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238. Product of Array Except Self

Medium

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 <= 105
  • -30 <= nums[i] <= 30
  • The product of any prefix or suffix of nums 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

class Solution:
    def productExceptSelf(self, nums: List[int]) -> List[int]:
        n = len(nums)
        lps = [1] * n
        rps = [1] * n

        for i in range(1, n):
            lps[i] = lps[i - 1] * nums[i - 1]

        for i in reversed(range(n - 1)):
            rps[i] = rps[i + 1] * nums[i + 1]

        return [lps[i] * rps[i] for i in range(n)]