# Question

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

Example:

Input:  [1,2,3,4]
Output: [24,12,8,6]


Note: Please solve it without division and in O(n).

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

# Solution

We can do this in two parts. The first part is to get the multiplication for all numbers left to position i. This can be done left to right by multiplying the value at position i-1 with nums[i-1]. The second part is to get the multiplication for all numbers right to position i. This can be done right to left.

class Solution(object):
def productExceptSelf(self, nums):
"""
:type nums: List[int]
:rtype: List[int]
"""
res = list()
res.append(1)

for i in range(1, len(nums)):
res.append(res[-1] * nums[i - 1])

right = 1
for i in range(len(nums) - 1, -1, -1):
res[i] *= right
right *= nums[i]

return res