beautiful method for an interview question

Given an array of numbers, nums, return an array of numbers products, where products is the product of all nums[j], j != i.

Input : [1, 2, 3, 4, 5]Output: [(2*3*4*5), (1*3*4*5), (1*2*4*5), (1*2*3*5), (1*2*3*4)]      = [120, 60, 40, 30, 24]

You must do this in O(N) without using division.

We can solve this question by O(n) time and O(n) space, or O(n) time and O(1)space by traversing the array two times.

Or

We can sovle in a recursive method.

code: https://gist.github.com/sing1ee/5175441

perl, but easy to understand.