We analyze charmless two-body non-leptonic B decays B → P P , P V under the framework of a factorization-assisted topological-amplitude approach, where P ( V ) denotes a light pseudoscalar (vector) meson. Compared with the conventional flavor diagram approach, we consider the flavor SU (3) breaking effect assisted by a 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 χ and the strong phase ϕ are universal; they can be extracted by χ 2 fit from current abundant experimental data of charmless B decays. The number of free parameters and the χ 2 per degree of freedom are both reduced compared with previous analyses. 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 π π and π K - CP puzzles are solved simultaneously.