))))))

;computes Cartesian product for a list of lists by applying cart-2
(define cart
(lambda (liste aux)
 (if (null? liste)
  aux
  (cart (cdr liste) (cart-2 (car liste) aux)))))


(define (cart-n l) (flat (cart (cdr l ) (car l))))

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