Stuck on exercise dealing with (mathematical) sets and sub-sets [closed] - c++

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I've been thinking about this for quite a few days and I can't really seem to be finding any answers for b).
It goes like this fellas:
Johnny has taken a very important course and wants a lot of his
friends to find out about his succes by posting on Facebook (// yes
stupid i know) Johnny knows N users represented by numbers from 1 to
N. Between them there are m friendships with the form i,j where i and
j are users; n,m != 0. A user cannot be friends with himself and a
friendship tells us that each user is friends with the other one.
Johnny wants to find out which are the most 'connected' people in his
friends list so that his post will be well spread accros Facebook. For
this, Johnny has to find out the biggest sub-set of well-known users.
In this sub-set, each user has at least k friends, which are also
present in the sub-set (k != 0). Input : N, m and k on the same line,
separated by a single space, also a sequence of 2*m natural numbers
(which can be found in the interval [1,N] Output (standard: a) The
number of friends of each user in order from 1 to N b) The members of
the biggest sub-set of users, having the property that each user in
this set has at least k friends (which, again, can be found in that
specific sub-set). If there is no such sub-set for a given k, print
"NO"
For this problem you can't use any specialised libraries, so i'm stuck
with the standards.
Again, this is concerning the mathematical concept of sets, NOT the C++ specialised set, multiset, etc libraries.
a) is pretty easy but like I said, b) is giving me some trouble.
Examples: 1)
Input: 5 5
2 1 2 5 1 3 2 4 5 1 4
Output:
a) 3 2 1 2 2 b) 1 4 5
2) Input:
5 5 3
1 2 5 1 3 2 4 5 1 4
Output:
a) 3 2 1 2 2
b) NO
and 3) Input:
11 18 3
1 8 4 7 7 10 11 10 2 1 2 3 8 9 8 3 9 3 9 2 5 6 5 11 1 4 10 6 7 6 2 8 11 7 11 6
Output:
a) 3 4 3 2 2 4 4 4 3 3 4
b) 2 3 6 7 8 9 10 11
Any help would be appreciated. Also, sorry for the bulky content, it had to be roughly translated. :)
Thx a lot

Answer 1

The problem calls for you to compute the k-core of an N-node graph with m edges. There's a simple algorithm for this: while the lowest degree vertex has degree less than k, delete it. The remaining vertices are the desired subset. Use a bucket queue to keep the nodes sorted by degree for efficient operation.
On second thought, we just need to track (1) the degree of each node (2) which nodes have degree less than k. In untested Python:
import collections
def kcore(edges, k):
neighbors = collections.defaultdict(set)
for u, v in edges:
neighbors[u].add(v)
neighbors[v].add(u)
bad = {u for (u, neigh) in neighbors.items() if len(neigh) < k}
while bad:
u = bad.pop()
for v in neighbors[u]:
neighbors[v].remove(u)
if len(neighbors[v]) < k:
bad.add(v)
del neighbors[u]
return set(neighbors)