Finding the product of each of the (n-1) subsets of a given array

Question

I'm sorry for deleting the original question, here it is: We have a bag or an array of n integers, we need to find the product of each of the (n-1) subsets. e.g:

S = {1, 0, 3, 6}
ps[1] = 0*3*6 = 0;
ps[2] = 1*3*6 = 18; etc.

After discussions, we need to take care of the three cases and they are illustrated in the following:

1. S is a set (contains one zero element)
  for i=1 to n
    if s[i]=0
      sp[i] = s[1] * s[2] * ...* s[i-1] * s[i+1] *.....*s[n]
    else
      sp[i] = 0;

2. S is a bag (contains more than one zero element) 
  for i=1 to n
      sp[i] = 0;

3. S is a set (contains no zero elements)
   product = 1
   for i=1 to n
     product *= s[i];
   for i=1 to n
     sp[i] = product / s[i];

Thanks.

Answer 1

If the set is very large, it may be convenient to:

• compute the product P of all the elements beforehand, and then
• for each element x, obtain a (n-1) product as P/x

If the set contains zero (i.e. P=0, x=0), you must deal with it as a special case.

EDIT. Here is a solution in Scheme, taking into account andand's answer. I'm a complete beginner - can someone help me improve the following code (make it more efficient, more readable, more lisp-ish)? (Feel free to edit my answer.)

#!/usr/bin/env guile !#
(use-modules (ice-9 pretty-print))

(define (count-zeros l)
    (cond ((null? l) 0)
          ((= 0 (car l)) (+ 1 (count-zeros (cdr l))))
          (else (count-zeros (cdr l)))))

(define (non-zero-product l)
    (define (non-zero-product-loop l product)
        (cond ((null? l) product)
              ((= 0 (car l)) (non-zero-product-loop (cdr l) product))
              (else (non-zero-product-loop (cdr l) (* (car l) product)))))
    (non-zero-product-loop l 1))

(define (n-1-products l)
    (let ((nzeros (count-zeros l)))
         (cond ((> nzeros 1)
                   (map (lambda (x) 0) l))
               ((= 1 nzeros)
                   (map (lambda (x) (if (= 0 x) (non-zero-product l) 0)) l))
               (else 
                   (map (lambda (x) (/ (non-zero-product l) x)) l)))))

(pretty-print (n-1-products '(1 2 3 4 5)))
(pretty-print (n-1-products '(0 1 2 3 4)))
(pretty-print (n-1-products '(0 1 2 3 0)))