[LeetCode] 238 Product of Array Except Self

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]

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 1. O(n) runtime, O(n) space 

 

class Solution {
    public int[] productExceptSelf(int[] nums) {
        if(nums == null || nums.length <= 1) {
            return nums;
        }
        int[] leftProduct = new int[nums.length];
        leftProduct[0] = nums[0];
        for(int i = 1; i < nums.length; i++) {
            leftProduct[i] = leftProduct[i- 1] * nums[i];
        }
        int[] rightProduct = new int[nums.length];
        rightProduct[nums.length - 1] = nums[nums.length - 1];
        for(int i = nums.length - 2; i >= 0; i--) {
            rightProduct[i] = rightProduct[i + 1] * nums[i];
        }
        int[] productArray = new int[nums.length];
        productArray[0] = rightProduct[1];
        productArray[nums.length - 1] = leftProduct[nums.length - 2];
        for(int i = 1; i < nums.length - 1; i++) {
            productArray[i] = leftProduct[i - 1] * rightProduct[i + 1];
        }
        return productArray;
    }
}

Solution 2. O(n) runtime, O(1) space, using the output array to store partial left-product results, then update the final product results on a 2nd pass from right to left.

class Solution {
    public int[] productExceptSelf(int[] nums) {
        if(nums == null || nums.length <= 1) {
            return nums;
        }
        int[] productArray = new int[nums.length];
        productArray[0] = 1;
        for(int i = 1; i < productArray.length; i++) {
            productArray[i] = productArray[i - 1] * nums[i - 1];
        }
        int rightProduct = nums[nums.length - 1];
        for(int i = productArray.length - 2; i >= 0; i--) {
            productArray[i] *= rightProduct;
            rightProduct *= nums[i];
        }
        return productArray;
    }
}