We study in this work the two-body hadronic charmed meson decays, including
both the PP and VP modes. The latest experimental data are first analyzed in
the diagrammatic approach. The magnitudes and strong phases of the flavor
amplitudes are extracted from the Cabibbo-favored (CF) decay modes using
$\chi^2$ minimization. The best-fitted values are then used to predict the
branching fractions of the singly-Cabibbo-suppressed (SCS) and
doubly-Cabibbo-suppressed decay modes in the flavor SU(3) symmetry limit. We
observe significant SU(3) breaking effects in some of SCS channels. In the case
of VP modes, we point out that the $A_P$ and $A_V$ amplitudes cannot be
completely determined based on currently available data. We conjecture that the
quoted experimental results for both $D_s^+\to\bar K^0K^{*+}$ and $D_s^+\to
\rho^+\eta'$ are overestimated. We compare the sizes of color-allowed and
color-suppressed tree amplitudes extracted from the diagrammatical approach
with the effective parameters $a_1$ and $a_2$ defined in the factorization
approach. The ratio $|a_2/a_1|$ is more or less universal among the $D \to
{\bar K} \pi$, ${\bar K}^* \pi$ and ${\bar K} \rho$ modes. This feature allows
us to discriminate between different solutions of topological amplitudes. For
the long-standing puzzle about the ratio $\Gamma(D^0\to
K^+K^-)/\Gamma(D^0\to\pi^+\pi^-)$, we argue that, in addition to the SU(3)
breaking effect in the spectator amplitudes, the long-distance resonant
contribution through the nearby resonance $f_0(1710)$ can naturally explain why
$D^0$ decays more copiously to $K^+ K^-$ than $\pi^+ \pi^-$ through the
$W$-exchange topology.Comment: 32 pages, 5 figures. An alternative method for error bar extraction
is used; last columns of Tables~I to VI, and all entries in Tables~VII, VIII
and X are modified. To appear in PRD