Using the entire sample of 467 × 10 6 Υ ( 4 S ) → B ¯¯¯ B decays collected with the BABAR detector at the PEP-II asymmetric-energy B factory at the SLAC National Accelerator Laboratory, we perform an analysis of B ± → D K ± decays, using decay modes in which the neutral D meson decays to either C P -eigenstates or non- C P -eigenstates. We measure the partial decay rate charge asymmetries for C P -even and C P -odd D final states to be A C P + = 0.25 ± 0.06 ± 0.02 and A C P − = − 0.09 ± 0.07 ± 0.02 , respectively, where the first error is the statistical and the second is the systematic uncertainty. The parameter A C P + is different from zero with a significance of 3.6 standard deviations, constituting evidence for direct C P violation. We also measure the ratios of the charged-averaged B partial decay rates in C P and non- C P decays, R C P + = 1.18 ± 0.09 ± 0.05 and R C P − = 1.07 ± 0.08 ± 0.04 . We infer frequentist confidence intervals for the angle γ of the unitarity triangle, for the strong phase difference δ B , and for the amplitude ratio r B , which are related to the B − → D K − decay amplitude by r B e i ( δ B − γ ) = A ( B − → ¯¯¯ D 0 K − ) / A ( B − → D 0 K − ) . Including statistical and systematic uncertainties, we obtain 0.24 < r B < 0.45 ( 0.06 < r B < 0.51 ) and, modulo 180°, 11.3 ° < γ < 22.7 ° or 80.8 ° < γ < 99.2 ° or 157.3 ° < γ < 168.7 ° ( 7.0 ° < γ < 173.0 ° ) at the 68% (95%) confidence level.