# 238. Product of Array Except Self Leetcode Solution

## Product of Array Except Self Leetcode 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].

The product of any prefix or suffix of nums is guaranteed to fit in a 32-bit integer.

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

## Product of Array Except Self Leetcode Solution :

### Constraints :

• 2 <= nums.length <= 105
• -30 <= nums[i] <= 30
• The product of any prefix or suffix of nums is guaranteed to fit in a 32-bit integer.

### Example 1:

• Input: nums = [-1,1,0,-3,3]
• Output: [0,0,9,0,0]

Intuition :

The code aims to find an array ans where ans[i] is the product of all elements in the original array nums except nums[i]. To achieve this, the code computes two auxiliary arrays pre and suff. pre[i] represents the product of all elements in nums from index 0 to i-1, and suff[i] represents the product of all elements in nums from index i+1 to the end.

Approach :

Prefix and Suffix Products:

Create two arrays, pre and suff, to store products from the left and right sides of each element.
Compute Prefix Products:

Go through the array from left to right and fill the pre array. For each element, pre[i] will store the product of all elements to its left.
Compute Suffix Products:

Go through the array from right to left and fill the suff array. For each element, suff[i] will store the product of all elements to its right.
Calculate Final Products:

For each element in the original array:
Multiply the product of elements to its left (pre[i-1] if i >= 1).
Multiply the product of elements to its right (suff[i+1] if i <= n-1).
Store this product in the new array.

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