238. Product of Array Except Self

Problem

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

/**
 * @param {number[]} nums
 * @return {number[]}
 */
var productExceptSelf = function(nums) {
  var len = nums.length;
  var left = Array(len + 1);
  var right = Array(len + 1);
  var res = Array(len);

  left[0] = 1;
  right[0] = 1;

  for (var i = 0; i < len; i++) {
    left[i + 1] = left[i] * nums[i];
  }

  for (var j = 0; j < len; j++) {
    right[j + 1] = right[j] * nums[len - 1 - j];
  }

  for (var k = 0; k < len; k++) {
    res[k] = left[k] * right[len - k - 1];
  }

  return res;
};

Explain:

nope.

Complexity:

• Time complexity : O(n).
• Space complexity : O(n).

Solution 2

/**
 * @param {number[]} nums
 * @return {number[]}
 */
var productExceptSelf = function(nums) {
  var len = nums.length;
  var res = Array(len);
  var right = 1;

  res[0] = 1;

  for (var i = 1; i < len; i++) {
    res[i] = res[i - 1] * nums[i - 1];
  }

  for (var j = len - 1; j >= 0; j--) {
    res[j] *= right;
    right *= nums[j];
  }

  return res;
};

Explain:

nope.

Complexity:

• Time complexity : O(n).
• Space complexity : O(1).