If we are interested in finding all the substrings of *y* which
are at a distance less or equal to a given value *k* of *x*
then it is
enough to initialize all the values of the first line of the table
with 0 (this means that the cost of insertions of letters of *y*
at the beginning of *x* is null).
The solutions are then given by all the values of the last row of
*T* which are less or equal to *k*.
This problem is know as **approximate string matching with k
differences**.

Example:

*x* = `GATAA` and *y* = `CAGATAAGAGAA` and
*k* = 1

Which gives the seven following alignments:

e-mails: {Christian.Charras, Thierry.Lecroq}@laposte.net