Click stream and similarity matrix

Question

I have a list of sequences that represent a user navigation path thru a website. The have the form of:

S1 = [2,5,3,7,3]

S2= [2,7,3,9,4,3,5,6,1]

And so on…

As you can see the length of the sequences does not have to be the same. I am trying to compute a similarity matrix to give as input to a clustering algorithm, in this case DBSCAN. The problem that I am having is that every example I find on internet, the sequences used have the same lengths. So the main challenge I am trying to address would be to compute a similarity matrix using sequences of different lengths. I would appreciate some help!