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238. Product of Array Except Self

mediumAsked at Elastic

Return an array where each element is the product of all other elements, without using division. Elastic uses this to test prefix/suffix scan thinking — the same cumulative-scan pattern drives Elasticsearch's pipeline aggregations that compute running totals across document sets.

By Alex Chen, Founder, InterviewChamp.AI · Last verified

Source citations

Public interview reports confirming this problem appears in Elastic loops.

  • Glassdoor (2025-12)— Elastic SWE candidates report prefix-product and prefix-sum problems appearing as mid-round algorithm questions.
  • Blind (2025-09)— Elastic interview threads list this problem as a reliable test of O(1) extra space thinking under the no-division constraint.

Problem

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.

Constraints

  • 2 <= nums.length <= 10^5
  • −30 <= nums[i] <= 30
  • The product of any prefix or suffix of nums is guaranteed to fit in a 32-bit integer.

Examples

Example 1

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

Explanation: answer[0] = 2*3*4=24; answer[1] = 1*3*4=12; answer[2] = 1*2*4=8; answer[3] = 1*2*3=6.

Example 2

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

Explanation: Presence of zero makes most products zero.

Approaches

1. Two-pass prefix and suffix products

First pass: compute left prefix products into the output array. Second pass: multiply by right suffix products using a running variable — no extra array needed.

Time
O(n)
Space
O(1) excluding output
function productExceptSelf(nums) {
  const n = nums.length;
  const result = new Array(n).fill(1);
  // Left pass: result[i] = product of all nums[j] for j < i
  let prefix = 1;
  for (let i = 0; i < n; i++) {
    result[i] = prefix;
    prefix *= nums[i];
  }
  // Right pass: multiply result[i] by product of all nums[j] for j > i
  let suffix = 1;
  for (let i = n - 1; i >= 0; i--) {
    result[i] *= suffix;
    suffix *= nums[i];
  }
  return result;
}

Tradeoff: O(n) time, O(1) auxiliary space (the output array does not count). This is the optimal and expected solution.

Elastic-specific tips

Explicitly state the O(1) extra space constraint before coding: 'The output array doesn't count as extra space per the problem — so I need one extra variable for the right suffix.' Walk through the example step-by-step. Elastic interviewers appreciate knowing you understand WHY division is forbidden: presence of zeros would require special-casing. Connect to pipeline aggregations: 'This is how a running-total pipeline works — accumulate from left, then from right, and combine.'

Common mistakes

  • Using division — fails when any element is zero and is explicitly prohibited.
  • Allocating two separate O(n) arrays for left and right products instead of reusing the output array.
  • Initializing prefix or suffix to 0 instead of 1 — the multiplicative identity is 1.
  • Off-by-one in the left pass — result[i] should be the product of elements BEFORE i, not including i.

Follow-up questions

An interviewer at Elastic may pivot to one of these next:

  • What if the constraint of no-division is lifted — how would you handle zeros?
  • Sum of all elements except self — can you do this in O(1) space? (prefix + suffix sums, same pattern.)
  • Maximum product subarray (LC 152) — uses a related running-max-and-min pattern.

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Output

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FAQ

Why does prefix start as 1 and not nums[0]?

result[0] should be the product of all elements to the LEFT of index 0, which is an empty product — equal to 1 (the multiplicative identity).

Why is the output array not counted as extra space?

The problem statement explicitly allows O(n) output space — the O(1) constraint refers to space used beyond what is needed for the output.

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