  We analyze charmless two-body non-leptonic B decays $B \to PP, PV$ under the
framework of factorization assisted topological amplitude approach, where
$P(V)$ denotes a light pseudoscalar (vector) meson. Compared with the
conventional flavor diagram approach, we consider flavor $SU(3)$ breaking
effect assisted by factorization hypothesis for topological diagram amplitudes
of different decay modes, factorizing out the corresponding decay constants and
form factors. The non-perturbative parameters of topology diagram magnitudes
$\chi$ and strong phase $\phi$ are universal that can be extracted by $\chi^2$
fit from current abundant experimental data of charmless B decays. The number
of free parameters and the $\chi^2$ per degree of freedom are both reduced
comparing with previous analysis. With these best fitted parameters, we predict
branching fractions and $CP$ asymmetry parameters of nearly 100 $B_{u,d}$ and
$B_s$ decay modes. The long-standing $\pi \pi$ and $\pi K$-$CP$ puzzles are
resolved simultaneoulsy.
