How do you compute the product of an array except self without division?

Q: How do you compute the product of an array except self without division?

**Target Audience:** Beginners to intermediate candidates — you should know arrays and loops; prefix sums help but are explained here. **Difficulty:** Medium **Language:** Python 3 > **How to read this doc:** Each idea is explained in plain language first, then tagged with `📌 Interview term:` so you also learn the exact words an interviewer expects. Every output shown in the **Verified** section was produced by actually running the Python code with `python3 main.py`; nothing is quoted from memory. ## 1. Why This Even Matters — A Story First Imagine four friends who each bring one ingredient to a shared recipe, and the recipe's strength is the product of all the ingredients. Now each friend asks: "how strong would it be *without me*?" The quick answer is "take the full product and divide by my part" — but the moment one friend brought an ingredient of strength 0, the full product is 0 and you cannot divide by zero. Worse, the interviewer has banned division outright. So each friend

The problem

Question presented to candidate: "Given a list of integers, return a new list where each position holds the product of every other element. You may not use division, and I want it in linear time. Please write it in Python."

What a strong answer should cover:

Answer at i = product of everything to the left times product of everything to the right.
Two passes: fill answer with prefix products, then multiply in a running suffix product walking backwards.
O(n) time, O(1) extra space (the output list is not counted); why division fails with zeros.
Python specifics: [1] * n is safe for ints, range(n - 1, -1, -1) walks backwards, ints never overflow, and itertools.accumulate(nums, operator.mul) gives prefix products.
Edge cases: one zero, several zeros, negatives.

Clarifying questions expected:

"Can there be zeros, and is division really off the table?" — zeros are what make division fail.
"Does the product fit in 32 bits, and does the output array count as extra space?"

Code / implementation expected: Yes — a two-pass function in Python.

arrays
prefix-product

Try it yourself

Sketch your approach before you read the solution. That is what the interview tests.

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A short nudge toward the approach. It will not give the answer away.

Solution

Target Audience: Beginners to intermediate candidates — you should know arrays and loops; prefix sums help but are explained here. Difficulty: Medium Language: Python 3

How to read this doc: Each idea is explained in plain language first, then tagged with 📌 Interview term: so you also learn the exact words an interviewer expects. Every output shown in the Verified section was produced by actually running the Python code with python3 main.py; nothing is quoted from memory.

1. Why This Even Matters — A Story First

Imagine four friends who each bring one ingredient to a shared recipe, and the recipe's strength is the product of all the ingredients. Now each friend asks: "how strong would it be without me?" The quick answer is "take the full product and divide by my part" — but the moment one friend brought an ingredient of strength 0, the full product is 0

The solution is hidden so you can try first

10 min read · 12 sections

Python code

Edit the code and run it here. Each printed line with an expected value becomes a test.

PythonTwo-pass product except self on five arrays

Practice

PythonCounting multiplications: brute force vs two passes

Practice

Discussion

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