Product of Array Except Self
描述
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].
Follow up:
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.)
分析
我们以一个4个元素的数组为例，nums=[a1,a2,a3,a4]，要想在O(n)的时间内输出结果，比较好的解决方法是提前构造好两个数组：
[1, a1, a1*a2, a1*a2*a3][a2*a3*a4, a3*a4, a4, 1]
然后两个数组一一对应相乘，即可得到最终结果 [a2*a3*a4, a1*a3*a4, a1*a2*a4, a1*a2*a3]。
不过，上述方法的空间复杂度为O(n)，可以进一步优化成常数空间，即用一个整数代替第二个数组。