if n_perm_elements -- 1: if (sum_total <- 15) & (sum_total >= 0): yield (sum_total,) else: for value in range(0, 16): for permutation in permutations_w_constraints( n_perm_elements - 1, sum_total - value): yield (value,) + permutation n - 10 k - 8 new_list - list(permutations_w_constraints(n,k)) print(len(new list))

Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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Question

How can the following function be simplified so that it has a time complexity of O(n) or faster?

For your information, the specifications of the functions are as follows:

Using numbers ranging from 0 to 15 (inclusive), create all possible lists which sum up to K and have a length of N. Duplicated numbers are allowed as long as it fulfills the conditions above (this means [0,0,1], [0,1,0] and [1,0,0] are all correct outputs if K=1 and N=3). When instantiated with the list function, the list size of the function should be the number of all lists.

For example, given K=23 and N=2, the expected list size is 8. The function must be able to accept N=10 and be finished before 9 seconds. Do not use itertools or external libraries.

def permutations_w_constraints(n_perm_elements, sum_total):
if n_perm_elements
== 1:
if (sum_total <= 15) & (sum_total >= 0):
yield (sum_total,)
else:
for value in range(0, 16):
for permutation in permutations_w_constraints(
n_perm_elements - 1, sum_total - value):
yield (value,) + permutation
n = 10
k
8
%3D
new_list
list(permutations_w_constraints(n,k))
print(len(new_list))
Transcribed Image Text:def permutations_w_constraints(n_perm_elements, sum_total): if n_perm_elements == 1: if (sum_total <= 15) & (sum_total >= 0): yield (sum_total,) else: for value in range(0, 16): for permutation in permutations_w_constraints( n_perm_elements - 1, sum_total - value): yield (value,) + permutation n = 10 k 8 %3D new_list list(permutations_w_constraints(n,k)) print(len(new_list))
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