Coding - Product of Array Except Self

Problem Statement: Product of Array Except Self

Description

Given an integer array nums, return an array output where output[i] is the product of all the elements of nums except nums[i]. Each product is guaranteed to fit in a 32-bit integer.

Follow-up: Could you solve it in O(n) time without using the division operation?

Constraints

• n is the length of the input array nums.
• 0 ≤ n ≤ 10^4
• The product of a single element is 1 as it is the identity for multiplication.
• The product of elements is guaranteed to fit within the range of a signed 32-bit integer.

Examples

1. Example 1:

   • Input: nums = [1,2,3,4]
   • Output: [24,12,8,6]

2. Example 2:

   • Input: nums = [0]
   • Output: [0]

3. Example 3:

   • Input: nums = [0,2]
   • Output: [0,0]

Hints

1. The challenge is to avoid division operations, which are costly in terms of computation.
2. Consider using a two-pass approach: one to calculate the product of all elements to the left of each index, and another to calculate the product of all elements to the right of each index.
3. Store these products in the output array, and then multiply corresponding elements to get the final result.

This problem can be solved using an O(n) time complexity algorithm by leveraging the properties of multiplication and avoiding division.