Clique Problem - Intro to Algorithms Udacity English (auto-generated) English

Clique Problem - Intro to AlgorithmsYouTube↗ IA↗(long shot)
Education 26.6K views 82 likes 5 dislikes 23 Feb 2015

Udacity 651K subscribers United States YouTube↗

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all right let's see if we can solve this problem we are looking for a four click

All right, let's see if we can solve this problem. We're looking for our four clique.

now for click is going to have to have the property that each of the nodes is

Now, four clique is going to have to have the property that each of the nodes is connected

connected to each of the other nodes so the out degree the degree of a node has

to each of the other nodes, so the alt degree or the degree of the node has to be at least 3.

to be at least three so that actually means we can we can eliminate some of these edges from the graph so the nodes

So that actually means we can eliminate some of these edges from the graph. All right.

from this graph to can't be part of our four clique because two only has a

So the nodes from this graph. Two can't be part of our four clique because two only has a degree of 2.

degree of 2 so let's get rid of that guy all right we can by the same argument we

So let's get rid of that guy. All right. We can device same argument.

can get rid of 6 because it only has a degree of 2 all right now everybody

We can get rid of 6 because it only has a degree of 2. All right.

that's left has degree at least 3 let's take a look at node 4 so node 4 has the

Now, everybody that's left has degree at least 3. Let's take a look at node 4.

property that it has exactly an out

So node 4 has the property that it has exactly line of degree of 3.

degree of 3 so if 4 is part of the clique then its neighbors have to be the rest of the clique 1 3 and 8 but you

So if four is part of the clique, then it's neighbors have to be the rest of the clique, 1, 3 and 8,

notice that 1 and 8 are not connected to each other so 4 can't be part of a fork

but you noticed that 1 and 8 are not connected to each so 4 can't be part of our four clique.

League all right and now that we've taken that those edges away we can see 8

All right, now that we've taken those edges away, we can see 8 has now a degree of 2.

has now a degree of 2 so 8 can't be part of the Fork Creek so the only possibility left is that these four

So 8 can't be part of the four clique, so the only possibility left is that these four nodes

nodes make up a four clique and that would mean one needs to be connected to 3 5 and 7 3 needs to be connected to 5 and 7 and 5 needs to be connected to 7

make up a four clique and that would mean 1 needs to be connected to 3, 5 and 7, 3 needs to be connected to 5 and 7, and 5 needs to be connected to 7, which it is.

which it is so if we add up these node numbers together 7 plus 3 plus 5 plus 1 is 16

So if we add these node numbers together, 7+3+5+1 is 16.

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