Array of array products - February 25, 2018 - dynamic programming method

ArrayOfArrayProducts_Feb25_2018.cs

using System;

class Solution
{
    public static int[] ArrayOfArrayProducts(int[] arr)
    {
      if(arr == null || arr.Length <= 1)
      {
        return new int[0]; 
      }
      
      int length = arr.Length; 
      
      int leftProduct = 1; 
      var product = new int[length]; 
      
      for(int i = 0; i < length; i++)
      {
        product[i] = leftProduct; 
        leftProduct *= arr[i]; 
      }
      
      int rightProduct = 1; 
      for(int i = length - 1; i >= 0; i--)
      {
        product[i]   *= rightProduct; 
        rightProduct *= arr[i]; 
      }
      
      return product; 
    }

    static void Main(string[] args)
    {

        var product = ArrayOfArrayProducts(new int[]{8, 10, 2}); 
        foreach(var item in product)
        {
          Console.WriteLine(item); 
        }
    }
}

/*
Keyword: integer array, 
ask: product of all integers except itself on the index 

dynamic programming 
[8, 10, 2]
----------->
one multiplication 
value = 1, value = 8
product =  new int[] {1, value*8, value * 10} -> 2 multiplication 

<---------------------
each time I will two mutliplication

product[i] = product[i] * arr[i + 1]  - wrong
product[i] = product[i] * rightProduct - correct 

[1, 8, 80]

   rightProduct = 1, 
   rightProduct *= arr[i + 1]
[1 * 20 , 8 * 2, 80 * 1]

time complexity: O(n)
space complexity: O(n)

*/