# 4. Array products

This problem was asked by Uber.

Given an array of integers, return a new array such that each element at index `i` of the new array is the product of all the numbers in the original array except the one at `i`.

For example, if our input was `[1, 2, 3, 4, 5]`, the expected output would be `[120, 60, 40, 30, 24]`. If our input was `[3, 2, 1]`, the expected output would be `[2, 3, 6]`.

Follow-up: what if you can't use division?

假設ary長度為n, 且被拆成左右兩部分

```python
def products(ary):
  result = []
  for i in range(len(ary)): # n
    ary1 = ary[0:i] # O(1)
    ary2 = ary[i+1:len(ary)] # O(1)
    p1 = p2 = 1
    for j in range(len(ary1)): # x
      p1 *= ary1[j] # O(1)
    for j in range(len(ary2)): # y
      p2 *= ary2[j] # O(1)
    result.append(p1*p2)
  return result
```

T = n \*\[ O(1) + O(1) + (O(x) + O(y)) ] # x+ y = n - 1