  We give an $O(p^{2})$ time algorithm to compute the generalized Heegaard
Floer complexes $A_{s_{1},s_{2}}^{-}(\overrightarrow{L})$'s for a two-bridge
link $\overrightarrow{L}=b(p,q)$ by using nice diagrams. Using the link surgery
formula of Manolescu-Ozsv\'{a}th, we also show that ${\bf HF}^{-}$ and their
$d$-invariants of all integer surgeries on two-bridge links are determined by
$A_{s_{1},s_{2}}^{-}(\overrightarrow{L})$'s. We obtain a polynomial time
algorithm to compute ${\bf HF}^{-}$ of all the surgeries on two-bridge links,
with $\mathbb{Z}/2\mathbb{Z}$ coefficients. In addition, we calculate some
examples explicitly:
  ${\bf HF}^{-}$ and the $d$-invariants of all integer surgeries on a family of
hyperbolic two-bridge links including the Whitehead link.
