How to Explain Product of Array Except Self in a Coding Interview (Step-by-Step)

This is one of the most instructive medium problems in existence — because the obvious solution is explicitly forbidden. No division. O(n) time. O(1) extra space. Every constraint is designed to push you toward the prefix × suffix insight, and explaining that cleanly is what makes or breaks the interview answer.

In this post, you’ll learn exactly how to walk an interviewer through LeetCode 238: why division is off the table, the two-pass prefix and suffix approach, the O(1) space optimisation that collapses both arrays into one, and every edge case worth raising.

Problem Statement

Examples

Constraints

• 2 <= nums.length <= 105
• -30 <= nums[i] <= 30
• The product of any prefix or suffix fits in a 32-bit integer
• No division allowed
• Follow-up: Can you solve it in O(1) extra space? (output array does not count)

What Is the Problem?

“For every index i, I need the product of everything to its left multiplied by everything to its right — skipping nums[i] itself. I can’t divide, and I need to do it in O(n). That means I can’t compute the total product and divide out each element, so I need a smarter way to express ‘everything except me’.”

Immediately acknowledging the no-division constraint and explaining why it rules out the obvious approach is the clearest possible signal that you understand the real challenge of the problem.

Step 1: Compare Approaches Before Jumping to Code

“I’ll present both — the two-array version is easier to explain and verify; the one-pass suffix optimisation collapses it to O(1) extra space. Both are O(n) time. Knowing both and being able to articulate the trade-off is the complete answer.”

The Key Insight — Every Answer is a Left Product × Right Product

“Once I see that the answer at each index is just a left-product times a right-product, it becomes clear that I need two passes — one left-to-right to build prefix values, one right-to-left to build suffix values. The trick in the optimised version is that I don’t need to store the suffix array — I can accumulate it on the fly.”

Step 2: Explain the Algorithm in Plain English

Prefix × Suffix Visualised — nums = [1, 2, 3, 4]

Walking through both passes step by step. Prefix products flow left → right; suffix products flow right → left.

The O(1) Space Optimisation

“The output array itself doesn’t count toward extra space by convention. So after writing prefix products into it, the only additional memory I’m using is a single integer variable for the running suffix. That’s O(1) extra space.”

Step 3: Talk Through the Code

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

        # Pass 1 — left to right: fill answer[i] with product of all elements LEFT of i
        prefix = 1
        for i in range(n):
            answer[i] = prefix      # Store current prefix BEFORE including nums[i]
            prefix *= nums[i]       # Extend prefix to include nums[i]

        # Pass 2 — right to left: multiply answer[i] by product of all elements RIGHT of i
        suffix = 1
        for i in range(n - 1, -1, -1):
            answer[i] *= suffix     # Fold in the suffix contribution
            suffix *= nums[i]       # Extend suffix to include nums[i]

        return answer

The key detail to narrate: in Pass 1, we store prefix into answer[i] before multiplying prefix by nums[i] — this is what gives us the product of everything strictly to the left, excluding index i itself. The same logic applies symmetrically to the suffix in Pass 2.

Step 4: Highlight Edge Cases

Step 5: State Time and Space Complexity

“Time is O(n) — two linear passes, each visiting every element exactly once. Space is O(1) extra — the only additional memory beyond the output array is two running integer variables. If the interviewer counts the output array, space is O(n), but the follow-up explicitly notes that the output array does not count toward the space constraint.”

Interview Checklist for Product of Array Except Self

• Restate — “product of everything to the left times everything to the right, no division, O(n)”
• Immediately address the no-division constraint and explain why total-product ÷ self fails on zeros
• State the core insight — answer[i] = prefix[i] × suffix[i]
• Describe the two-array version first — easier to explain and verify
• Then describe the O(1) space optimisation — running suffix variable, no second array
• Narrate the update order in Pass 1: store prefix BEFORE multiplying — gives strictly left products
• Same for Pass 2: multiply answer[i] by suffix BEFORE updating suffix
• Call out: single zero → only one non-zero output; two zeros → all zeros output
• Call out: output array does not count toward extra space by convention
• State O(n) time and O(1) extra space

Related Problems to Practice

If you can solve Product of Array Except Self cleanly, try these next: