Question

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.

Example 1:

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

Example 2:

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

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.

Algorithm

1. Typical array questions, use prefix product to solve it.
2. Handle the result segment by segment
3. Multiply numbers from left and move forward one digit, so res[i] = res[i-1] * nums[i-1], current index is not included;
4. Multiply numbers from right and move backwards one digit, right here is the product of right part (except the current element itself)

Code

class Solution {
    public int[] productExceptSelf(int[] nums) {
        int[] res = new int[nums.length];
        res[0] = 1;
        for (int i = 1; i < nums.length; i++) {
            res[i] = res[i - 1] * nums[i - 1];
        }
        
        int right = 1;
        for (int i = nums.length - 1; i >= 0; i--) {
            res[i] *= right;
            right *= nums[i];
        }
        
        return res;
    }
}