  From the constrained discrete KP (cdKP) hierarchy, the Ablowitz-Ladik lattice
has been derived. By means of the gauge transformation, the Wronskian solution
of the Ablowitz-Ladik lattice have been given. The $u_1$ of the cdKP hierarchy
is a Y-type soliton solution for odd times of the gauge transformation, but it
becomes a dark-bright soliton solution for even times of the gauge
transformation. The role of the discrete variable $n$ in the profile of the
$u_1$ is discussed.
