  In this work, we consider a family of sure-success quantum algorithms, which
is grouped into even and odd members for solving a generalized Grover search
problem. We prove the matching conditions for both groups and give the
corresponding formulae for evaluating the iterations or oracle calls required
in the search computation. We also present how to adjust the phase angles in
the generalized Grover operator to ensure the sure-success if minimal oracle
calls are demanded in the search.
