Array of array products - dynamic programming - talk about space complexity, time complexity, how many multiplications are involved.

ArrayOfArrayProducts.cs

using System;

class Solution
{
    public static int[] ArrayOfArrayProducts(int[] arr)  // [8, 10, 2]
    {
      if(arr == null || arr.Length <= 1) // false 
      {
        return new int[0]; 
      }
      
      var length = arr.Length; // 3
      
      int leftToRightProduct = 1; 
      
      var product = new int[length]; 
      
      for(int index = 0; index < length; index++ ) // 0, 1, 2  (n - 1)
      {
        product[index] = leftToRightProduct; // 1
        leftToRightProduct *= arr[index]; // one multiplication, *8
      }
      
      var rightToLeftProduct = 1; 
      
      for(int index = length - 1; index >= 0; index--) // 2 * n
      {
        product[index] *= rightToLeftProduct; // extra multiplication 
        rightToLeftProduct *= arr[index];     // one more multiplcation 
      }
      
      return product;       
    }

    static void Main(string[] args)
    {
       var productOfArray =  ArrayOfArrayProducts(new int[]{8, 10, 2}); 
      
       foreach(var item in productOfArray)
       {
         Console.WriteLine(item); 
       }
    }
}

/*
division -> multiple n - 1
[8, 10, 2, 5]

[10 * 2 * 5, 8 * 2 * 5, 8 * 10 * 5, 8 * 10 * 2]  - one multiplication 
(n-1) * n = O(n^2) - brute force solution - time complexity 
O(n)
leftToRightProduct

[1, 8, 8 * 10, 8* 10 * 2], 
[1, 8 * leftToRightProduct[i -1], 10 * leftToRightProduct[i-1]] -> O(n) -> variable -> O(1)

rightToLeftProduct
[,,,  2 * rigthToLeftProduct[i +1], 1]
product[]

productArray

*/