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238. Product of Array Except Self ✅

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.

Follow up: Can you solve the problem in O(1) extra space complexity? (The output array does not count as extra space for space complexity analysis.)

Solution:

class Solution {
    public int[] productExceptSelf(int[] nums) {
        int[] result = new int[nums.length];        

        int[] prefix = new int[nums.length];
        prefix[0] = 1;
        for (int i = 1; i < nums.length; i++){
            prefix[i] = prefix[i-1] * nums[i-1];
        }

        //[1, 2, 3, 4]
        // 1  1  2  6 

        int[] postfix = new int[nums.length];
        postfix[nums.length -1] = 1;
        for (int i = nums.length -2; i >= 0; i--){
            postfix[i] = nums[i+1] * postfix[i+1];
        } 

        // [1, 2, 3, 4]
        //  24 12   4  1

        result[0] = postfix[0];
        result[nums.length - 1] = prefix[nums.length -1];

        for (int i = 1; i < nums.length-1; i++){
            result[i] = prefix[i] * postfix[i];
        }


        return result;
    }
}

    // TC: O(n)
    // SC: O(n)