Product of Array Except Self

Problem Source: Leetcode

Problem Description

Given an integer array nums, return an array answer such that answer[i] is equal to the product of all the elements of nums except nums[i].

The product of any prefix or suffix of nums is guaranteed to fit in a 32-bit integer.

You must write an algorithm that runs in O(n) time and without using the division operation.

Can you solve the problem in O(1) extra space complexity? (The output array does not count as extra space for space complexity analysis.)

tests

def test(fn):
    nums = [1,2,3,4]
    expected =  [24,12,8,6]
    actual = fn(nums)
    assert actual == expected

    nums = [-1,1,0,-3,3] 
    expected = [0,0,9,0,0]
    actual = fn(nums)
    assert actual == expected

Solution

• Time Complexity: O(n)
• Space Complexity: O(1)

from typing import List
def productExceptSelf(nums: List[int]) -> List[int]:
    prefix, postfix = 1,1
    out = [1] * len(nums)
    
    for i in range(len(nums)):
        out[i] = prefix
        prefix *= nums[i]

    for i in range(len(nums)-1,-1,-1):
        out[i] *= postfix
        postfix *= nums[i]
    return out

test(productExceptSelf)