ProductOfArrayExceptSelf

Problem

https://leetcode.com/problems/product-of-array-except-self/

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.

Example 1:

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

Example 2:

Input: nums = [-1,1,0,-3,3]
Output: [0,0,9,0,0]

Constraints:

2 <= nums.length <= 10:sup:`5`
-30 <= nums[i] <= 30
The input is generated such that answer[i] is guaranteed to fit in a 32-bit integer.

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

Solution

Observe that the product of all elements except the element at index i is the product of all elements nums[:i - 1] multiplied by the product of all elements nums[i + 1:]. Iterate through nums once to compute the product of all elements nums[:i - 1] and store the result in a list products. Start with left_product = 1 and append it to products before multiplying with the next element in nums. Iterate through nums in reverse to compute the product of all elements nums[i + 1:] and multiply the result by the corresponding element in products to obtains the product of all elements except the element at index \(i\).

Pattern

Array, Prefix Sum

Code

from typing import List


def productExceptSelf(nums: List[int]) -> List[int]:
    """Product of all elements except the element at index ``i`` for each index
    ``i`` in ``nums``.
    """
    products = []

    left_product = 1
    for num in nums:
        products.append(left_product)
        left_product *= num

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

    return products

Test

>>> from ProductOfArrayExceptSelf import productExceptSelf
>>> productExceptSelf([1, 2, 3, 4])
[24, 12, 8, 6]
>>> productExceptSelf([-1, 1, 0, -3, 3])
[0, 0, 9, 0, 0]

ProductOfArrayExceptSelf.productExceptSelf(nums: List[int]) → List[int]: Product of all elements except the element at index i for each index i in nums.