import numpy as np

def calculate_discounted_return_backwards(value, gamma, normalize=True):
	ret = np.zeros(value.shape[0]) 		                    # initialize the array we hold our values in
	i = value.shape[0]-1                                    # starting at the end, heading backwards
	while i >= 0:                                           # until we reach the start of the array
		ret[i] += value[i]								    # add the
		try:                                                # we surround in a try catch in case we are at the start
			ret[i] += (ret[i+1] * gamma)                    # we add the previous return with a decay
		except:                                        					# if there was no ret[i+1]
			pass                                            # should only occur for first element
		i -= 1                                              # move to the next element

	cut_off = int(1./(1. - gamma))*2
	if normalize:
		return ret[:len(ret)-cut_off]*(1.-gamma)
	return ret[:len(ret)-cut_off]