To determine the memory required by a program, one must consider where memory is created - either statically through variable declarations or dynamically each time a statement is executed. The document asks to analyze the memory created on each line of a recursive program that sums the elements of a list. It notes that slicing a list to create a sublist requires steps proportional to the number of elements sliced since Python makes a copy of those elements into a new list. Finally, it asks the reader to determine a space function S(n) that represents the memory required by the program when its input list has length n.

1. To determine how much "space" (i.e, memory or RAM) a program requires, we need to figure
cut where memory is created. Memory can be created statically (i.e. variable declarations) or
dynamically (i.e. when each statement is executed). In the program prob 8 below, for each line of
code from 5 to 12, specify if memory is created statically, dynamically, or not at all ]: # Input: L
is a list of numbers # def probs(L): if len (L)<=1 : return 1 total =0 for x in L: total +=xx left
=1.[:len(L)//2] right = L. [len(L)//2:Ien(L)] return probs (left)+probs(right)+tota1
Find the space functionlequation, S(n), of prob8 (defined in the previous problem). Note that
S(n) is the space (memoryIRAM) allocated to probs, when its input (Le. L) has n numbers.
(Conceptually, if the input size is 10 , the amount of spaco required is S(10)) Note that slicing k
things from a list (e.g- lines 10 and 11 below) takes k steps because Python creates a new list,
then copies these things into a new list, and retums it. For example, in line 10, Python wil copy
all items from 0 to len(L) y/2, put them in a new list and then retums it (save it into "leh").