238. Product of Array Except Self

At a Glance

Topic: arrays-hashing
Pattern: Prefix Sum / Suffix (prefix–suffix products)
Difficulty: Medium
Companies: Amazon, Meta, Google, Apple, Microsoft
Frequency: Very High
LeetCode: 238

Given an integer array numbers, return an array answer where answer[index] equals the product of all elements of numbers except numbers[index]. Solve without division; output fits in 32-bit signed.

Recognition Cues

"Product of all except self", "no division operator"
Left products × right products or running prefix/suffix

Diagram

At-a-glance flow (replace with problem-specific Mermaid as you refine this note). camelCase node IDs; no spaces in IDs.

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Approaches

Brute force — recompute product per index — O(n²) time.
Better — total product / self — O(n) but invalid when zeros or problem forbids division.
Optimal — prefix products left-to-right, suffix right-to-left — O(n) time / O(1) extra excluding output.

Optimal Solution

Go

package main

func productExceptSelf(numbers []int) []int {
	length := len(numbers)
	answer := make([]int, length)
	prefix := 1
	for index := 0; index < length; index++ {
		answer[index] = prefix
		prefix *= numbers[index]
	}
	suffix := 1
	for index := length - 1; index >= 0; index-- {
		answer[index] *= suffix
		suffix *= numbers[index]
	}
	return answer
}

JavaScript

function productExceptSelf(numbers) {
	const length = numbers.length;
	const answer = new Array(length);
	let prefix = 1;
	for (let index = 0; index < length; index++) {
		answer[index] = prefix;
		prefix *= numbers[index];
	}
	let suffix = 1;
	for (let index = length - 1; index >= 0; index--) {
		answer[index] *= suffix;
		suffix *= numbers[index];
	}
	return answer;
}