product-list.py

# Space comp = O(n) where n = number of numbers
class ProductList:
  def __init__(self):
    self.prefixProd = []

  # Time Comp = O(1) 
  def add(self, n):
    prefixProd = self.prefixProd
    if n == 0:
      self.prefixProd = []
    else:
      prev = 1 if not prefixProd else prefixProd[-1] 
      prefixProd.append(prev * n)

  # Time Comp O(1)  
  def product(self, m):
    prefixProd = self.prefixProd
    size = len(prefixProd)
    if not prefixProd or m > size:
      return 0

    prevPos, prev = size-1-m, 1
    if prevPos > -1:
      prev = prefixProd[prevPos]

    return prefixProd[-1]//prev

#p = ProductList()
#p.add(7)         
#p.add(0)         
#p.add(2)         
#p.add(5)         
#p.add(4)   
# print(p.product(100)) # return 0  
# print(p.product(3)) # return 40 because 2 * 5 * 4
# print(p.product(4)) # return 0 

# p.add(0)
# p.add(1)
# print(p.product(1)) # return 1

#p.add(2)
#p.add(0)
#p.add(-5)
#p.add(6)
#p.add(2)
#print(p.product(2)) # return 12 
#print(p.product(3)) # return -60