如何在DrRacket中进行电源设置?

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我正在使用带有DrRacket列表缩写的开始语言，并且想递归地创建一个Powerset，但无法弄清楚该怎么做.我目前有这么多

I'm using the beginning language with list abbreviations for DrRacket and want to make a powerset recursively but cannot figure out how to do it. I currently have this much

(define (powerset aL) (cond [(empty? aL) (list)]

任何帮助都会很好.

推荐答案

What's in a powerset? A set's subsets! An empty set is any set's subset, so powerset of empty set's not empty. Its (only) element it is an empty set:

(define (powerset aL) (cond [(empty? aL) (list empty)] [else

As for non-empty sets, there is a choice, for each set's element, whether to be or not to be included in subset which is a member of a powerset. We thus include both choices when combining first element with smaller powerset, that, which we get recursively applying the same procedure to the rest of input:

(combine (first aL) (powerset (rest aL)))])) (define (combine a r) ; `r` for Recursive Result (cond [(empty? r) empty] ; nothing to combine `a` with [else (cons (cons a (first r)) ; Both add `a` and (cons (first r) ; don't add, to first subset in `r` (combine ; and do the same a ; with (rest r))))])) ; the rest of `r`

"There are no answers, only choices". Rather, the choices made, are what the answer's made of.