Product of Array Except Self

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]. You must write an algorithm that runs in O(n) time and without using the division operation.

Examples

The brute-force approach

For each index i, loop through the entire array and multiply every element except nums[i].

result = []
for i in range(len(nums)):
    product = 1
    for j in range(len(nums)):
        if j != i:
            product *= nums[j]
    result.append(product)
return result

Two nested loops — O(n²). For n=100,000 that's 10 billion multiplications.

Spotting the pattern

This is a Prefix Sum problem. The key question to ask yourself:

What is the product of all elements to the left of index i? What is the product to the right?

Answering that is where it clicks, and it's exactly what the guided walkthrough below builds with you: the pattern reasoning, a progressive hint ladder that never spoils the answer, a row-by-row dry run, the optimized solution, and an in-browser editor to run your code against real test cases.