So, this is the first full cycle that we discovered, so we start the length is 19,

so we marked that the best total length that we've seen so far is 19.

Then we go back, then we backtrack actually to consider as a possibilities.

The last vertex on our pass, when there were some possibilities, is the vertex 2.

Instead of going to vertex 3, we might want to go to vertex 4.

This gives us the total of the current length is 3.

Then we continue on now is the current length is 6.

And finally, when we get to the leaf of this tree,

we see that the current cycle give us gives us total length 7,

so we update our variable which is responsible for

the best solution found so far it is 7, okay.

Then again we backtrack.

Now the last vertex where there is still a possibility to go

to another vertex is the root of this tree.

So, we tried to go from 1 to vertex 3 but not to 2.

So, the line says the current solution is 1.

Then we, from 3 we go to 6, from 6 we go to 4.

And now we see that the lengths of the total

of the current partial solution is always greater.

So, 8 is greater than 7.

So, out current solution is not going to be extended to some scene which is better

than some scenes that we found so far.

So, there is no sense to extend the current branch puzzle.

So, we just go back, so we return back to this vertex and

we try to go from 3 to another vertex, namely to 4.

Then when we go to 4,

we discover another copy of the same cycle, so its length is 7.

Then it doesn't update our variable, so we just backtrack.

We go to the root and we try to visit the vertex 4.

But already when we go from 1 to 4 we see that

we already traversed the edge of length 10, right.

The length of this partial solution is already 10.

It is already worse than the solution that we found before of total length 7.

So, there is just no sense of extending this branch and we cut it immediately.

So, if we do this a little bit smarter,

then we do not need to go through all possible candidates solutions.

So this is the one small branch that we cut.

And this is another small branch that we don't need.