product of array except self

Given an array of n integers where n > 1, nums, return an array output such that output[i] is equal to the product of all the elements of nums except nums[i].

Solve it without division and in O(n).

For example, given [1,2,3,4], return [24,12,8,6].

Write a function to compute the next state (after one update) of the board given its current state.

Could you solve it with constant space complexity? (Note: The output array does not count as extra space for the purpose of space complexity analysis.)

这题主要是要求不使用除法，Time O(n)（必须）和 Space O(1) （建议），联想到之前求前缀和的题，这道题也可以用左右扫描的处理方式，核心思想是res[i] = mul(i-1) * mul(i+1)。