Product of Array Except Self问题及解法

问题描述：

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).

示例

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.)
问题分析：

对于第i个元素，我们考虑把前i - 1项的积sum1[i]和后n - i 项的积sum2[i]先算出来，则output[i] = sum1 * sum2.

过程详见代码：

class Solution {
public:
vector<int> productExceptSelf(vector<int>& nums) {
vector<int> res = nums;
int sum = res[0];
nums[0] = 1;
for (int i = 1; i < res.size(); i++)
{
nums[i] = sum;
sum *= res[i];
}
sum = 1;
int t;
for (int i = res.size() - 1; i >= 0;i--)
{
t = sum;
sum *= res[i];
res[i] = nums[i] * t;
}
return res;
}
};