# product-of-array-except-itself

## Problem

[Product of Array Except Self](https://leetcode.com/explore/challenge/card/30-day-leetcoding-challenge/530/week-3/3300/)

## Problem Description

```
Given an array nums of n integers where n > 1,  return an array output such that output[i] is equal to the product of all the elements of nums except nums[i].

Example:

Input:  [1,2,3,4]
Output: [24,12,8,6]
Constraint: It's guaranteed that the product of the elements of any prefix or suffix of the array (including the whole array) fits in a 32 bit integer.

Note: Please solve it without division and in O(n).

Follow up:
Could you solve it with constant space complexity? (The output array does not count as extra space for the purpose of space complexity analysis.)
```

## Solution

Intuitive solution is to product the whole array, result is to divide itself. Notice from problem, without division and solve it in `O(n)`.

Idea is to product from left to right, then right to left:

1. Init `res[len]`, res\[0] = 1, left = 1;
2. Scan array from left to right, skip the last number, from 

   `index = 1, left = left * nums[index -1], res[index] = left;`
3. init right = nums\[len - 1], from second right most element, from 

   `index = len - 2, res[index] = res[index] * right, right = nums[index] * right`
4. return res.

For example:

![Product of Array Except Itself](/files/-M50Mr4HHQjSA8IW3orU)

### Complexity Analysis

**Time Complexity:** `O(N)`

**Space Complexity:** `O(N)`

* N - the length of array nums

### Code

```java
class Solution {
    public int[] productExceptSelf(int[] nums) {
        int len = nums.length;
        int[] res = new int[len];
        res[0] = 1;
        // from left to right
        for (int i = 1; i < len; i++) {
            res[i] = res[i - 1] * nums[i - 1];
        }
        // from right to left
        int right = nums[len - 1];
        for (int i = len - 2; i >= 0; i--) {
            res[i] *= right;
            right *= nums[i];
        }
        return res;
    }
}
```


---

# Agent Instructions: Querying This Documentation

If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question.

Perform an HTTP GET request on the current page URL with the `ask` query parameter:

```
GET https://snowan.gitbook.io/study-notes/leetcode/30daychallenge/product-of-array-except-itself.md?ask=<question>
```

The question should be specific, self-contained, and written in natural language.
The response will contain a direct answer to the question and relevant excerpts and sources from the documentation.

Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.