# maximum clique problem solve

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Parth Tushar Deodhar on 14 Mar 2021
Commented: ghazal on 3 Jul 2022
Maximum Clique
People in the social network are identified by unique IDs, consecutive integers from 1 to N. Who follows who is captured in a cell array called sn: the ii th element of sn is a vector that contains a list of IDs the person with ID ii follows. You may assume that these lists are ordered in ascending order by ID. Note that the follows relationship is not necessarily symmetrical: if person A follows person B, person B may or may not follow person A. :
function clique = max_clique(graph, clique)
if nargin < 2
clique = [];
end
max_clq = clique;
if isempty(clique)
for ii= 1:length(graph)
clq = max_clique(graph,ii);
if length(clq) > length(max_clq)
max_clq = clq;
end
end
else
for node=1:length(graph)
if isempty(find(node==clique))
if check_clique(clique,node,graph)
clq = max_clique(graph, [clique node]);
if length(clq) > length(max_clq)
max_clique == clq
end
end
end
end
end
clique = max_clq;
end
function ok = check_clique(clq,node,graph)
ok = false;
for ii=1:length(clq)
if isempty(find(clq(ii) == graph{node})) || isempty (find(node == graph{clq(ii)}))
return;
end
end
ok = true;
end
Unfortunately, it is too slow and the grader will time out. Your task is to modify the code to speed it up. Remember, the question to ask: am I doing any unncessary work? Call the modified function max_clique. (Hint: when we try to expand the current clique, do we really need to consider all the nodes?)
Please solve this problem with entire new code that is fast.
Mehrail Nabil on 17 Aug 2021
If you reach a code send it here to me ???

Jan on 15 Mar 2021
Edited: Jan on 15 Mar 2021
With replacing
if isempty(find(node==clique))
...
if isempty(find(clq(ii) == graph{node})) || isempty (find(node == graph{clq(ii)}))
by
if ~any(node==clique)
...
if ~any(clq(ii) == graph{node}) || ~any(node == graph{clq(ii)})
the processing time is reduced from 350 seconds to 193 seconds on my Matlab R2018b.
As next step inline the frequently called function check_clique in the main function:
function clique = max_clique(graph, clique)
if nargin < 2
clique = [];
end
max_clq = clique;
if isempty(clique)
for ii= 1:length(graph)
clq = max_clique(graph, ii);
if length(clq) > length(max_clq)
max_clq = clq;
end
end
else
for node = 1:length(graph)
if ~any(node == clique)
ok = true; % Inlined check_clique:
for ii = 1:length(clique)
if ~any(clique(ii) == graph{node}) || ...
~any(node == graph{clique(ii)})
ok = false;
break;
end
end
if ok % check_clique(clique,node,graph)
clq = max_clique(graph, [clique, node]);
if length(clq) > length(max_clq)
max_clq = clq;
end
end
end
end
end
clique = max_clq;
end
This needs 72 seconds on my computer. 5 times faster with just tiny modifications.
Rawan Mohamed on 21 Aug 2021
anyone reach the answer of this code ??

### More Answers (2)

Mehrail Nabil on 17 Aug 2021
Anyone can send me in comment the answer of it???? The code please
##### 1 CommentShowHide None
@Mehrail Nabil Were you able to solve the problem? I would appreciate if you help me with the code. Please.

MR MB on 4 Sep 2021
Edited: MR MB on 4 Sep 2021
%if true
function clique = max_clique(graph,clique)
if nargin < 2 % originaly we call the function with just the graph
clique = []; % hence, the clique is initialized to an empty vector
end
max_clq = clique; % max_clq will store the current largest clique
if isempty(clique) % when we first call the function
ii = 1:length(graph);
s = max_clique(graph,ii); %out of the loop
for ii = 1:length(graph) % we need to test potential cliques starting from every possible node
clq = s;
if length(clq) > length(max_clq) % if the new one is larger than the current
max_clq = clq; % we store the new one
end
end
else
for node = 1:length(graph) % we are in a recursive call now: we test every node as a new member
if isempty(find(node == clique)) % unless it is already in the clique
if check_clique(clique,node,graph) % if adding this node is still a clique
clq = max_clique(graph,[clique node]); % we call ourself with the new expanded clique
if length(clq) > length(max_clq) % if what we get is larger the curent max
max_clq = clq; % we store the new one
end
end
end
end
end
clique = max_clq; % return the largest one
end
%if true
function ok = check_clique(clq,node,graph) % adding node to clq still a clique?
ok = false;
for ii = 1:length(clq) % for every current member
if isempty(find(clq(ii) == graph{node})) || ... % the member must be on the follows list of the new guy
isempty(find(node == graph{clq(ii)})) % the new guy must be on the follows list of the member
return;
end
end
ok = true;
end
end
It is so so so fast but with wrong answer Can any one help me to find the mistake?!?
ghazal on 3 Jul 2022
Thanks alot friend my problem solved