1. Prerequisites

Before delving into the problem, it's essential to have a solid understanding of basic programming concepts and familiarity with arrays and loops. Additionally, knowledge of algorithmic thinking, particularly in problem-solving with arrays, will be beneficial.

2. Understanding the Problem

The "Product of Array Except Self" problem presents a scenario where you are given an array of integers. The task is to return an array where each element is the product of all elements in the original array except itself. This problem challenges us to find an efficient solution with a time complexity of O(n) and without using division.

3. Solution with Algorithm

Algorithm Overview

To solve this problem efficiently, we can use a prefix and postfix product approach. The idea is to maintain two arrays - one for the prefix products and another for the postfix products. By multiplying the corresponding prefix and postfix products for each element, we can obtain the final result.

Step-by-Step Algorithm

1. Initialize an array result of the same length as the input array, filled with 1.

2. Initialize variables prefix and postfix to 1.

3. Iterate through the array from left to right, updating result and prefix at each step.

4. Iterate through the array from right to left, updating result and postfix at each step.

5. Return the resulting array.

4. Code in JavaScript

Now, let's translate the algorithm into JavaScript code:

javascriptCopy codefunction productExceptSelf(nums) {
  const result = new Array(nums.length).fill(1);

  let prefix = 1;
  let postfix = 1;

  // Left-to-Right Pass
  for (let i = 0; i < nums.length; i++) {
    result[i] *= prefix;
    prefix *= nums[i];
  }

  // Right-to-Left Pass
  for (let i = nums.length - 1; i >= 0; i--) {
    result[i] *= postfix;
    postfix *= nums[i];
  }

  return result;
}

This JavaScript function takes an array nums as input and returns the array of products except self.

By following this systematic approach, you can not only understand the problem thoroughly but also implement an efficient solution in JavaScript.