  Giant planets can interact with multiple and chemically diverse environments
in protoplanetary discs while they form and migrate to their final orbits. The
way this interaction affects the accretion of gas and solids shapes the
chemical composition of the planets and of their atmospheres. Here we
investigate the effects of different chemical structures of the host
protoplanetary disc on the planetary composition. We consider both scenarios of
molecular (inheritance from the pre-stellar cloud) and atomic (complete
chemical reset) initial abundances in the disc. We focus on four elemental
tracers of different volatility: C, O, N, and S. We explore the entire
extension of possible formation regions suggested by observations by coupling
the disc chemical scenarios with N-body simulations of forming and migrating
giant planets. The planet formation process produces giant planets with
chemical compositions significantly deviating from that of the host disc. We
find that the C/N, N/O, and S/N ratios follow monotonic trends with the extent
of migration. The C/O ratio shows a more complex behaviour, dependent on the
planet accretion history and on the chemical structure of the formation
environment. The comparison between S/N* and C/N* (where * indicates
normalisation to the stellar value), constrains the relative contribution of
gas and solids to the total metallicity. Giant planets whose metallicity is
dominated by the contribution of the gas are characterised by N/O* > C/O* >
C/N* and allow for constraining the disc chemical scenario. When the planetary
metallicity is instead dominated by the contribution of the solids we find that
C/N* > C/O* > N/O*.
