Explain what the use of O(n) memory means in the context of algorithm analysis with an example.

Using O(n) memory means that the amount of memory used grows linearly with the size of the input data n.

For example, if you have a function that copies a list of n elements into a new list, it will use memory proportional to n:

def copy_list(lst):
    new_lst = []
    for item in lst:
        new_lst.append(item)
    return new_lst

Here, memory is allocated for the new list equal to the number of elements in the input list. If the input list doubles, the used memory will roughly double.

In contrast, an algorithm using O(1) memory will use a fixed amount of memory, independent of the size of the input data.